Publications

High-confidence (≥0.9) publications: 271

• Automatic speech recognition predicts contemporaneous earthquake fault displacement (2025) — Christopher W. Johnson, Kun Wang, Paul A. Johnson — Nature Communications
  Abstract

  Abstract Significant progress has been made in probing the state of an earthquake fault by applying machine learning to continuous seismic waveforms. The breakthroughs were originally obtained from laboratory shear experiments and numerical simulations of fault shear, then successfully extended to slow-slipping faults. Here we apply the Wav2Vec-2.0 self-supervised framework for automatic speech recognition to continuous seismic signals emanating from a sequence of moderate magnitude earthquakes during the 2018 caldera collapse at the Kīlauea volcano on the island of Hawai’i. We pre-train the Wav2Vec-2.0 model using caldera seismic waveforms and augment the model architecture to predict contemporaneous surface displacement during the caldera collapse sequence, a proxy for fault displacement. We find the model displacement predictions to be excellent. The model is adapted for near-future prediction information and found hints of prediction capability, but the results are not robust. The results demonstrate that earthquake faults emit seismic signatures in a similar manner to laboratory and numerical simulation faults, and artificial intelligence models developed for encoding audio of speech may have important applications in studying active fault zones.
• Operator-Theoretic Methods for Differential Games (2025) — Craig Bakker et al. — arXiv preprint arXiv:2507.02203, 2025
  Abstract

  Abstract Differential game theory offers an approach for modeling interactions between two or more agents that occur in continuous time. The goal of each agent is to optimize its objective cost functional. In this paper, we present two different methods, based on the Koopman Operator (KO), to solve a zero-sum differential game. The first approach uses the resolvent of the KO to calculate a continuous-time global feedback solution over the entire domain. The second approach uses a discrete-time, data-driven KO representation with control to calculate open-loop control policies one trajectory at a time. We demonstrate these methods on a turret defense game from the literature, and we find that the methods' solutions replicate the behavior of the analytical solution provided in the literature.. Following that demonstration, we highlight the relative advantages and disadvantages of each method and discuss potential future work for this line of research.
• Unsupervised discovery of extreme weather events using universal representations of emergent organization (2025) — Adam Rupe et al. — Chaos: An Interdisciplinary Journal of Nonlinear Science
  Abstract

  Spontaneous self-organization is ubiquitous in systems far from thermodynamic equilibrium. While organized structures that emerge dominate transport properties, universal representations that identify and describe these key objects remain elusive. Here, we introduce a theoretically grounded framework for describing emergent organization that, via data-driven algorithms, is constructive in practice. Its building blocks are spacetime lightcones that embody how information propagates across a system through local interactions. We show that predictive equivalence classes of lightcones—local causal states—capture organized behaviors in complex spatiotemporal systems. Employing an unsupervised physics-informed machine learning algorithm and a high-performance computing implementation, we demonstrate automatically discovering organized structures in two real-world domain science problems. We show that local causal states identify vortices and track their power-law decay behavior in two-dimensional fluid turbulence. We then show how to detect and track familiar extreme weather events—hurricanes and atmospheric rivers—and discover other novel structures associated with precipitation extremes in high-resolution climate data at the grid-cell level.
• Constrained Turret Defense with Fixed Final Time (2024) — Alexander Von Moll et al. — IFAC-PapersOnLine
• Deep learning to predict time to failure of lab foreshocks and earthquakes from fault zone raw acoustic emissions (2024) — Laura Laurenti et al. — EGU General Assembly Conference Abstracts, 14239, 2024
  Abstract

  Earthquake forecasting and prediction are going through achievements in short-term early warning systems, hazard assessment of natural and human-induced seismicity, and prediction of laboratory earthquakes.In laboratory settings, frictional stick-slip events serve as an analog for the complete seismic cycle. These experiments have been pivotal in comprehending the initiation of failure and the dynamics of earthquake rupture. Additionally, lab earthquakes present optimal opportunities for the application of machine learning (ML) techniques, as they can be generated in long sequences and with variable seismic cycles under controlled conditions. Indeed, recent ML studies demonstrate the predictability of labquakes through acoustic emissions (AE). In particular, Time to Failure (TTF) (defined as the time remaining before the next main labquake and retrieved from recorded shear stress) has been predicted for the main lab-event considering simple AE features as the variance.A step forward in the state of the art is the prediction of Time To Failure (TTF) by using raw AE waveforms. Here we use deep learning (DL) to predict not only the TTF of the mainshock with raw AE time series but also the TTF of all the labquakes, foreshocks or aftershocks, above a certain amplitude. This is a great finding for several reasons, mainly: 1) we can predict TTF by using traces that don’t contain EQ (but only noise); 2) we can improve our knowledge of seismic cycle predicting also TTF of foreshocks and aftershocks.This work is promising and opens new opportunities for the study of natural earthquakes just by analyzing the continuous raw seismogram. In general laboratory data studies underscore the significance of subtle deformation signals and intricate patterns emanating from slipping and/or locked faults before major earthquakes. Insights gained from laboratory experiments, coupled with the exponential growth in seismic data recordings worldwide, are diving into a new era of earthquake comprehension.
• On principles of emergent organization (2024) — Adam Rupe, James P. Crutchfield — Physics Reports
• On the Anatomy of Acoustic Emission (2024) — Robert A. Guyer et al. — The Journal of the Acoustical Society of America 156 (6), 4116-4122, 2024
  Abstract

  Abrupt frictional fault failure is normally accompanied by acoustic emission (AE)—impulsive elastic wave broadcast—with amplitude proportional to particle velocity. The cumulative sum of the fault particle velocities is a slip displacement.In laboratory shear experiments described here, measurements of a sequence of laboratory earthquakes includes local measurement of fault displacement and AE. Using these measurements we illuminate the connections between “cumulative sum of AE” and “slip displacement“. Additionally, the composition of the AE broadcasts reveals inhomogeneity in the fault mechanical structure from which they arise. This inhomogeneity, leading to a time invariant white AE component and an articulated AE, indicates that the articulated cumulative sum of the AE reveals a fault “state of the mechanical structure” diagnostic, that follows a distinctive pattern to frictional failure. This pattern explains why the continuous AE map to fault displacement as well as fault friction, shear stress, etc., as shown in many recent studies.
• Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous groups (2024) — Nicola Garofalo, Annunziata Loiudice, Dimiter Vassilev — Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  Abstract

  In this paper, we establish the sharp asymptotic decay of positive solutions of the Yamabe type equation $\mathcal {L}_s u=u^{\frac {Q+2s}{Q-2s}}$ in a homogeneous Lie group, where $\mathcal {L}_s$ represents a suitable pseudodifferential operator modelled on a class of nonlocal operators arising in conformal CR geometry.
• Overdetermined problems in groups of Heisenberg type: Conjectures and partial results (2024) — Nicola Garofalo, Dimiter Vassilev — Journal of Functional Analysis
• Predicting Critical Transitions in Multiscale Data (2024) — Rogene Eichler West et al. — Pacific Northwest National Laboratory (PNNL), Richland, WA (United States), 2024
• Seismic Features Predict Ground Motions During Repeating Caldera Collapse Sequence (2024) — Christopher W. Johnson, Paul A. Johnson — Geophysical Research Letters
  Abstract

  Abstract Applying machine learning to continuous acoustic emissions, signals previously deemed noise, from laboratory faults and slowly slipping subduction‐zone faults, demonstrates hidden signatures are emitted that describe physical details, including fault displacement and friction. However, no evidence currently exists to demonstrate that similar hidden signals occur during seismogenic stick‐slip on earthquake faults—the damaging earthquakes of most societal interest. We show that continuous seismic emissions emitted during the 2018 multi‐month caldera collapse sequence at the Kı̄lauea volcano in Hawai'i contain hidden signatures characterizing the earthquake cycle. Multi‐spectral data features extracted from 30 s intervals of the continuous seismic emission are used to train a gradient boosted tree regression model to predict the GNSS‐derived contemporaneous surface displacement and time‐to‐failure of the upcoming collapse event. This striking result suggests that at least some faults emit such signals and provide a potential path to characterizing the instantaneous and future behavior of earthquake faults.
• Earthquake fault slip and nonlinear dynamics (2023) — Paul A. Johnson, Chris W. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Earthquake fault slip under shear forcing can be envisioned as a nonlinear dynamical process dominated by a single slip plane. In contrast, nonlinear behavior in Earth materials (e.g., rock) is driven by a strain-induced ensemble activation and slip of a large number of distributed features—cracks and grain boundary slip across many scales in the volume. The bulk recovery of a fault post-failure and that of a rock sample post dynamic or static forcing (”aging” or the “slow dynamics”) is very similar with approximate log(time) dependence for much of the recovery. In our work, we analyze large amounts of continuous acoustic emission (AE) data from a laboratory “earthquake machine,” applying machine learning, with the task of determining what information regarding fault slip the AE signal may carry. Applying the continuous AE as input to machine learning models and using measured fault friction, displacement, etc., as model labels, we find that the AE are imprinted with information regarding the fault friction and displacement. We are currently developing approaches to probe stick-slip on Earth faults, those that are responsible for damaging earthquakes. A related goal is to quantitatively relate nonlinear elastic theory (e.g., PM space, Arrhenius) to frictional theory (e.g., rate-state).
• First and second laws of information processing by nonequilibrium dynamical states (2023) — Mikhael T. Semaan, James P. Crutchfield — Physical Review E
• Mapping glacier basal sliding applying machine learning (2023) — Josefine Umlauft et al. — Journal of Geophysical Research: Earth Surface 128 (11), e2023JF007280, 2023
  Abstract

  During the RESOLVE project ("High-resolution imaging in subsurface geophysics: development of a multi-instrument platform for interdisciplinary research"), continuous surface displacement and seismic array observations were obtained on Glacier d'Argentière in the French Alps for 35 days during May in 2018. This unique data set offers the chance to perform a detailed, local study of targeted processes within the highly dynamic cryospheric environment. In particular, the physical processes controlling glacial basal motion are poorly understood and remain challenging to observe directly. Especially in the Alpine region for temperate based glaciers where the ice rapidly responds to changing climatic conditions and thus, processes are strongly intermittent in time and heterogeneous in space. Spatially dense seismic and GPS measurements are analyzed with machine learning techniques to gain insight into the underlying processes controlling glacial motions of Glacier d'Argentière.Using multiple bandpass-filtered copies of the continuous seismic waveforms, we compute energy-based features, develop a matched field beamforming catalogue and include meteorological observations.Features describing the data are analyzed with a gradient boosting decision tree model to directly estimate the GPS displacements from the seismic records.We posit that features of the seismic noise provide direct access to the dominant parameters that drive displacement on the highly variable and unsteady surface of the glacier. The machine learning model infers daily fluctuations as well as longer term trends and the results show on-ice displacement rates are strongly modulated by activity at the base of the glacier. The techniques presented provide a new approach to study glacial basal sliding and discover its full complexity.
• Mapping glacier basal sliding with machine learning (2023) — Josefine Umlauft et al. — EarthArXiv, 2023
  Abstract

  During the RESOLVE project ("High-resolution imaging in subsurface geophysics: development of a multi-instrument platform for interdisciplinary research"), continuous surface displacement and seismic array observations were obtained on Glacier d'Argentière in the French Alps for 35 days in May 2018. The data set is used to perform a detailed study of targeted processes within the highly dynamic cryospheric environment. In particular, the physical processes controlling glacial basal motion are poorly understood and remain challenging to observe directly.Especially in the Alpine region for temperate based glaciers where the ice rapidly responds to changing climatic conditions and thus, processes are strongly intermittent in time and heterogeneous in space. Spatially dense seismic and GPS measurements are analyzed applying machine learning to gain insight into the processes controlling glacial motions of Glacier d'Argentière.Using multiple bandpass-filtered copies of the continuous seismic waveforms, we compute energy-based features, develop a matched field beamforming catalogue and include meteorological observations.Features describing the data are analyzed with a gradient boosting decision tree model to directly estimate the GPS displacements from the seismic noise.We posit that features of the seismic noise provide direct access to the dominant parameters that drive displacement on the highly variable and unsteady surface of the glacier. The machine learning model infers daily fluctuations and longer term trends. The results show on-ice displacement rates are strongly modulated by activity at the base of the glacier. The techniques presented provide a new approach to study glacial basal sliding and discover its full complexity.
• Seismic fingerprint predicts ground motions during the 2018 Kilauea collapse sequence (2023) — Christopher Johnson, Paul Johnson
  Abstract

  Abstract Continuous acoustic emissions from laboratory earthquake faults and slowly-slipping subduction zone faults, signals previously deemed to be dominantly noise, are rich with physical details including the fault displacement and friction. However, no evidence currently exists demonstrating that the hidden signals observed in the laboratory and subduction slow-slip occur during seismogenic stick-slip on earthquake faults-the damaging earthquakes of most societal interest. Here, we show that seismic emissions associated with the 2018 caldera collapse at the Kilauea volcano in Hawai'i contain hidden signatures of instantaneous surface displacement and the time-to-failure of the upcoming collapse event. This striking result suggests that at least some faults in Earth emit such signals and provide a potential path to characterizing the instantaneous and future behavior of earthquake faults.
• Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group (2023) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — Analysis & PDE
• Straining to find the permeability (2023) — Bryan Euser et al. — Earth and Planetary Science Letters
• Algebraic Theory of Patterns as Generalized Symmetries (2022) — Adam Rupe, James P. Crutchfield — Symmetry
  Abstract

  We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories.
• ARIMA modeling of simulated and of real-time pollutant data (2022) — Paul Johnson, Caroline Johnson, Ling Huang — American Chemical Society SciMeetings 3 (1), 2022
• Damage detection in a laboratory-scale wellbore applying Time Reversal and Nonlinear Elastic Wave Spectroscopy (TR NEWS) (2022) — Erin Dauson et al. — NDT & E International
• Detecting and Characterizing Fluid Leakage Through Wellbore Flaws Using Fiber-Optic Distributed Acoustic Sensing (2022) — Ishtiaque Anwar et al. — 56th U.S. Rock Mechanics/Geomechanics Symposium
  Abstract

  ABSTRACT: A primary concern associated with the utilization of subsurface systems is that there may be pathways for fluid leakage from the resource storage, or disposal reservoir. Leakage of any fluid can contaminate groundwater, cause geo-environmental pollution, generate hazardous surface conditions, and potentially compromise the functionality of the subsurface system. A low-cost, innovative technique to detect and characterize fracture leakage that is functional over many years is needed for applications such as geothermal reservoirs, CO2 sequestration wells, deep borehole storage of nuclear waste, and strategic petroleum reserve caverns. In this experimental study, we investigate the use of fiber-optic distributed acoustic sensing (DAS) to measure dynamic strain changes caused by acoustic signals induced by fluid flow with an eventual goal of developing instrumentation and analytical techniques to detect and characterize the movement of fluids through leaky wellbores. In the first phase of the experiments reported here, we conducted fluid flow tests in a porous medium as an analog to a fracture filled with comminuted material. The measured effective permeability is then compared with the signals generated by the fiber-optic cable. The study indicated that acoustic signals generated from fluid flow through porous media could be effectively captured by the fiber-optic cable DAS technology. 1. INTRODUCTION Wellbores are used for gaining access to various subsurface systems such as underground fluid reserve (Miyazaki, 2009), CO2 sequestration (Watson and Bachu, 2008; Zhang and Bachu, 2011), geothermal energy development (Shadravan, Ghasemi, & Alfi, 2015), waste disposal, oil and gas exploration (Davies et al., 2014), etc. A primary concern associated with the utilization of subsurface systems is that there may be pathways for fluid leakage from the resource storage, or disposal reservoir through the wellbore flaws. Leakage of any fluid from a leaky wellbore can contaminate groundwater, cause geo-environmental pollution (Davies et al., 2014; Ingraffea, Wells, Santoro, & Shonkoff, 2014; Jackson, 2014), generate hazardous surface conditions, and potentially compromise the functionality of the subsurface system (Gasda, Celia, Wang, & Duguid, 2013). Researchers has identified different potential leakage pathways, including fractures in the cement or micro annuli from de-bonding at the cement-casing or cement-formation interface (Celia, Bachu, Nordbotten, Gasda, & Dahle, 2005; Theresa L Watson & Bachu, 2009) or the casing corrosion product (Anwar, Chojnicki, Bettin, Taha, & Stormont, 2019; Beltrán-Jiménez et al., 2021).
• Detection of earthquake precursors using neural networks (2022) — Veda Lye Sim Ong et al. — Authorea Preprints, 2022
• EQDetect: Earthquake phase arrivals and first motion polarity applying deep learning (2022) — Christopher W Johnson, Paul A. Johnson — ESS Open Archive eprints 105, essoar. 10511191, 2022
• Homeostatic and adaptive energetics: Nonequilibrium fluctuations beyond detailed balance in voltage-gated ion channels (2022) — Mikhael T. Semaan, James P. Crutchfield — Physical Review E
• Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems (2022) — Adam Rupe, Velimir V Vesselinov, James P Crutchfield — New Journal of Physics
  Abstract

  Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.
• On Sub-Riemannian and Riemannian Spaces Associated to a Lorentzian Manifold (2022) — Roman Sverdlov, Dimiter Vassilev — Trends in Mathematics
• PNNL Technical Interview [Slides] (2022) — Adam Rupe — Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2022
• Predicting Future Laboratory Fault Friction Through Deep Learning Transformer Models (2022) — Kun Wang et al. — Geophysical Research Letters
  Abstract

  Abstract Machine learning models using seismic emissions as input can predict instantaneous fault characteristics such as displacement and friction in laboratory experiments, and slow slip in Earth. Here, we address whether the seismic/acoustic emission (AE) from laboratory experiments contains information about future frictional behavior. The approach uses a convolutional encoder‐decoder containing a transformer model in the latent space, similar to models used for natural language processing. We test the model limits using progressively larger AE input time windows and progressively larger output friction time windows. The results demonstrate that very near‐term friction predictions are indeed contained in the AE signal, and predictions are progressively worse farther into the future. The future predictions by the model of impending failure in the near‐term are remarkably robust. This first effort predicting future fault frictional behavior with machine learning will aid in guiding efforts for applications in Earth.
• Probing Seismogenic Faults with Machine Learning (2022) — Paul A. Johnson, Christopher W. Johnson — 2022 IEEE International Conference on Image Processing (ICIP)
  Abstract

  We analyze continuous seismic data with a variety of classical machine learning (ML) and deep learning (DL) models with the goal of identifying hidden signals connected to the earthquake cycle. In the laboratory, we find that continuous seismic waves originating in the fault zone are imprinted with fundamental information regarding the physics of the fault. Statistics of these low-amplitude, noise-like signals identified with supervised ML approaches can be used to estimate fault friction, fault displacement, and forecast upcoming failure with great accuracy. These results hold true for both stick-slip and slow-slip frictional regimes. Similarly, when we scale the approach to study slow-slip events in the Cascadia subduction zone and the San Andreas Fault, we find that continuous seismic waves contain information about the instantaneous fault displacement at all times. Direct application of these approaches to seismogenic faults in Earth is highly challenging to date. As a result, we are developing more generalized DL approaches where the model is trained on fault simulations and applied to laboratory fault data.
• Should we regress Y on X or X on Y? Question for chemical applications (2022) — Paul Johnson, Caroline Johnson, Ling Huang — American Chemical Society SciMeetings 3 (1), 2022
• Straining to Learn Permeability (2022) — Bryan Euser et al. — EarthArXiv, 2022
  Abstract

  Characterizing fluid flow in a porous material with permeability is fundamental to energy and hydrological applications, yet direct measurements of permeability are very difficult to conduct in situ. However, attending fluid flow through a material are various mechanical responses, e.g., strain fields, acoustic emission. These mechanical responses may hold important clues to the fluid flow in the material, to the permeability. Here we report results from a numerical study of fluid flow in a channel, defined by confining side blocks, that contains a particle bed. For a range of inlet velocities, we study the strain and acoustic emission in the side blocks. Simulations are repeated for different configurations of the particle bed. We find that the observed mechanical response accords with an analytic model of this system, providing promising evidence for using mechanical measurements, particularly strain and acoustic emission, as surrogates for direct measurement of permeability.
• Temporal earthquake forecasting (2022) — Veda Lye Sim Ong et al. — Authorea Preprints, 2022
• The Michaelis-Menten model used to model product yield (2022) — Paul Johnson, Caroline Johnson, Ling Huang — American Chemical Society SciMeetings 3 (2), 2022
• The temporal limits of predicting fault failure (2022) — Kun Wang et al. — arXiv preprint arXiv:2202.03894, 2022
• Tremor Waveform Extraction and Automatic Location With Neural Network Interpretation (2022) — Claudia Hulbert et al. — IEEE Transactions on Geoscience and Remote Sensing
  Abstract

  Active faults release tectonic stress imposed by plate motion through a spectrum of slip modes, from slow, aseismic slip, to dynamic, seismic events. Slow earthquakes are often associated with tectonic tremor, nonimpulsive signals that can easily be buried in seismic noise and go undetected. We present a new methodology aimed at improving the detection and location of tremors hidden within seismic noise. After identifying tremors with a classic convolutional neural network (CNN), we rely on neural network attribution to extract core tremor signatures. We observe that the signals resulting from the neural network attribution analysis correspond to a waveform traveling in the Earth’s crust and mantle at wavespeeds consistent with seismological estimates. We then use these waveforms signatures to locate the source of tremors with standard array-based techniques. We apply this method to the Cascadia subduction zone, where we identify tremor patches consistent with existing catalogs. This approach allows us to extract small signals hidden within the noise, and to locate more tremors than in existing catalogs.
• A convolutional neural network approach to estimate earthquake kinematic parameters from back-projection images (2021) — Marina Corradini et al. — EarthArXiv, 2021
  Abstract

  The retrieval of earthquake finite-fault kinematic parameters after the occurrence of an earthquake is a crucial task in observational seismology. Routinely-used source inversion techniques are challenged by limited data coverage and computational effort, and are subject to a variety of assumptions and constraints that restrict the range of possible solutions. Back-projection (BP) imaging techniques do not need prior knowledge of the rupture extent and propagation, and can track the high-frequency (HF) radiation emitted during the rupture process. While classic source inversion methods work at lower frequencies and return an image of the slip over the fault, the BP method underlines fault areas radiating HF seismic energy. HF radiation is attributed to the spatial and temporal complexity of the rupture process (e.g., slip heterogeneities, changes in rupture speed and in slip velocity). However, the quantitative link between the BP image of an earthquake and its rupture kinematics remains unclear. Our work aims at reducing the gap between the theoretical studies on the generation of HF radiation due to earthquake complexity and the observation of HF emissions in BP images. To do so, we proceed in two stages, in each case analyzing synthetic rupture scenarios where the rupture process is fully known. We first investigate the influence that spatial heterogeneities in slip and rupture velocity have on the rupture process and its radiated wave field using the BP technique. We simulate different rupture processes using a 1D line source model. For each rupture model, we calculate synthetic seismograms at three teleseismic arrays and apply the BP technique to identify the sources of HF radiation. This procedure allows us to compare the BP images with the causative rupture, and thus to interpret HF emissions in terms of along-fault variation of the three kinematic parameters controlling the synthetic model: rise time, final slip, rupture velocity. Our results show that the HF peaks retrieved from BP analysis are better associated with space-time heterogeneities of slip acceleration. We then build on these findings by testing whether one can retrieve the kinematic rupture parameters along the fault using information from the BP image alone. We apply a machine learning, convolutional neural network (CNN) approach to the BP images of a large set of simulated 1D rupture processes to assess the ability of the network to retrieve from the progression of HF emissions in space and time the kinematic parameters of the rupture. These rupture simulations include along-strike heterogeneities whose size is variable and within which the parameters of rise-time, final slip, and rupture velocity change from the surrounding rupture. We show that the CNN trained on 40,000 pairs of BP images and kinematic parameters returns excellent predictions of the rise time and the rupture velocity along the fault, as well as good predictions of the central location and length of the heterogeneous segment. Our results also show that the network is insensitive towards the final slip value, as expected from a theoretical standpoint.
• AI for Extreme Volcanic Climate Forcing and Feedback Forecasting in the 21st century (2021) — Manvendra Dubey et al. — Artificial Intelligence for Earth System Predictability (AI4ESP�…, 2021
  Abstract

  Focal Areas: Our paradigm-shifting framework will apply machine learning and perform physical analysis of contemporary volcanoes to develop sound forecasts of extreme eruptions in the 21st century and their abrupt drying and cooling impacts on the warming climate. We will also bridge climate data driven regression models and earth system model output to trace teleconnections that exacerbate regional impacts such as Arctic amplification and western US droughts.
• Attention Network Forecasts Time‐to‐Failure in Laboratory Shear Experiments (2021) — Hope Jasperson et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Abstract Rocks under stress deform by creep mechanisms that include formation and slip on small‐scale internal cracks. Intragranular cracks and slip along grain contacts release energy as elastic waves termed acoustic emissions (AE). AEs are thought to contain predictive information that can be used for fault failure forecasting. Here, we present a method using unsupervised classification and an attention network to forecast labquakes using AE waveform features. Our data were generated in a laboratory setting using a biaxial shearing device with granular fault gouge intended to mimic the conditions of tectonic faults. Here, we analyzed the temporal evolution of AEs generated throughout several hundred laboratory earthquake cycles. We used a Conscience Self‐Organizing Map (CSOM) to perform topologically ordered vector quantization based on waveform properties. The resulting map was used to interactively cluster AEs. We examined the clusters over time to identify those with predictive ability. Finally, we used a variety of LSTM and attention‐based networks to test the predictive power of the AE clusters. By tracking cumulative waveform features over the seismic cycle, the network is able to forecast the time‐to‐failure (TTF) of lab earthquakes. Our results show that analyzing the data to isolate predictive signals and using a more sophisticated network architecture are key to robustly forecasting labquakes. In the future, this method could be applied on tectonic faults to monitor earthquakes and augment early warning systems.
• Deep Learning for Autonomous Extraction of Millimeter-scale Deformation in InSAR Time Series (2021) — Bertrand Rouet-Leduc et al. — Nature communications 12 (1), 6480, 2021
  Abstract

  <p>Systematically characterizing slip behaviours on active faults is key to unraveling the physics of tectonic faulting and the interplay between slow and fast earthquakes. Interferometric Synthetic Aperture Radar (InSAR), by enabling measurement of ground deformation at a global scale every few days, may hold the key to those interactions. <br>However, atmospheric propagation delays often exceed ground deformation of interest despite state-of-the art processing, and thus InSAR analysis requires expert interpretation and a priori knowledge of fault systems, precluding global investigations of deformation dynamics. <br>We show that a deep auto-encoder architecture tailored to untangle ground deformation from noise in InSAR time series autonomously extracts deformation signals, without prior knowledge of a fault's location or slip behaviour.<br>Applied to InSAR data over the North Anatolian Fault, our method reaches  2 mm detection, revealing a slow earthquake twice as extensive as previously recognized.<br>We further explore the generalization of our approach to inflation/deflation-induced deformation, applying the same methodology to the geothermal field of Coso, California. </p>
• Estimation of the orientation of stress in the Earth’s crust without earthquake or borehole data (2021) — Andrew A. Delorey et al. — Communications Earth & Environment
  Abstract

  Abstract Mechanical stress acting in the Earth’s crust is a fundamental property that is important for a wide range of scientific and engineering applications. The orientation of maximum horizontal compressive stress can be estimated by inverting earthquake source mechanisms and measured directly from borehole-based measurements, but large regions of the continents have few or no observations. Here we present an approach to determine the orientation of maximum horizontal compressive stress by measuring stress-induced anisotropy of nonlinear susceptibility, which is the derivative of elastic modulus with respect to strain. Laboratory and Earth experiments show that nonlinear susceptibility is azimuthally dependent in an anisotropic stress field and is maximum in the orientation of maximum horizontal compressive stress. We observe this behavior in the Earth—in Oklahoma and New Mexico, U.S.A, where maximum nonlinear susceptibility coincides with the orientation of maximum horizontal compressive stress measured using traditional methods. Our measurements use empirical Green’s functions and solid-earth tides and can be applied at different temporal and spatial scales.
• Geo Thermal Cloud: Cloud Fusion of Big Data and Multi-Physics Models using Machine Learning for Discovery, Exploration, and Development of Hidden Geothermal Resources (2021) — Velimir Vesselinov et al. — Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2021
• Laboratory earthquake forecasting: A machine learning competition (2021) — Paul A. Johnson et al. — Proceedings of the National Academy of Sciences
  Abstract

  Earthquake prediction, the long-sought holy grail of earthquake science, continues to confound Earth scientists. Could we make advances by crowdsourcing, drawing from the vast knowledge and creativity of the machine learning (ML) community? We used Google’s ML competition platform, Kaggle, to engage the worldwide ML community with a competition to develop and improve data analysis approaches on a forecasting problem that uses laboratory earthquake data. The competitors were tasked with predicting the time remaining before the next earthquake of successive laboratory quake events, based on only a small portion of the laboratory seismic data. The more than 4,500 participating teams created and shared more than 400 computer programs in openly accessible notebooks. Complementing the now well-known features of seismic data that map to fault criticality in the laboratory, the winning teams employed unexpected strategies based on rescaling failure times as a fraction of the seismic cycle and comparing input distribution of training and testing data. In addition to yielding scientific insights into fault processes in the laboratory and their relation with the evolution of the statistical properties of the associated seismic data, the competition serves as a pedagogical tool for teaching ML in geophysics. The approach may provide a model for other competitions in geosciences or other domains of study to help engage the ML community on problems of significance.
• Learning the Low Frequency Earthquake Activity on the Central San Andreas Fault (2021) — Christopher W. Johnson, Paul A. Johnson — Geophysical Research Letters
  Abstract

  Abstract Low frequency earthquakes (LFEs) originating below the central San Andreas Fault are associated with slow‐slip beneath the seismogenic zone within the more ductile portion of the crust. Monitoring efforts over 15 years detected >1 million LFEs. We train a gradient boosted tree model using statistical features describing the seismic waveforms to estimate the hourly LFE event count. The burst‐like LFE behavior is reproduced, while lower amplitudes are predicted during the most active periods. The hourly event counts are up to 18% greater than the catalog. The ability to continuously monitor LFE activity provides insight to when geodetic measurements of slow slip are possible, without the need for developing a computational‐intensive template‐matching catalog. Similar waveform statistical features are found between detecting LFEs and tremors, which provides additional evidence tremors are composed of LFEs. The approach extracts information contained in continuous seismic waveforms that might benefit detecting precursory signals.
• Measuring SHmax with Stress-Induced Anisotropy in Nonlinear Anelastic Behavior (2021) — Andrew Delorey et al.
  Abstract

  Abstract Mechanical stress acting in the Earth`s crust is a fundamental property that has a wide range of geophysical applications, from tectonic movements to energy production. The orientation of maximum horizontal compressive stress, S Hmax can be estimated by inverting earthquake source mechanisms and directly from borehole-based measurements, but large regions of the continents have few or no observations. Available observations often represent a variety of length scales and depths, and can be difficult to reconcile. Here we present a new approach to determine S Hmax by measuring stress induced anisotropy of nonlinear susceptibility. We observe that nonlinear susceptibility is azimuthally dependent in the Earth and maximum when parallel to S Hmax , as predicted by laboratory experiments. Our measurements use empirical Green’s functions that are applicable for different temporal and spatial scales. The method can quantify the orientation of S Hmax in regions where no measurements exist today.
• Nonlinear Acoustics Applications for Near-Wellbore Formation Evaluation (2021) — Christopher Skelt et al. — Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description
  Abstract

  We present experimental and modeling results and a downhole logging tool concept resulting from a research collaboration between Chevron Energy Technology Company and Los Alamos National Laboratory investigating using nonlinear acoustics applications for natural fracture characterization and assessing near-wellbore mechanical integrity or drilling-induced damage. The generation of a scattered wave by noncollinear mixing of two acoustic plane waves in an acoustically nonlinear medium was first documented several decades ago. If the frequency ratio and convergence angle of the two waves and the compressional-to-shear velocity ratio of the medium where they intersect meet certain conditions, their interaction creates a scattered third wave, propagating in a predictable direction, with a frequency equal to the sum or difference between the two primary wave frequencies and an amplitude dependent on the nonlinearity at the intersection location. The conditions resulting in this scattering and the properties of the scattered wave are thus governed by the physics of the interaction, resulting in a set of “selection rules” that are the key to the measurement principle introduced here. If the two transmitted plane waves are oriented such that the third wave returns to the borehole, the phenomenon may be used as the basis for a logging tool measuring acoustic nonlinearity around the wellbore circumference, with a secondary measurement of the compressional-to-shear velocity ratio. Laboratory measurements supported by finite-difference and analytical modeling confirmed that the mixing of two plane compressional waves generated a shear wave as predicted by the selection rules in a large Berea sandstone block, confirming the potential for a downhole tool with a depth of investigation in the range 15 to 20 cm. Historical data show that nonlinearity in core samples is primarily caused by a lack of mechanical integrity. In the oil field, this may be microfractures in tight rock unconventional reservoirs or incipient near-wellbore failure while drilling. This prompts applications to fracture characterization and calibration of mechanical earth models. The main practical challenge for a downhole logging tool is injecting powerful directional acoustic energy into the formation. We envisage an openhole tool making sequential station measurements using transmitters built into hydraulically controlled pads contacting the borehole wall. Noncollinear mixing may be activated by maintaining the frequency of one transmitter constant while sweeping the other through the range of frequency ratios predicted by the selection rules, resulting in a received sum or difference frequency signal that rises to a peak and then falls. Alternatively, the frequency ratio may be maintained while steering one of the acoustic beams. The peak signal amplitude indicates the coefficient of nonlinearity, which is sensitive to lack of mechanical integrity caused by natural fractures or mechanical disaggregation. The frequency ratio at which it occurs is an indicator of the shear-to-compressional velocity at the location where the two beams cross. In this manner, a record of nonlinearity along or around the borehole can be envisaged. The physics of acoustic nonlinearity is well established, and our laboratory measurements have determined that the phenomenon of interest should occur and be measurable in the subsurface. Overcoming the engineering challenges would bring new formation evaluation insights unique to this measurement principle.
• Predicting fault slip via transfer learning (2021) — Kun Wang et al. — Nature Communications
  Abstract

  Abstract Data-driven machine-learning for predicting instantaneous and future fault-slip in laboratory experiments has recently progressed markedly, primarily due to large training data sets. In Earth however, earthquake interevent times range from 10’s-100’s of years and geophysical data typically exist for only a portion of an earthquake cycle. Sparse data presents a serious challenge to training machine learning models for predicting fault slip in Earth. Here we describe a transfer learning approach using numerical simulations to train a convolutional encoder-decoder that predicts fault-slip behavior in laboratory experiments. The model learns a mapping between acoustic emission and fault friction histories from numerical simulations, and generalizes to produce accurate predictions of laboratory fault friction. Notably, the predictions improve by further training the model latent space using only a portion of data from a single laboratory earthquake-cycle. The transfer learning results elucidate the potential of using models trained on numerical simulations and fine-tuned with small geophysical data sets for potential applications to faults in Earth.
• Probing the Damage Zone at Parkfield (2021) — Andrew A. Delorey et al. — Geophysical Research Letters
  Abstract

  Abstract Rocks are heterogeneous materials that exhibit nonlinear elastic (anelastic) behavior at scales ranging from the laboratory to Earth. In the laboratory, typical, complex relationships exist between stress and strain that include hysteresis, finite relaxation times, strain rate, and history dependence. These behaviors are linked to important characteristics such as stress, porosity, permeability, material integrity, and material failure. We adopted a “pump‐probe” type experiment common in laboratory studies, using solid earth tides as the low‐frequency pump and empirical Green's function as the high‐frequency probe. By probing the velocity at different points in the pump cycle, we constrained important information about the strain‐modulus relationship. Near the San Andreas Fault, we observed strongly nonlinear elastic behavior that characterizes the damage zone. We also constrained important aspects of hysteretic behavior that are related to damage properties and possibly pore pressure. Away from the fault, the nonlinear behavior is diminished.
• Probing the damage zone on the San Andreas Fault at Parkfield (2021) — Andrew Delorey, Paul Johnson — EGU General Assembly Conference Abstracts, EGU21-10926, 2021
  Abstract

  <p>Rocks are heterogeneous materials that exhibit nonlinear elastic (anelastic) behavior in both the laboratory and Earth. In the laboratory, investigators have observed complex relationships between stress and strain that include hysteresis, finite relaxation times, and rate and stress path dependence.  These behaviors are linked to stress, porosity, permeability, material integrity and material failure, many of the characteristics we care about in the upper crust.  A limited number of studies in the Earth have confirmed that nonlinear elasticity can be measured in situ, but due to logistical challenges these investigations have not achieved the full potential of what can ultimately be learned from this type of investigation.  We adapted a ‘pump-probe’ type experiment common in laboratory studies, using solid earth tides as the low frequency pump and empirical Green’s function as the high frequency probe.  By probing the velocity at different points in the pump cycle, we constrain some important information about the stress-strain relationship.  Near the San Andreas Fault, we observe strongly nonlinear elastic behavior that increases with decreasing distance to the fault that characterizes the damage zone.  We also constrain important aspects of hysteretic behavior that are related to damage properties and possibly pore pressure.</p>
• Single mode nonlinear resonance acoustic spectroscopy for damage detection in quasi-brittle materials (2021) — K.E.-A. Van Den Abeele et al. — Emerging Technologies in NDT
• The Search For Thermodynamic Principles of Organization [Slides] (2021) — Adam Rupe — Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2021
• The Seismic Noise is the Signal: Applying Machine Learning to Earthquake Forecasting (2021) — Christopher Johnson, Paul Johnson — Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2021
• Transfer Operator Framework for Earth System Predictability and Water Cycle Extremes (2021) — Adam Rupe et al. — Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2021
  Abstract

  For chaotic dynamical systems, nonlinear instabilities lead to exponentially divergent trajectories in the evolution of system states. Unless a simulation is initialized with an infinite-precision snapshot of the state of the true system and all known physical effects that go into its evolution are directly computed, the future state predicted by the simulation will quickly diverge from that of the true system. Moreover, the Earth system is highly structured and contains localized coherent structures that are particularly important to predict. Predicting extreme events associated with coherent structures, like hurricanes and blocking events, is crucial for understanding the effects of global warming on the water cycle.
• Tremor Waveform Denoising and Automatic Location with Neural Network Interpretation (2021) — Claudia Hulbert et al. — arXiv preprint arXiv:2012.13847, 2020
  Abstract

  <p>Active faults release tectonic stress imposed by plate motion through a spectrum of slip modes, from slow, aseismic slip, to dynamic, seismic events. Slow earthquakes are often associated with tectonic tremor, non-impulsive signals that can easily be buried in seismic noise and go undetected. </p><p>We present a new methodology aimed at improving the detection and location of tremors hidden within seismic noise. After detecting tremors with a classic convolutional neural network, we rely on neural network attribution to extract core tremor signatures. By identifying and extracting tremor characteristics, in particular in the frequency domain, the attribution analysis allows us to uncover structure in the data and denoise input waveforms. In particular, we show that these cleaned signals correspond to a waveform traveling in the Earth's crust and mantle at wavespeeds consistent with local estimates. We then use these cleaned waveforms to locate tremors with standard array-based techniques. </p><p>We apply this method to the Cascadia subduction zone. We analyze a slow slip event that occurred in 2018 below the southern end of the Vancouver Island, Canada, where we identify tremor patches consistent with existing catalogs. Having validated our new methodology in a well-studied area, we further apply it to various tectonic contexts and discuss the implications of tremor occurrences in the scope of exploring the interplay between seismic and aseismic slip.</p>
• An exponential build-up in seismic energy suggests a months-long nucleation of slow slip in Cascadia (2020) — Claudia Hulbert et al. — Nature Communications
  Abstract

  Abstract Slow slip events result from the spontaneous weakening of the subduction megathrust and bear strong resemblance to earthquakes, only slower. This resemblance allows us to study fundamental aspects of nucleation that remain elusive for classic, fast earthquakes. We rely on machine learning algorithms to infer slow slip timing from statistics of seismic waveforms. We find that patterns in seismic power follow the 14-month slow slip cycle in Cascadia, arguing in favor of the predictability of slow slip rupture. Here, we show that seismic power exponentially increases as the slowly slipping portion of the subduction zone approaches failure, a behavior that shares a striking similarity with the increase in acoustic power observed prior to laboratory slow slip events. Our results suggest that the nucleation phase of Cascadia slow slip events may last from several weeks up to several months.
• An integrated analytical and experimental study of contact acoustic nonlinearity at rough interfaces of fatigue cracks (2020) — Jiang Jin, Paul Johnson, Parisa Shokouhi — Journal of the Mechanics and Physics of Solids
• Cylinder Test (2020) — Emily Johnson — Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2020
• Imaging Stress and Faulting Complexity Through Earthquake Waveform Similarity (2020) — Daniel T. Trugman, Zachary E. Ross, Paul A. Johnson — Geophysical Research Letters
  Abstract

  Abstract While the rupture processes of nearby earthquakes are often highly similar, characterizing the differences can provide insight into the complexity of the stress field and fault network in which the earthquakes occur. Here we perform a comprehensive analysis of earthquake waveform similarity to characterize rupture processes in the vicinity of Ridgecrest, California. We quantify how similar each earthquake is to neighboring events through cross correlation of full waveforms. The July 2019 Ridgecrest mainshocks impose a step reduction in earthquake similarity, which suggests variability in the residual stress field and activated fault structures on length scales of hundreds of meters or less. Among these aftershocks, we observe coherent spatial variations of earthquake similarity along the mainshock rupture trace, and document antisimilar aftershock pairs with waveforms that are nearly identical but with reversed polarity. These observations provide new, high‐resolution constraints on stress transfer and faulting complexity throughout the Ridgecrest earthquake sequence.
• Machine learning and fault rupture: a review (2020) — Christopher Ren et al. — Advances in Geophysics 61, 57-107, 2020
  Abstract

  Geophysics has historically been a data-driven field, however in recent years the exponential increase of available data has lead to increased adoption of machine learning techniques and algorithm for analysis, detection and forecasting applications to faulting. This work reviews recent advances in the application of machine learning in the study of fault rupture ranging from the laboratory to Solid Earth.
• Machine Learning Reveals the Seismic Signature of Eruptive Behavior at Piton de la Fournaise Volcano (2020) — C. X. Ren et al. — Geophysical Research Letters
  Abstract

  Abstract Volcanic tremor is key to our understanding of active magmatic systems, but due to its complexity, there is still a debate concerning its origins and how it can be used to characterize eruptive dynamics. In this study we leverage machine learning techniques using 6 years of continuous seismic data from the Piton de la Fournaise volcano (La Réunion island) to describe specific patterns of seismic signals recorded during eruptions. These results unveil what we interpret as signals associated with various eruptive dynamics of the volcano, including the effusion of a large volume of lava during the August–October 2015 eruption as well as the closing of the eruptive vent during the September–November 2018 eruption. The machine learning workflow we describe can easily be applied to other active volcanoes, potentially leading to an enhanced understanding of the temporal and spatial evolution of volcanic eruptions.
• Plate motion in sheared granular fault system (2020) — Ke Gao et al. — Earth and Planetary Science Letters
• Probing Slow Earthquakes With Deep Learning (2020) — Bertrand Rouet‐Leduc et al. — Geophysical Research Letters
  Abstract

  Abstract Slow earthquakes may trigger failure on neighboring locked faults that are stressed sufficiently to break, and slow slip patterns may evolve before a nearby great earthquake. However, even in the clearest cases such as Cascadia, slow earthquakes and associated tremor have only been observed in intermittent and discrete bursts. By training a convolutional neural network to detect known tremor on a single seismic station in Cascadia, we isolate and identify tremor and slip preceding and following known larger slow events. The deep neural network can be used for the detection of quasi‐continuous tremor, providing a proxy that quantifies the slow slip rate. Furthermore, the model trained in Cascadia recognizes tremor in other subduction zones and also along the San Andreas Fault at Parkfield, suggesting a universality of waveform characteristics and source processes, as posited from experiments and theory.
• Randomised controlled trial for high-dose intravenous zinc as adjunctive therapy in SARS-CoV-2 (COVID-19) positive critically ill patients: trial protocol (2020) — Marlon Perera et al. — BMJ Open
  Abstract

  Introduction SARS-CoV-2 (COVID-19) has caused an international pandemic of respiratory illness, resulting in significant healthcare and economic turmoil. To date, no robust vaccine or treatment has been identified. Elemental zinc has previously been demonstrated to have beneficial effects on coronaviruses and other viral respiratory infections due to its effect on RNA polymerase. Additionally, zinc has well-demonstrated protective effects against hypoxic injury—a clear mechanism of end-organ injury in respiratory distress syndrome. We aimed to assess the effect of high-dose intravenous zinc (HDIVZn) on SARS-CoV-2 infection. The end of study analyses will evaluate the reduction of impact of oxygen saturations or requirement of oxygen supplementation. Methods and analysis We designed a double-blind randomised controlled trial of daily HDIVZn (0.5 mg/kg) versus placebo. Primary outcome measures are lowest oxygen saturation (or greatest level of supplemental oxygenation) for non-ventilated patients and worst PaO 2 /FiO 2 for ventilated patients. Following power calculations, 60 hospitalised patients and 100 ventilated patients will be recruited to demonstrate a 20% difference. The duration of follow-up is up to the point of discharge. Ethics and dissemination Ethical approval was obtained through the independent Human Research Ethics Committee. Participant recruitment will commence in May 2020. Results will be published in peer-reviewed medical journals. Trial registration number ACTRN126200000454976.
• Seasonal and Coseismic Velocity Variation in the Region of L'Aquila From Single Station Measurements and Implications for Crustal Rheology (2020) — Piero Poli et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Abstract We performed measurements of velocity variations for variable coda waves time lapse using empirical Green's functions reconstructed by autocorrelation of seismic noise recorded during a period of 17 years in the region of L'Aquila, Italy. The time lapse approach permitted us to evaluate the spatial (depth) dependence of velocity variation (dv/v). By quantitatively comparing the 17 years of dv/v time series with independent data (e.g., strain induced by earthquakes and hydrological loading), we unravel a group of physical processes inducing velocity variations in the crust over multiple time and spatial scales. We find that rapid shaking due to three magnitude 6+ earthquakes mainly induced near surface velocity variations. On the other hand, slow strain perturbation (period 5 years, in the preseismic period) associated with hydrological cycles, induced velocity changes primarily in the middle crust. The observed behavior suggests the existence of a large volume of fluid‐filled cracks exist deep in the crust. Our study highlights the possibility of using seasonal and multiyear perturbations to probe the physical properties of seismogenic fault volumes and shed new light into the depth‐dependent rheology of crustal rocks in the region or L'Aquila.
• Tackling 21st Century Geoscience Problems with Machine Learning (2020) — Andrew Curtis et al. — Eos
  Abstract

  A new cross-journal special collection invites contributions on how machine learning can be used for solid Earth observation, modeling and understanding.
• The Spatiotemporal Evolution of Granular Microslip Precursors to Laboratory Earthquakes (2020) — Daniel T. Trugman et al. — Geophysical Research Letters
  Abstract

  Abstract Laboratory earthquake experiments provide important observational constraints for our understanding of earthquake physics. Here we leverage continuous waveform data from a network of piezoceramic sensors to study the spatial and temporal evolution of microslip activity during a shear experiment with synthetic fault gouge. We combine machine learning techniques with ray theoretical seismology to detect, associate, and locate tens of thousands of microslip events within the gouge layer. Microslip activity is concentrated near the center of the system but is highly variable in space and time. While microslip activity rate increases as failure approaches, the spatiotemporal evolution can differ substantially between stick‐slip cycles. These results illustrate that even within a single, well‐constrained laboratory experiment, the dynamics of earthquake nucleation can be highly complex.
• Continuous chatter of the Cascadia subduction zone revealed by machine learning (2019) — Bertrand Rouet-Leduc, Claudia Hulbert, Paul A. Johnson — Nature Geoscience
• Curious nonlinearity of rocks (2019) — Carly M. Donahue, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Many geological materials, ranging from “rocks to unconsolidated sand,” exhibit highly nonlinear elastic properties. Rocks fall in to a class of materials know as Nonlinear Mesoscopic Elastic Mesoscopic materials (NMEMs) in which the nonlinearity they possess is not derived from the constituent material, but rather the microscopic structure. Their behavior manifests as characteristic wave distortion, and slow dynamics, a recovery process to equilibrium that takes place over hours, days, weeks and sometimes years after a wave disturbance. A number of acoustic techniques have been developed to quantify a the material’s nonlinear elastic coefficients and image localized damaged areas; and while much has been learned, much is left unknown, particularly identifying and understanding the underlying physical mechanisms that give rise to a rock’s nonlinear elastic response, such as frictional losses, soft regions, and the influence of water content. But rocks also are a platform to understand other localized and distributed nonlinearity. Nondestructive evaluation techniques of metal and concrete are being developed with applications towards crack detection and wellbore integrity. Nonlinear acoustic techniques have recently appeared promising for performance evaluation of pressed powders and additively manufactured materials. In this presentation, we will provide an overview of nonlinear elasticity as illustrated by some examples.
• DeepDetect: A Cascaded Region-Based Densely Connected Network for Seismic Event Detection (2019) — Yue Wu et al. — IEEE Transactions on Geoscience and Remote Sensing
  Abstract

  Automatic event detection from time series signals has broad applications. Traditional detection methods detect events primarily by the use of similarity and correlation in data. Those methods can be inefficient and yield low accuracy. In recent years, machine learning techniques have revolutionized many sciences and engineering domains. In particular, the performance of object detection in a 2-D image data has significantly improved due to deep neural networks. In this paper, we develop a deep-learning-based detection method, called “DeepDetect,” to detect events from seismic signals. We find that the direct adaptation of similar ideas from 2-D object detection to our problem faces two challenges. The first challenge is that the duration of earthquake event varies significantly; the other is that the proposals generated are temporally correlated. To address these challenges, we propose a novel cascaded region-based convolutional neural network to capture earthquake events in different sizes while incorporating contextual information to enrich features for each proposal. To achieve a better generalization performance, we use densely connected blocks as the backbone of our network. Because some positive events are not correctly annotated, we further formulate the detection problem as a learning-from-noise problem. To verify the performance, we employ the seismic data generated from the Pennsylvania State University Rock and Sediment Mechanics Laboratory, and we acquire labels with the help of experts. We show that our techniques yield high accuracy. Therefore, our novel deep-learning-based detection methods can potentially be powerful tools for identifying events from the time series data in various applications.
• Earthquake Detection in 1D Time‐Series Data with Feature Selection and Dictionary Learning (2019) — Zheng Zhou et al. — Seismological Research Letters
  Abstract

  Earthquakes can be detected by matching spatial patterns or phase properties from 1-D seismic waves. Current earthquake detection methods, such as waveform correlation and template matching, have difficulty detecting anomalous earthquakes that are not similar to other earthquakes. In recent years, machine-learning techniques for earthquake detection have been emerging as a new active research direction. In this paper, we develop a novel earthquake detection method based on dictionary learning. Our detection method first generates rich features via signal processing and statistical methods and further employs feature selection techniques to choose features that carry the most significant information. Based on these selected features, we build a dictionary for classifying earthquake events from non-earthquake events. To evaluate the performance of our dictionary-based detection methods, we test our method on a labquake dataset from Penn State University, which contains 3,357,566 time series data points with a 400 MHz sampling rate. 1,000 earthquake events are manually labeled in total, and the length of these earthquake events varies from 74 to 7151 data points. Through comparison to other detection methods, we show that our feature selection and dictionary learning incorporated earthquake detection method achieves an 80.1% prediction accuracy and outperforms the baseline methods in earthquake detection, including Template Matching (TM) and Support Vector Machine (SVM).
• From Stress Chains to Acoustic Emission (2019) — Ke Gao et al. — Physical Review Letters
  Abstract

  A numerical scheme using the combined finite-discrete element method is employed to study a model of an earthquake system comprising a granular layer embedded in a formation. When the formation is driven so as to shear the granular layer, a system of stress chains emerges. The stress chains endow the layer with resistance to shear and on failure launch broadcasts into the formation. These broadcasts, received as acoustic emission, provide a remote monitor of the state of the granular layer of the earthquake system.
• Koopman operator and its approximations for systems with symmetries (2019) — Anastasiya Salova et al. — Chaos: An Interdisciplinary Journal of Nonlinear Science
  Abstract

  Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, often described by complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and to simplify their analysis. The Koopman operator is an infinite dimensional linear operator that fully captures a system’s nonlinear dynamics through the linear evolution of functions of the state space. Importantly, in contrast with local linearization, it preserves a system’s global nonlinear features. We demonstrate how the presence of symmetries affects the Koopman operator structure and its spectral properties. In fact, we show that symmetry considerations can also simplify finding the Koopman operator approximations using the extended and kernel dynamic mode decomposition methods (EDMD and kernel DMD). Specifically, representation theory allows us to demonstrate that an isotypic component basis induces a block diagonal structure in operator approximations, revealing hidden organization. Practically, if the symmetries are known, the EDMD and kernel DMD methods can be modified to give more efficient computation of the Koopman operator approximation and its eigenvalues, eigenfunctions, and eigenmodes. Rounding out the development, we discuss the effect of measurement noise.
• Machine learning for data-driven discovery in solid Earth geoscience (2019) — Karianne J. Bergen et al. — Science
  Abstract

  Automating geoscience analysis Solid Earth geoscience is a field that has very large set of observations, which are ideal for analysis with machine-learning methods. Bergen et al. review how these methods can be applied to solid Earth datasets. Adopting machine-learning techniques is important for extracting information and for understanding the increasing amount of complex data collected in the geosciences. Science , this issue p. eaau0323
• Machine Learning in Geoscience: Riding a Wave of Progress (2019) — Daniel Trugman, Gregory Beroza, Paul Johnson — Eos
  Abstract

  2nd Annual Machine Learning in Solid Earth Geoscience Conference; Santa Fe, New Mexico, 18–22 March 2019
• Machine Learning Reveals the Seismic Signature of Eruptive Behavior at Piton de la Fournaise Volcano (2019) — Christopher Ren et al. — AGU Fall Meeting Abstracts 2019, S53A-05, 2019
• Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds (2019) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — International Mathematics Research Notices
  Abstract

  Abstract It is shown that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. In the non-compact case, it is proved that a seven-dimensional everywhere non-umbilical qc-hypersurface embedded in a hyper-Kähler manifold is qc-conformal to a qc-Einstein structure which is locally qc-equivalent to the 3-Sasakian sphere, the quaternionic Heisenberg group or the hyperboloid.
• Nonlinear Resonant Ultrasound Spectroscopy: Assessing Global Damage (2019) — James A. TenCate, Paul A. Johnson — Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation
• Pairwise Association of Seismic Arrivals with Convolutional Neural Networks (2019) — Ian W. McBrearty, Andrew A. Delorey, Paul A. Johnson — Seismological Research Letters
  Abstract

  Correctly determining the association of seismic phases across a network is crucial for developing accurate earthquake catalogs. Nearly all established methods use travel-time information as the main criterion for determining associations, and in problems in which earthquake rates are high and many false arrivals are present, many standard techniques may fail to resolve the problem accurately. As an alternative approach, in this work we apply convolutional neural networks (CNNs) to the problem of associations; we train CNNs to read earthquake waveform arrival pairs between two stations and predict the binary classification of whether the two waveforms are from a common source or different sources. Applying the method to a large training dataset of previously cataloged earthquakes in Chile, we obtain > 80% true positive prediction rates for high-frequency data ( > 2 Hz ) and stations separated in excess of 100 km. As a secondary benefit, the output of the neural network can also be used to infer predicted phase types of arrivals. The method is ideally applied in conjunction with standard travel-time-based association routines and can be adapted for arbitrary network geometries and applications, so long as sufficient training data are available.
• Separating Sea and Slow Slip Signals on the Seafloor (2019) — Joan Gomberg et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Abstract Seafloor pressure measurements hold promise for estimating vertical displacements from transient slow slip events on submarine faults. We assess the accuracy of pressure offset estimates that evolve over days to weeks and the confidence with which they may be attributed to tectonic deformation or to the ocean water column. One common approach to resolve this ambiguity assumes water column pressures vary insignificantly over the study region and are represented by stable reference site pressures. Assessing the validity of this assumption requires independent evidence. Correlations between pressures and colocated temperatures collected during the Hikurangi Ocean Bottom Investigation of Tremor and Slow Slip experiment suggest temperatures might provide a useful independent proxy for water column pressures. We compared offsets estimated using several methods, with temperature and other proxies. The use of a temperature proxy was unsuccessful, because seafloor temperatures did not track the seasonal signal that contributes significantly to seafloor pressure changes over the slow slip event period. Regardless of the estimation method, offsets varied within a few cm around some uncertain reference level. Commonly used statistical measures are shown not to be reliable indicators of offset accuracy since offsets contribute minimally to the total variance. Offsets estimated using identical methods but with seafloor pressures simulated using a regional ocean model were larger than those derived from the data but had a similar pattern. Since the model simulates only water column processes, this suggests a significant fraction of the estimated pressure offsets are due to seasonal water column signal and are not of tectonic origin.
• Simulation of crack induced nonlinear elasticity using the combined finite-discrete element method (2019) — Ke Gao et al. — Ultrasonics
• Earthquake Catalog‐Based Machine Learning Identification of Laboratory Fault States and the Effects of Magnitude of Completeness (2018) — Nicholas Lubbers et al. — Geophysical Research Letters
  Abstract

  Abstract Machine learning regression can predict macroscopic fault properties such as shear stress, friction, and time to failure using continuous records of fault zone acoustic emissions. Here we show that a similar approach is successful using event catalogs derived from the continuous data. Our methods are applicable to catalogs of arbitrary scale and magnitude of completeness. We investigate how machine learning regression from an event catalog of laboratory earthquakes performs as a function of the catalog magnitude of completeness. We find that strong model performance requires a sufficiently low magnitude of completeness, and below this magnitude of completeness, model performance saturates.
• Evolution of b-value during the seismic cycle: Insights from laboratory experiments on simulated faults (2018) — J. Rivière et al. — Earth and Planetary Science Letters
• Local causal states and discrete coherent structures (2018) — Adam Rupe, James P. Crutchfield — Chaos: An Interdisciplinary Journal of Nonlinear Science
  Abstract

  Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis’ main tool employs the local causal states, which are used to uncover a system’s hidden spatiotemporal symmetries and which identify coherent structures as spatially localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.
• Convexity of the entropy of positive solutions to the heat equation on quaternionic contact and CR manifolds (2017) — Dimiter Vassilev — Pacific Journal of Mathematics
• Do Fluids Modify the Stick-Slip Behavior of Sheared Granular Media? (2017) — Omid Dorostkar et al. — Sixth Biot Conference on Poromechanics
• Dynamic induced softening in frictional granular materials investigated by discrete-element-method simulation (2017) — Laure Lemrich et al. — Physical Review E
• Linear and nonlinear elastic properties of dense granular packings: a DEM exploration (2017) — Laure Lemrich et al. — EPJ Web of Conferences
• Nonlinear acoustics evaluation of CO2 exposed sandstone (2017) — James Bittner et al. — The Journal of the Acoustical Society of America
  Abstract

  In an effort to better understand the hygro-thermo-mechanical behavior of geologic CO2 reservoir material, we investigate the non-linear behavior of elastic wave propagation in Berea sandstone samples, which are used as a standard for reservoir rock formations. Nonlinear characterization methods, including resonant ultrasound spectroscopy (RUS), dynamic acousto-elasticity (DAET), and single-impact nonlinear resonance techniques, are applied to pristine, damaged (distributed microfractures), and CO2 injected Berea samples; conventional linear vibrational and wave propagation measurements are also applied to the samples. The results of these sensitive test methods are compared to reveal the characteristics of geologic reservoir materials that are most affected by varying microstructural and environmental conditions. An analysis of the work also leads to potential bases for test methods that could be deployed in the field in the future to monitor the condition of reservoir formations and lead to better understanding of CO2 injection-induced seismic events. This work is done within the framework of the GSCO2 center for geologic storage of CO2 from the U.S. department of Energy whose purpose is to better understand CO2 sequestration to make it safer and more efficient. As such the results obtained by elastic waves measurement will also be compared to other testing, providing an insight on the physical origin of the nonlinear behavior of geomaterials.
• Nonlinear softening of unconsolidated granular earth materials (2017) — Charles Lieou et al. — The Journal of the Acoustical Society of America
  Abstract

  Unconsolidated granular earth materials exhibit softening behavior due to external perturbations such as seismic waves, namely, the wave speed and elastic modulus decrease upon increasing the strain amplitude. In this letter, we describe a theoretical model for such behavior. The model is based on the idea that shear transformation zones (STZs)—clusters of grains that are loose and susceptible to contact changes and rearrangement—are responsible for plastic deformation and softening of the material. We apply the theory to experiments on simulated fault gouge composed of glass beads, and demonstrate that the theory predicts nonlinear resonance shifts and reduction of the P-wave modulus, in agreement with experiments. The theory thus offers insights on the nature of the critical state prior to failure on earthquake faults.
• On the micromechanics of slip events in sheared, fluid‐saturated fault gouge (2017) — Omid Dorostkar et al. — Geophysical Research Letters
  Abstract

  Abstract We used a three‐dimensional discrete element method coupled with computational fluid dynamics to study the poromechanical properties of dry and fluid‐saturated granular fault gouge. The granular layer was sheared under dry conditions to establish a steady state condition of stick‐slip dynamic failure, and then fluid was introduced to study its effect on subsequent failure events. The fluid‐saturated case showed increased stick‐slip recurrence time and larger slip events compared to the dry case. Particle motion induces fluid flow with local pressure variation, which in turn leads to high particle kinetic energy during slip due to increased drag forces from fluid on particles. The presence of fluid during the stick phase of loading promotes a more stable configuration evidenced by higher particle coordination number. Our coupled fluid‐particle simulations provide grain‐scale information that improves understanding of slip instabilities and illuminates details of phenomenological, macroscale observations.
• Slow Dynamics and Strength Recovery in Unconsolidated Granular Earth Materials: A Mechanistic Theory (2017) — Charles K. C. Lieou et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Abstract Rock materials often display long‐time relaxation, commonly termed aging or “slow dynamics,” after the cessation of acoustic perturbations. In this paper, we focus on unconsolidated rock materials and propose to explain such nonlinear relaxation through the shear‐transformation‐zone theory of granular media, adapted for small stresses and strains. The theory attributes the observed relaxation to the slow, irreversible change of positions of constituent grains and posits that the aging process can be described in three stages: fast recovery before some characteristic time associated with the subset of local plastic events or grain rearrangements with a short time scale, log linear recovery of the elastic modulus at intermediate times, and gradual turnover to equilibrium steady state behavior at long times. We demonstrate good agreement with experiments on aging in granular materials such as simulated fault gouge after an external disturbance. These results may provide insights into observed modulus recovery after strong shaking in the near surface region of earthquake zones.
• Slow dynamics of consolidated granular systems: Multi-scale relaxation (2017) — Parisa Shokouhi et al. — Applied Physics Letters
  Abstract

  Dynamic acousto-elastic testing, a pump-probe scheme, is employed to investigate the recovery of consolidated granular media systems from the non-equilibrium steady state established by a pump strain field. This measurement scheme makes it possible to follow the recovery from the non-equilibrium steady state over many orders of magnitude in time. The recovery is described with a relaxation time spectrum that is found to be independent of the amplitude of the non-equilibrium steady state (pump amplitude) and of the environment in which samples reside. The non-equilibrium steady state and its slow recovery are the laboratory realization of phenomena that are found in many physical systems of practical importance.
• The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven (2017) — Stefan Ivanov, Alexander Petkov, Dimiter Vassilev — Journal of Spectral Theory
  Abstract

  On a compact quaternionic contact (qc) manifold of dimension bigger than seven and satisfying a Lichnerowicz type lower bound estimate we show that if the rst positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard 3-Sasakian sphere. The same conclusion is shown to hold on a non-compact qc manifold which is complete with respect to the associated Riemannian metric assuming the existence of a function with traceless horizontal Hessian.
• Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault (2017) — Andrew A. Delorey, Nicholas J. van der Elst, Paul A. Johnson — Earth and Planetary Science Letters
• Constraining depth range of <i>S</i> wave velocity decrease after large earthquakes near Parkfield, California (2016) — Chunquan Wu et al. — Geophysical Research Letters
  Abstract

  Abstract We use noise correlation and surface wave inversion to measure the S wave velocity changes at different depths near Parkfield, California, after the 2003 San Simeon and 2004 Parkfield earthquakes. We process continuous seismic recordings from 13 stations to obtain the noise cross‐correlation functions and measure the Rayleigh wave phase velocity changes over six frequency bands. We then invert the Rayleigh wave phase velocity changes using a series of sensitivity kernels to obtain the S wave velocity changes at different depths. Our results indicate that the S wave velocity decreases caused by the San Simeon earthquake are relatively small (~0.02%) and access depths of at least 2.3 km. The S wave velocity decreases caused by the Parkfield earthquake are larger (~0.2%), and access depths of at least 1.2 km. Our observations can be best explained by material damage and healing resulting mainly from the dynamic stress perturbations of the two large earthquakes.
• Dynamically triggered slip leading to sustained fault gouge weakening under laboratory shear conditions (2016) — P. A. Johnson et al. — Geophysical Research Letters
  Abstract

  Abstract We investigate dynamic wave‐triggered slip under laboratory shear conditions. The experiment is composed of a three‐block system containing two gouge layers composed of glass beads and held in place by a fixed load in a biaxial configuration. When the system is sheared under steady state conditions at a normal load of 4 MPa, we find that shear failure may be instantaneously triggered by a dynamic wave, corresponding to material weakening and softening if the system is in a critical shear stress state (near failure). Following triggering, the gouge material remains in a perturbed state over multiple slip cycles as evidenced by the recovery of the material strength, shear modulus, and slip recurrence time. This work suggests that faults must be critically stressed to trigger under dynamic conditions and that the recovery process following a dynamically triggered event differs from the recovery following a spontaneous event.
• Fast and slow nonlinear elastic response of disparate rocks and the influence of moisture (2016) — Jacques Riviere et al. — Journal of the Acoustical Society of America
  Abstract

  We study nonlinear elastic phenomena in rocks at the laboratory scale, with the goal of characterizing and understanding observations at crustal scales, for instance, during strong ground motion and earthquake slip processes. A dynamic perturbation of microstrain amplitude in rocks results in a transient elastic softening followed by a log(t)-type relaxation back to the initial unperturbed elastic modulus as soon as the excitation is removed. Here we use Dynamic Acousto-Elastic Testing (DAET) to investigate the relaxation behavior over 7 orders of magnitude in time (from 10-4s to more than 103s). We find that relaxation starts for all samples between 10-3 and 10-2s. Some samples then exhibit a nearly perfect log(t)-relaxation, implying that no characteristic time can be extracted, while some other samples show a preferential relaxation around 0.1s/1s. Such features appear insensitive to the amplitude of the dynamic perturbation and to the moisture content within the sample. The full nonlinear elastic response (fast dynamics) is also extracted at all amplitudes and moisture content. Adsorption of water on the grains strongly increases the elastic softening during the dynamic perturbation and the non-classical nonlinear features, whereas the classical features seem rather unaffected.
• Fortnightly modulation of San Andreas tremor and low-frequency earthquakes (2016) — Nicholas J. van der Elst et al. — Proceedings of the National Academy of Sciences
  Abstract

  Significance The sun and moon exert a gravitational tug on Earth that stretches and compresses crustal rocks. This cyclic stressing can promote or inhibit fault slip, particularly at the deep roots of faults. The amplitude of the solid Earth tide varies over a fortnightly (2-wk) cycle, as the sun and moon change their relative positions in the sky. In this study, we show that deep, small earthquakes on the San Andreas Fault are most likely to occur during the waxing fortnightly tide—not when the tidal amplitude is highest, as might be expected, but when the tidal amplitude most exceeds its previous value. The response of faults to the tidal cycle opens a window into the workings of plate tectonics.
• Island nucleation and growth with anomalous diffusion (2016) — Jacques G. Amar, Mikhael Semaan — Physical Review E
• Nonlinear dynamics induced in a structure by seismic and environmental loading (2016) — Philippe Guéguen, Paul Johnson, Philippe Roux — The Journal of the Acoustical Society of America
  Abstract

  In this study, it is shown that under very weak dynamic and quasi-static deformation that is orders of magnitude below the yield deformation of the equivalent stress−strain curve (around 10−3), the elastic parameters of a civil engineering structure (resonance frequency and damping) exhibit nonlinear softening and recovery. These observations bridge the gap between laboratory and seismic scales where elastic nonlinear behavior has been previously observed. Under weak seismic or atmospheric loading, modal frequencies are modified by around 1% and damping by more than 100% for strain levels between 10−7 and 10−4. These observations support the concept of universal behavior of nonlinear elastic behavior in diverse systems, including granular materials and damaged solids that scale from millimeter dimensions to the scale of structures to fault dimensions in the Earth.
• A set of measures for the systematic classification of the nonlinear elastic behavior of disparate rocks (2015) — Jacques Rivière et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Abstract Dynamic acoustoelastic testing is performed on a set of six rock samples (four sandstones, one soapstone, and one granite). From these studies at 20 strain levels 10 −7 &lt; ϵ &lt;10 −5 , four measures characterizing the nonlinear elastic response of each sample are found. Additionally, each sample is tested with nonlinear resonant ultrasonic spectroscopy and a fifth measure of nonlinear elastic response is found. These five measures of the nonlinear elastic response of the samples (approximately 3 × 6×20 × 5 numbers as each measurement is repeated 3 times) are subjected to careful analysis using model‐independent statistical methods, principal component analysis, and fuzzy clustering. This analysis reveals differences among the samples and differences among the nonlinear measures. Four of the nonlinear measures are sensing much the same physical mechanism in the samples. The fifth is seeing something different. This is the case for all samples. Although the same physical mechanisms (two) are operating in all samples, there are distinctive features in the way the physical mechanisms present themselves from sample to sample. This suggests classification of the samples into two groups. The numbers in this study and the classification of the measures/samples constitute an empirical characterization of rock nonlinear elastic properties that can serve as a valuable testing ground for physically based theories that relate rock nonlinear elastic properties to microscopic elastic features.
• Acoustically induced slip in sheared granular layers: Application to dynamic earthquake triggering (2015) — Behrooz Ferdowsi et al. — Geophysical Research Letters
  Abstract

  Abstract A fundamental mystery in earthquake physics is “how can an earthquake be triggered by distant seismic sources?” Here we use discrete element method simulations of a granular layer, during stick slip, that is subject to transient vibrational excitation to gain further insight into the physics of dynamic earthquake triggering. Using Coulomb friction law for grains interaction, we observe delayed triggering of slip in the granular gouge. We find that at a critical vibrational amplitude (strain) there is an abrupt transition from negligible time‐advanced slip (clock advance) to full clock advance; i.e., transient vibration and triggered slip are simultaneous. The critical strain is of order 10 −6 , similar to observations in the laboratory and in Earth. The transition is related to frictional weakening of the granular layer due to a dramatic decrease in coordination number and the weakening of the contact force network. Associated with this frictional weakening is a pronounced decrease in the elastic modulus of the layer. The study has important implications for mechanisms of triggered earthquakes and induced seismic events and points out the underlying processes in response of the fault gouge to dynamic transient stresses.
• Cascading elastic perturbation in Japan due to the 2012 <i>M</i> _w 8.6 Indian Ocean earthquake (2015) — Andrew A. Delorey et al. — Science Advances
  Abstract

  Seismic waves from the 2012 M w 8.6 Indian Ocean earthquake trigger changes in elastic properties and the stress field in Japan.
• Mimicking surface plasmons in acoustics at low frequency (2015) — Li Quan et al. — Physical Review B
• Poromechanics of stick‐slip frictional sliding and strength recovery on tectonic faults (2015) — Marco M. Scuderi et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Abstract Pore fluids influence many aspects of tectonic faulting including frictional strength aseismic creep and effective stress during the seismic cycle. However, the role of pore fluid pressure during earthquake nucleation and dynamic rupture remains poorly understood. Here we report on the evolution of pore fluid pressure and porosity during laboratory stick‐slip events as an analog for the seismic cycle. We sheared layers of simulated fault gouge consisting of glass beads in a double‐direct shear configuration under true triaxial stresses using drained and undrained fluid conditions and effective normal stress of 5–10 MPa. Shear stress was applied via a constant displacement rate, which we varied in velocity step tests from 0.1 to 30 µm/s. We observe net pore pressure increases, or compaction, during dynamic failure and pore pressure decreases, or dilation, during the interseismic period, depending on fluid boundary conditions. In some cases, a brief period of dilation is attendant with the onset of dynamic stick slip. Our data show that time‐dependent strengthening and dynamic stress drop increase with effective normal stress and vary with fluid conditions. For undrained conditions, dilation and preseismic slip are directly related to pore fluid depressurization; they increase with effective normal stress and recurrence time. Microstructural observations confirm the role of water‐activated contact growth and shear‐driven elastoplastic processes at grain junctions. Our results indicate that physicochemical processes acting at grain junctions together with fluid pressure changes dictate stick‐slip stress drop and interseismic creep rates and thus play a key role in earthquake nucleation and rupture propagation.
• Quaternionic Heisenberg Group and Heterotic String Solutions with Non-Constant Dilaton in Dimensions 7 and 5 (2015) — Marisa Fernández et al. — Communications in Mathematical Physics
• Statistical tests on clustered global earthquake synthetic data sets (2015) — Eric G. Daub, Daniel T. Trugman, Paul A. Johnson — Journal of Geophysical Research: Solid Earth
  Abstract

  Abstract We study the ability of statistical tests to identify nonrandom features of earthquake catalogs, with a focus on the global earthquake record since 1900. We construct four types of synthetic data sets containing varying strengths of clustering, with each data set containing on average 10,000 events over 100 years with magnitudes above M = 6. We apply a suite of statistical tests to each synthetic realization in order to evaluate the ability of each test to identify the sequences of events as nonrandom. Our results show that detection ability is dependent on the quantity of data, the nature of the type of clustering, and the specific signal used in the statistical test. Data sets that exhibit a stronger variation in the seismicity rate are generally easier to identify as nonrandom for a given background rate. We also show that we can address this problem in a Bayesian framework, with the clustered data sets as prior distributions. Using this new Bayesian approach, we can place quantitative bounds on the range of possible clustering strengths that are consistent with the global earthquake data. At M = 7, we can estimate 99th percentile confidence bounds on the number of triggered events, with an upper bound of 20% of the catalog for global aftershock sequences, with a stronger upper bound on the fraction of triggered events of 10% for long‐term event clusters. At M = 8, the bounds are less strict due to the reduced number of events. However, our analysis shows that other types of clustering could be present in the data that we are unable to detect. Our results aid in the interpretation of the results of statistical tests on earthquake catalogs, both worldwide and regionally.
• Synchronous low frequency earthquakes and implications for deep San Andreas Fault slip (2015) — Daniel T. Trugman et al. — Earth and Planetary Science Letters
• The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds (2015) — Stefan Ivanov, Dimiter Vassilev — Nonlinear Analysis
• Acceleration of acoustical emission precursors preceding failure in sheared granular material (2014) — Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Earthquake precursor observations are becoming progressively more widespread as instrumentation improves, in particular, for interplate earthquakes (e.g., Bouchon et al., Nature Geosci., 2013). One question regarding precursor behavior is whether or not they are due to a triggering cascade where one precursor triggers the next, or if they are independent events resulting from slow slip. We investigate this topic in order to characterize the physics of precursors, by applying laboratory experiments of sheared granular media in a bi-axial configuration. We sheared layers of glass beads under applied normal loads of 2–8 MPa, shearing rates of 5–10 μm/s at room temperature and humidity. We show that above ~3 MPa load, precursors are manifest by an exponential increase in time of the acoustic emission (AE), with an additional acceleration of event rate leading to the primary stick-slip failure event. The recorded AE are clearly correlated with small drops in shear stress during slow slip prior to the main stick-slip failure. Event precursors take place where the material is still modestly dilating, yet while the macroscopic frictional strength is no longer increasing. The precursors are of order 100× smaller in recorded strain amplitude than the stick-slip events. We are currently working on statistical methods to determine whether or not the precursors are triggered cascades. [Bouchon et al., Nature Geosci. 6, 299–302 (2013).]
• Effect of boundary vibration on the frictional behavior of a dense sheared granular layer (2014) — B. Ferdowsi et al. — Acta Mechanica
• Effective impedance boundary optimization and its contribution to dipole radiation and radiation pattern control (2014) — Li Quan et al. — Nature Communications
• Modern Application of Time-Reversal to Seismic Source characterization (2014) — Carene Larmat et al. — Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2014
• Non-Kaehler heterotic string solutions with non-zero fluxes and non-constant dilaton (2014) — Marisa Fernández et al. — Journal of High Energy Physics
• Optimized Dynamic Acousto-elasticity Applied to Fatigue Damage and Stress Corrosion Cracking (2014) — Sylvain Haupert et al. — Journal of Nondestructive Evaluation
• Three-dimensional discrete element modeling of triggered slip in sheared granular media (2014) — Behrooz Ferdowsi et al. — Physical Review E
• Triggering of repeating earthquakes in central California (2014) — Chunquan Wu et al. — Geophysical Research Letters
  Abstract

  Abstract Dynamic stresses carried by transient seismic waves have been found capable of triggering earthquakes instantly in various tectonic settings. Delayed triggering may be even more common, but the mechanisms are not well understood. Catalogs of repeating earthquakes, earthquakes that recur repeatedly at the same location, provide ideal data sets to test the effects of transient dynamic perturbations on the timing of earthquake occurrence. Here we employ a catalog of 165 families containing ~2500 total repeating earthquakes to test whether dynamic perturbations from local, regional, and teleseismic earthquakes change recurrence intervals. The distance to the earthquake generating the perturbing waves is a proxy for the relative potential contributions of static and dynamic deformations, because static deformations decay more rapidly with distance. Clear changes followed the nearby 2004 M w 6 Parkfield earthquake, so we study only repeaters prior to its origin time. We apply a Monte Carlo approach to compare the observed number of shortened recurrence intervals following dynamic perturbations with the distribution of this number estimated for randomized perturbation times. We examine the comparison for a series of dynamic stress peak amplitude and distance thresholds. The results suggest a weak correlation between dynamic perturbations in excess of ~20 kPa and shortened recurrence intervals, for both nearby and remote perturbations.
• Acoustic emission and microslip precursors to stick‐slip failure in sheared granular material (2013) — P. A. Johnson et al. — Geophysical Research Letters
  Abstract

  Abstract We investigate the physics of laboratory earthquake precursors in a biaxial shear configuration. We conduct laboratory experiments at room temperature and humidity in which we shear layers of glass beads under applied normal loads of 2–8 MPa and with shearing rates of 5–10 µm/s. We show that above ~ 3 MPa load, acoustic emission (AE), and shear microfailure (microslip) precursors exhibit an exponential increase in rate of occurrence, culminating in stick‐slip failure. Precursors take place where the material is in a critical state—still modestly dilating, yet while the macroscopic frictional strength is no longer increasing.
• Applying an old appealing idea to modern seismology: Time reversal to characterize earthquakes (2013) — Carene Larmat et al. — The Journal of the Acoustical Society of America
  Abstract

  Wave physics is one domain where reversing time is possible and has led to interesting applications. In acoustics, Parvulescu and Clay (1965) used what they termed a “matched signal technique” to beat multi-reverberation in the shallow sea. In seismology, McMechan (1982) demonstrated the feasibility of what he termed “wavefield extrapolation” to locate seismic sources. Since then, other concepts and applications, all related to time-reversal, have often been proved to be successful where other techniques have failed. This success is due to the inherent ability of time-reversal to function well in complex propagation media as well as the remarkable robustness of the method with sparse receiver coverage. The key aspect of time-reversal for future applications in seismology is that it relies on no a priori assumption about the source. This allows automatic location of earthquakes and the study of seismic events for which the assumption of point source breaks down. This is the case of big earthquakes (Mw &amp;gt;8) for which the rupture length and source duration extend to hundreds of kilometers and several tens of seconds. We will show an application to the 2011 Japan earthquake, to icequakes related to glaciers motions in Greenland and to seismic tremor with no clear onset.
• Dynamic acousto-elasticity in Berea sandstone: Influence of the strain rate (2013) — Jacques Riviere et al. — The Journal of the Acoustical Society of America
  Abstract

  In comparison with standard nonlinear ultrasonic methods such as frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. To improve our understanding of these phenomena, this work aims at comparing static and dynamic acousto-elasticity to evaluate the influence of strain rate. To this purpose, we perform acousto-elasticity on a sample of Berea sandstone and a glass beads pack, oscillating them from 0.001 to 10 Hz. These results are then compared to DAE measurements made in the kHz range. We observe that the average decrease in modulus increases with frequency, meaning that conditioning effects are higher at high strain rate, when relaxation characteristic time is higher than the oscillation period. This result, together with previous quasi-static measurements (Claytor et al., GRL 2009) showing that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate, confirms that a rate dependent nonlinear elastic model has to considered for a more complete description (Gusev et al., PRB 2004).
• Microslips as precursors of large slip events in the stick‐slip dynamics of sheared granular layers: A discrete element model analysis (2013) — B. Ferdowsi et al. — Geophysical Research Letters
  Abstract

  We investigate the stick‐slip behavior of a granular system confined and sheared by deformable solid blocks using three‐dimensional discrete element method simulations. Our modeling results show that large slip events are preceded by a sequence of small slip events—microslips—whose occurrence accelerates exponentially before the large slip event onset. Microslips exhibit energy release several orders of magnitude smaller than the large slip events. The microslip event rate is proposed as a measure of slip activity in the granular gouge layer. A statistical analysis shows that microslip event rate correlates well with large slip event onset and that variations in it can be used to predict large slip events. The emergence of microslips and their duration are found to be controlled by the value of the slipping contact ratio and are therefore related to the jamming/unjamming transition of frictional granular packings.
• Modeling dynamic triggering of tectonic tremor using a brittle‐ductile friction model (2013) — Daniel T. Trugman et al. — Geophysical Research Letters
  Abstract

  Abstract We study the physics of dynamically triggered tectonic tremor by applying a brittle‐ductile friction model in which we conceptualize the tremor source as a rigid block subject to driving and frictional forces. To simulate dynamic triggering of tremor, we apply a stress perturbation that mimics the surface waves of remote earthquakes. The tectonic and wave perturbation stresses define a phase space that demonstrates that both the timing and amplitude of the dynamic perturbations control the fundamental characteristics of triggered tremor. Tremor can be triggered instantaneously or with a delayed onset if the dynamic perturbation significantly alters the frictional state of the tremor source.
• Pump and probe waves in dynamic acousto-elasticity: Comprehensive description and comparison with nonlinear elastic theories (2013) — J. Rivière et al. — Journal of Applied Physics
  Abstract

  Standard nonlinear ultrasonic methods such as wave frequency mixing or resonance based measurements allow one to extract average, bulk variations of modulus and attenuation versus strain level. In contrast, dynamic acousto-elasticity (DAE) provides the elastic behavior over the entire dynamic cycle including hysteresis and memory effects, detailing the full nonlinear behavior under tension and compression. In this work, we address experimental difficulties and apply new processing methods, illustrating them with a Berea sandstone sample. A projection procedure is used to analyze the complex nonlinear signatures and extract the harmonic content. Amplitude dependences of the harmonic content are compared with existing models. We show that a combination of classical and hysteretic nonlinear models capture most of the observed phenomena. Some differences between existing models and experimental data are highlighted, however. A progressive decrease of the power-law amplitude dependence is found for harmonics larger than the second and for strains larger than 10−6. This observation is related to the phenomenon of acoustic conditioning that brings the material to a metastable state for each new excitation amplitude. Analysis of the steady-state regime provides additional information regarding acoustic conditioning, i.e., a progressive decrease of the amplitude of odd harmonics during excitation time with a log(t)-dependence. This observation confirms that the harmonic content is affected by the conditioning. Experimental challenges addressed include the fact that the compressional mode used for DAE can be affected by bending/torsion modes: their influence is evaluated, and guidances are given to minimize effects.
• Recurrence statistics of great earthquakes (2013) — E. Ben‐Naim, E. G. Daub, P. A. Johnson — Geophysical Research Letters
  Abstract

  Abstract We investigate the sequence of great earthquakes over the past century. To examine whether the earthquake record includes temporal clustering, we identify aftershocks and remove those from the record. We focus on the recurrence time, defined as the time between two consecutive earthquakes. We study the variance in the recurrence time and the maximal recurrence time. Using these quantities, we compare the earthquake record with sequences of random events, generated by numerical simulations, while systematically varying the minimal earthquake magnitude M min . Our analysis shows that the earthquake record is consistent with a random process for magnitude thresholds 7.0≤ M min ≤8.3, where the number of events is larger. Interestingly, the earthquake record deviates from a random process at magnitude threshold 8.4≤ M min ≤8.5, where the number of events is smaller; however, this deviation is not strong enough to conclude that great earthquakes are clustered. Overall, the findings are robust both qualitatively and quantitatively as statistics of extreme values and moment analysis yield remarkably similar results.
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven (2013) — S. Ivanov, A. Petkov, D. Vassilev — Nonlinear Analysis: Theory, Methods &amp; Applications
• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion (2012) — Stefan Ivanov, Dimiter Vassilev — Journal of Geometry
• Application of nonlinear elastic resonance spectroscopy for damage detection in concrete (2012) — Loren W. Byers, Paul A. Johnson, James A. Tencate — XVII International Conference on Nonlinear Elasticity in Materials
• Are megaquakes clustered? (2012) — Eric G. Daub et al. — Geophysical Research Letters
  Abstract

  We study statistical properties of the number of large earthquakes over the past century. We analyze the cumulative distribution of the number of earthquakes with magnitude larger than threshold M in time interval T , and quantify the statistical significance of these results by simulating a large number of synthetic random catalogs. We find that in general, the earthquake record cannot be distinguished from a process that is random in time. This conclusion holds whether aftershocks are removed or not, except at magnitudes below M = 7.3. At long time intervals ( T = 2–5 years), we find that statistically significant clustering is present in the catalog for lower magnitude thresholds ( M = 7–7.2). However, this clustering is due to a large number of earthquakes on record in the early part of the 20th century, when magnitudes are less certain.
• Auto‐acoustic compaction in steady shear flows: Experimental evidence for suppression of shear dilatancy by internal acoustic vibration (2012) — Nicholas J. van der Elst et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Granular shear flows are intrinsic to many geophysical processes, ranging from landslides and debris flows to earthquake rupture on gouge‐filled faults. The rheology of a granular flow depends strongly on the boundary conditions and shear rate. Earthquake rupture involves a transition from quasi‐static to rapid shear rates. Understanding the processes controlling the transitional rheology is potentially crucial for understanding the rupture process and the coseismic strength of faults. Here we explore the transition experimentally using a commercial torsional rheometer. We measure the thickness of a steady shear flow at velocities between 10 −3 and 10 2 cm/s, at very low normal stress (7 kPa), and observe that thickness is reduced at intermediate velocities (0.1–10 cm/s) for angular particles, but not for smooth glass beads. The maximum reduction in thickness is on the order of 10% of the active shear zone thickness, and scales with the amplitude of shear‐generated acoustic vibration. By examining the response to externally applied vibration, we show that the thinning reflects a feedback between internally generated acoustic vibration and granular rheology. We link this phenomenon to acoustic compaction of a dilated granular medium, and formulate an empirical model for the steady state thickness of a shear‐zone in which shear‐induced dilatation is balanced by a newly identified mechanism we call auto‐acoustic compaction. This mechanism is activated when the acoustic pressure is on the order of the confining pressure, and results in a velocity‐weakening granular flow regime at shear rates four orders of magnitude below those previously associated with the transition out of quasi‐static granular flow. Although the micromechanics of granular deformation may change with greater normal stress, auto‐acoustic compaction should influence the rheology of angular fault gouge at higher stresses, as long as the gouge has nonzero porosity during shear.
• Elastic Linear and Nonlinear Behaviors in Slip Processes (2012) — Paul A. Johnson — XVII International Conference on Nonlinear Elasticity in Materials
• Meso-mechanical analysis of deformation characteristics for dynamically triggered slip in a granular medium (2012) — M. Griffa et al. — Philosophical Magazine
• Nonlinear acoustic/seismic waves in earthquake processes (2012) — Paul A. Johnson — NONLINEAR ACOUSTICS STATE-OF-THE-ART AND PERSPECTIVES: 19th International Symposium on Nonlinear Acoustics
• Nonlinear dynamical triggering of slow slip on simulated earthquake faults with implications to Earth (2012) — P. A. Johnson et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Among the most fascinating, recent discoveries in seismology are the phenomena of dynamically triggered fault slip, including earthquakes, tremor, slow and silent slip—during which little seismic energy is radiated—and low frequency earthquakes. Dynamic triggering refers to the initiation of fault slip by a transient deformation perturbation, most often in the form of passing seismic waves. Determining the frictional constitutive laws and the physical mechanism(s) governing triggered faulting is extremely challenging because slip nucleation depths for tectonic faults cannot be probed directly. Of the spectrum of slip behaviors, triggered slow slip is particularly difficult to characterize due to the absence of significant seismic radiation, implying mechanical conditions different from triggered earthquakes. Slow slip is often accompanied by nonvolcanic tremor in close spatial and temporal proximity. The causal relationship between them has implications for the properties and physics governing the fault slip behavior. We are characterizing the physical controls of triggered slow slip via laboratory experiments using sheared granular media to simulate fault gouge. Granular rock and glass beads are sheared under constant normal stress, while subjected to transient stress perturbation by acoustic waves. Here we describe experiments with glass beads, showing that slow and silent slip can be dynamically triggered on laboratory faults by ultrasonic waves. The laboratory triggering may take place during stable sliding (constant friction and slip velocity) and/or early in the slip cycle, during unstable sliding (stick‐slip). Experimental evidence indicates that the nonlinear‐dynamical response of the gouge material is responsible for the triggered slow slip.
• Nonlinear ultrasound: Potential of the cross-correlation method for osseointegration monitoring (2012) — Jacques Rivière et al. — The Journal of the Acoustical Society of America
  Abstract

  Recently the concept of probing nonlinear elasticity at an interface prosthesis/bone has been proposed as a promising method to monitor the osseointegration/sealing of a prosthesis. However, the most suitable method to achieve this goal is a point of debate. To this purpose, two approaches termed the scaling subtraction method and the cross-correlation method are compared here. One nonlinear parameter derived from the cross-correlation method is as sensitive as a clinical device based on linear elasticity measurement. Further, this study shows that cross-correlation based methods are more sensitive than those based on subtraction/addition, such like pulse inversion and similar methods.
• Potential of the scaling subtraction and the cross-correlation methods for osseointegration monitoring (2012) — Jacques Riviere et al. — XVII International Conference on Nonlinear Elasticity in Materials
• Revealing highly complex elastic nonlinear (anelastic) behavior of Earth materials applying a new probe: Dynamic acoustoelastic testing (2012) — G. Renaud, P.‐Y. Le Bas, P. A. Johnson — Journal of Geophysical Research: Solid Earth
  Abstract

  Recent work in medical nonlinear acoustics has led to the development of refined experimental method to measure material elastic nonlinear (anelastic) response. The technique, termed dynamic acoustoelastic testing, has significant implications for the development of a physics‐based theory because it provides information that existing methods cannot. It provides the means to dynamically study the velocity‐strain and attenuation‐strain relations through the full wave cycle in contrast to most methods that measure average response. The method relies on vibrating a sample at low frequency in order to cycle it through different levels of stress‐strain. Simultaneously, an ultrasonic source applies pulses and the change in wave speed and attenuation as a function of the low frequency strain is measured. We report preliminary results in eleven room‐dry rock samples. In crystalline rock, we expect that the elastic nonlinearity arises from the microcracks and dislocations contained within individual crystals. In contrast, sedimentary rocks may have other origins of elastic nonlinearity, currently under debate. A large quadratic elastic nonlinearity is observed in Berkeley blue granite, presumably due to microcracks and dislocation‐point defect interactions. In sedimentary rocks that include limestones and sandstones we observe behaviors that can differ markedly from the granite, potentially indicating different mechanical mechanisms. We further observe changes in measured nonlinear coefficients that are wave‐strain amplitude dependent. Ultimately we hope that the new approach will provide the means to quantitatively relate material nonlinear elastic behavior to the responsible features, that include soft bonds dislocations, microcracks, and the modulating influences of water content, temperature and pressure.
• The optimal constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group (2012) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
• Time reversed elastic nonlinearity diagnostic applied to mock osseointegration monitoring applying two experimental models (2012) — Jacques Rivière et al. — The Journal of the Acoustical Society of America
  Abstract

  This study broadens vibration-like techniques developed for osseointegration monitoring to the nonlinear field. The time reversed elastic nonlinearity diagnostic is applied to two mock models. The first one consists of tightening a dental implant at different torques in a mock cortical bone; the second one allows one to follow glue curing at the interface between a dental implant and a mock jaw. Energy is focused near the implant interface using the time reversal technique. Two nonlinear procedures termed pulse inversion and the scaling subtraction method, already used successfully in other fields such as contrast agents and material characterization, are employed. These two procedures are compared for both models. The results suggest that nonlinear elasticity can provide new information regarding the interface, complementary to the linear wave velocity and attenuation. The curing experiment exhibits an overall low nonlinear level due to the fact that the glue significantly damps elastic nonlinearity at the interface. In contrast, the torque experiment shows strong nonlinearities at the focus time. Consequently, a parallel analysis of these models, both only partially reflecting a real case, enables one to envisage future in vivo experiments.
• $L^{p}$ estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities (2011) — Dimiter Vassilev — Transactions of the American Mathematical Society
• An alternative quantitative acoustical and electrical method for detection of cell adhesion process in real‐time (2011) — Delphine Le Guillou‐Buffello et al. — Biotechnology and Bioengineering
  Abstract

  Abstract Sauerbrey [(1956), Z Phys 55:206–222] showed that the shift in resonance frequency of thickness shear mode (TSM) of a quartz crystal sensor is proportional to the mass, which is deposited on it. However, new powerful electrical circuits were developed that are capable of operating TSM quartz crystal sensors in fluids which enabled this method to be introduced into electrochemical and biological applications. These applications include the detection of virus capsids, bacteria, mammalian cells, the interaction of DNA and RNA with complementary strands, specific recognition of protein ligands by immobilized receptors, and last but not least the study of complete immunosensors. Piezoelectric quartz transducers allow a label‐free identification of molecules; they are more than mass sensors since the biosensor response is also influenced by the surface charge of adsorbed proteins, interfacial phenomena, surface roughness and viscoelastic properties of the adhered biomaterial. These new characteristics have recently been used to investigate cell, liposome, and protein adhesion onto surfaces, thus permitting the rapid determination of morphological cell changes as a response to pharmacological substances, and changes in the water content of biopolymers avoiding of time‐consuming methods. We validated an alternative quantitative acoustical engineering for cell adhesion process monitored by the TSM. Shear acoustical results (motional resistance) are further correlated to cell counting procedures and are sensitive of adhesion processes in real‐time. Biotechnol. Bioeng. 2011; 108:947–962. © 2010 Wiley Periodicals, Inc.
• Brittle and ductile friction and the physics of tectonic tremor (2011) — Eric G. Daub et al. — Geophysical Research Letters
• Defining and Describing Human-Powered Products: Exploring Diverse Applications of Future Technology (2011) — Paul Johnson, Hyunjae Shin, Luke Harmer — Key Engineering Materials
  Abstract

  The research has monitored both real time and concepts of human-powered products (HPP) ranging from conscious user interaction and fun concepts, to parasitic harvesting concepts. These ‘products’ have been characterised and mapped onto an ‘Interaction Map’ which is defined and described by two intersecting dimensions: one is defined by a sub/conscious user interaction and the other is defined by the mechanism of the product. This paper presents the results of a case study conducted with first year product design undergraduate students at Nottingham Trent University in January 2011. Students were briefed to select an electronic product and (re)design it into an interactive ‘off the grid product’, where its functional power is not being supplied by neither the power grid nor any kind of technology driven power units such as photovoltaic power cells. The results produced a comparative analysis, mapping student project concepts against results from real time HPP monitoring of existing products. Many HPP concepts arose from this study, and the design approach highlighted potential applications of human-power systems, more specific form of engineering requirements, as well as insight into further potential future technological approaches for HPP.
• Experimental implementation of reverse time migration for nondestructive evaluation applications (2011) — Brian E. Anderson et al. — The Journal of the Acoustical Society of America
  Abstract

  Reverse time migration (RTM) is a commonly employed imaging technique in seismic applications (e.g., to image reservoirs of oil). Its standard implementation cannot account for multiple scattering/reverberation. For this reason it has not yet found application in nondestructive evaluation (NDE). This paper applies RTM imaging to NDE applications in bounded samples, where reverberation is always present. This paper presents a fully experimental implementation of RTM, whereas in seismic applications, only part of the procedure is done experimentally. A modified RTM imaging condition is able to localize scatterers and locations of disbonding. Experiments are conducted on aluminum samples with controlled scatterers.
• High-accuracy acoustic detection of nonclassical component of material nonlinearity (2011) — Sylvain Haupert et al. — The Journal of the Acoustical Society of America
  Abstract

  The aim is to assess the nonclassical component of material nonlinearity in several classes of materials with weak, intermediate, and high nonlinear properties. In this contribution, an optimized nonlinear resonant ultrasound spectroscopy (NRUS) measuring and data processing protocol applied to small samples is described. The protocol is used to overcome the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic nonlinearity. External temperature fluctuation is identified as a primary source of measurement contamination. For instance, a variation of 0.1 °C produced a frequency variation of 0.01%, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to overcome environmental effects, the reference frequency measurements are repeated before each excitation level and then used to compute nonlinear parameters. Using this approach, relative resonant frequency shifts of 10−5 can be measured, which is below the limit of 10−4 often considered as the limit of NRUS sensitivity under common experimental conditions. Due to enhanced sensitivity resulting from the correction procedure applied in this work, nonclassical nonlinearity in materials that before have been assumed to only be classically nonlinear in past work (steel, brass, and aluminum) is reported.
• Localization of a nonlinear source in the bulk of a solid. (2011) — Pierre-Yves Le Bas et al. — The Journal of the Acoustical Society of America
  Abstract

  Time reversal (TR) has the potential to become a powerful tool in non-destructive evaluation. Coupled with nonlinear properties of cracks in a group of techniques known as Time reverse nonlinear elastic wave spectroscopy, it provides the means to detect and image mechanical damage in complex solids. In this prototype experimental study, we show that we can excite a buried nonlinear feature applying TR. The feature scatters energy that is detected on the sample perimeter. The time signals are filtered about the nonlinear-generated components and are broadcast back, focusing on their source, the buried nonlinear feature. The current challenge is introducing sufficient energy in order to excite the buried feature and produce nonlinear scattering that can be detected on the edges of the sample. This was achieved using a 30 channel system. Two features were localized: a part of the interface between two blocks submitted to a high amplitude signal, and a defect on the same interface (a cured drop of glue creating hard contact between the two solids). Results are visualized using the energy flux quantity.
• Probing the interior of a solid volume with time reversal and nonlinear elastic wave spectroscopy (2011) — P. Y. Le Bas et al. — The Journal of the Acoustical Society of America
  Abstract

  A nonlinear scatterer is simulated in the body of a sample and demonstrates a technique to locate and define the elastic nature of the scatterer. Using the principle of time reversal, elastic wave energy is focused at the interface between blocks of optical grade glass and aluminum. Focusing of energy at the interface creates nonlinear wave scattering that can be detected on the sample perimeter with time-reversal mirror elements. The nonlinearly generated scattered signal is bandpass filtered about the nonlinearly generated components, time reversed and broadcast from the same mirror elements, and the signal is focused at the scattering location on the interface.
• Time reversal reconstruction of finite sized sources in elastic media (2011) — Brian E. Anderson et al. — The Journal of the Acoustical Society of America
  Abstract

  The ability of the time reversal process to reconstruct sources of finite size relative to a wavelength is investigated. Specifically the quality of the spatial reconstruction of a finite sized source will be presented through the use of time reversal experiments conducted on an aluminum plate. The data presented in the paper show that time reversal can reconstruct a source equally well regarding less of its size, when the source is a half wavelength or less in size. The quality of spatial reconstruction when the source is larger than a half wavelength progressively decreases with the size of the source.
• Time-reversal in seismology. (2011) — Carene Larmat, Paul Johnson, Robert Guyer — The Journal of the Acoustical Society of America
  Abstract

  This talk is a review of the use and history of time-reversal in seismology. time-reversal has been developed independently in the field of acoustics and in geophysics exploration, without the two communities being aware of the fact, as testifies the lack of the cross-references in early papers. The elegance of time-reversal is that it thrives with complexity. Seismologists have to deal with complex signal transmitted through the earth. Moreover, earthquakes are complex sources, involving different episodes of slip along the fault. Early in the development of time-reversal in seismology, emphasis has been put on the need of accurate numerical schemes to back-propagate the wavefield and the need of relatively dense data. In addition to presenting several of the landmark applications of time-reversal in seismology, several of our results will be outlined. In the last decade, our group has studied the potential of TR with the unique approach of combining laboratory experiments with application to seismology problems. Several applications will be presented: location and characterization of the rupture of the 2004 Parkfield earthquake, location, and retrieval of the sliding motion of glaciers in Greenland, finally imaging of the source location of a seismic signal of particularly emergent nature, the tremor.
• Vibration-induced slip in sheared granular layers and the micromechanics of dynamic earthquake triggering (2011) — M. Griffa et al. — EPL (Europhysics Letters)
• Advances in Modelling and Inversion of Seismic Wave Propagation (2010) — V. Hermann et al. — High Performance Computing in Science and Engineering, Garching/Munich 2009
• Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem (2010) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — Journal of the European Mathematical Society
  Abstract

  A complete solution to the quaternionic contact Yamabe problem on the seven dimensional sphere is given. Extremals for the Sobolev inequality on the seven dimensional Heisenberg group are explicitly described and the best constant in the L2 Folland–Stein embedding theorem is determined.
• Nonlinear acoustic resonances to probe a threaded interface (2010) — Jacques Rivière et al. — Journal of Applied Physics
  Abstract

  We evaluate the sensitivity of multimodal nonlinear resonance spectroscopy to torque changes in a threaded interface. Our system is comprised of a bolt progressively tightened in an aluminum plate. Different modes of the system are studied in the range 1–25 kHz, which correspond primarily to bending modes of the plate. Nonlinear parameters expressing the importance of resonance frequency and damping variations are extracted and compared to linear ones. The influence of each mode shape on the sensitivity of nonlinear parameters is discussed. Results suggest that a multimodal measurement is an appropriate and sensitive method for monitoring bolt tightening. Further, we show that the nonlinear components provide new information regarding the interface, which can be linked to different friction theories. This work has import to study of friction and to nondestructive evaluation of interfaces for widespread application and basic research.
• Optimized Wellbore Positioning Delivers Section 100% in the Pay Zone and Reduces Operational Time by 12 Days (2010) — P. Johnson, F. Hveding — Geosteering and Well Placement Workshop - Geosteering: Balancing Value and Risk
• Probing hysteretic elasticity in weakly nonlinear materials (2010) — Sylvain Haupert et al. — 2010 IEEE Ultrasonics Symposium (IUS)
• Quaternionic contact manifolds with a closed fundamental 4-form (2010) — Stefan Ivanov, Dimiter Vassilev — Bulletin of the London Mathematical Society
• Time-reversal methods in geophysics (2010) — Carène S. Larmat, Robert A. Guyer, Paul A. Johnson — Physics Today
  Abstract

  Classical earthquakes are easily located by triangulation. For more obscure seismic events, geophysicists are developing the trick of playing the movie backward.
• Using time-reversal to locate non-volcanic tremor and to fulfill the monitoring objectives of the nuclear-test ban treaty (2010) — Carene S. Larmat, Paul A. Johnson, Robert A. Guyer — XV International Conference on Nonlinear Elasticity in Materials
• Determination of third order elastic constants in a complex solid applying coda wave interferometry (2009) — C. Payan et al. — Applied Physics Letters
  Abstract

  In this letter we describe the development of coda wave interferometry to determine acoustoelastically derived third order nonlinear coefficients of a highly complex material, concrete. Concrete, a structurally heterogeneous and volumetrically mechanically damaged material, is an example of a class of materials that exhibit strong multiple scattering as well as significant elastic nonlinear response. We show that intense scattering can be applied to robustly determine velocity changes at progressively increasing applied stress using coda wave interferometry, and thereby extract nonlinear coefficients.
• Nonlinear Mesoscopic Elasticity (2009) — Robert A. Guyer, Paul A. Johnson — John Wiley Sons, 2009
• Robustness of computational time reversal imaging in media with elastic constant uncertainties (2009) — M. Scalerandi, M. Griffa, P. A. Johnson — Journal of Applied Physics
  Abstract

  In order to image a source or a scatterer embedded in a three dimensional solid, acoustic/elastic wave data from an actual experiment are time reversed and backpropagated through a numerical model of the medium. The model makes use of estimates for the elastic constants of the laboratory solid. These estimates may not be very precise, for example, due to experimental uncertainties. Poor characterization of the medium leads to the degradation of the time reversal focus, therefore, to poor medium imaging. In this work, we report on the results of investigating the time reversal focus degradation as the estimates depart from the real values. Very small deviations from the medium’s actual elastic constants degrade the time reversal focus dramatically. However, decreasing the total duration of the signals used for time reversal can attenuate the degradation in some cases. We propose a new method to compensate for the deviations of the model medium’s elastic constants from the actual values. Finally, we explore the effects of scatterers that may exist in the laboratory medium, but are not included in the model medium, and show that their presence does not produce significant effects on the time reversal focus.
• The parametric array in Berea sandstone: definitive experiments. (2009) — Pierre-Yves Le Bas et al. — The Journal of the Acoustical Society of America
  Abstract

  Previous measurements of the characteristics of the parametric array in sandstone by Johnson and Shankland [J. Geophys. Res. 94, 17729–17734 (1989)] were difficult to perform and only qualitative. Scanning laser vibrometers (Polytec) now make parametric array measurements in rock easier. However, hysteresis and memory effects play a strong role in the dynamic behavior of rocks and have the potential to mess up the creation of the parametric array in the medium. Thus, an experimental study was performed to find out just how well the “classical” theory of nonlinear acoustics works for a granular solid, a sandstone. An array of alternating PZT disk transducers was epoxied to a large block of Berea sandstone (1.2, 0.4, 0.4 m), every other one broadcasting with separate frequency generators and amps. Primary frequencies were around 100 kHz; difference frequencies of 10 to 20 kHz were observed. Two-D beampattern scans were taken and the results compared with calculations based on classical theory. The agreement is surprisingly good with a beta of around 200 and a Q (inverse attenuation) of 50.
• Time reversal of continuous-wave, steady-state signals in elastic media (2009) — Brian E. Anderson et al. — Applied Physics Letters
  Abstract

  Experimental observations of spatial focusing of continuous-wave, steady-state elastic waves in a reverberant elastic cavity using time reversal are reported here. Spatially localized focusing is achieved when multiple channels are employed, while a single channel does not yield such focusing. The amplitude of the energy at the focal location increases as the square of the number of channels used, while the amplitude elsewhere in the medium increases proportionally with the number of channels used. The observation is important in the context of imaging in solid laboratory samples as well as problems involving continuous-wave signals in Earth.
• Time reversal of monochromatic signals in elastic media. (2009) — Brian E. Anderson et al. — The Journal of the Acoustical Society of America
  Abstract

  A set of experiments has been conducted to show that time reversal of steady state monochromatic signals can produce spatial focusing in a reverberant elastic cavity when multiple channels are used. The transient portion of the received signals is not used. A single channel does not produce spatial focusing as it only drives the system according to its modal distribution. The amplitude of the energy at the focal location increases as the square of the number of channels used, while the amplitude elsewhere in the medium increases proportionally with the number of channels used. This work has importance in the field of medical ultrasound where the use of a long duration monochromatic excitation may be used for lithotripsy or other ultrasonic therapy. [This work is supported by Institutional Support (LDRD) at Los Alamos National Laboratory.]
• Tremor source location using time reversal: Selecting the appropriate imaging field (2009) — C. S. Larmat, R. A. Guyer, P. A. Johnson — Geophysical Research Letters
  Abstract

  Studying triggered Non Volcanic Tremor (NVT) is important because it may help to map the depth of the locked zones of faults associated with high seismic risk. The success of this mapping depends on precisely locating the depth of tremor. Tremor, like other long‐lived signals (e.g., Earth hum) lacks distinct sharp timing features making it impossible to locate with classical approaches. Time Reversal has the advantage of exploiting the full waveform with no a priori assumption regarding the source or the observed signal. We perform a synthetic study of time reversal location of a long‐lasting source in the Los Angeles basin with a realistic 3D velocity model and sparse station set. We show that, the key to successfully locating NVT, is application of suitable imaging fields, such as the wave divergence, curl and energy current.
• 2004 M6.0 Parkfield earthquake characterization using Time Reversal (2008) — Carene Larmat, Paul A. Johnson, Lianjie Huang — The Journal of the Acoustical Society of America
  Abstract

  Time reversal has proved to be a robust source location method in acoustics and is now being developed for a number of seismic applications. One problem of particular interest is locating sources where the signal-to-noise ratio is small. These include small earthquakes (&amp;lt;M5.5) or atypical seismic sources with a small seismic energy radiation (e.g., tremor, slow earthquakes). Time reversal has been shown to be very robust and work in the presence of poor data, low signal to noise ratio, etc. We present a prototype study showing the power of time reversal, using seismic data from the 2004 M6.0 Parkfield earthquake, which is the world's best recorded event to date and thus one of the most studied. The back-propagation of recorded seismic data in a 3D Earth velocity model is numerically carried out. We show that the reconstructed reverse wave-field exhibits clear focusing at the source point but also displays a four-lobe radiation pattern for each type of rebroadcast waves (body, surface), which is consistent with the known source mechanism: a right-lateral strike slip along the almost-vertical San Andrea fault.
• Computational time reversal acoustics imaging of embedded defects in solid media (2008) — Michele Griffa et al. — The Journal of the Acoustical Society of America
  Abstract

  Time reversal acoustics (TRA) techniques can exploit the nonlinear processes emerging from the interaction between the incident waves and nonlinear scatterers in solid media in order to localize and characterize the scatterers themselves. When nonlinear scatterers are embedded, their localization can be obtained through a mixed experimental/numerical TRA procedure: the forward propagation is performed experimentally, while the time reversal (TR) backward propagation is simulated using computational codes and a reference model of the solid. The synergetic use of dedicated processing of the forward propagation signals collected at the time reversal mirror (TRM), for example with nonlinear elastic wave spectroscopy (NEWS) techniques, and the calculation of the backpropagated wave fields at each point within the specimen leads to imaging of the nonlinear scatterers. We show examples of nonlinear scatterer (macroscopic cracks, distributed microcracks) imaging by such a procedure, exploiting high performance (parallel) computational codes. We address issues in the imaging method related to the discrepancy between the reference model of the specimen and the real specimen itself. Finally, we address the implementation of the technique for non-destructive Evaluation (NDE) real-world applications using multi-threaded computational codes to be run on common multicore desktop computers.
• Effects of acoustic waves on stick–slip in granular media and implications for earthquakes (2008) — Paul A. Johnson et al. — Nature
• Induced Dynamic Nonlinear Ground Response at Garner Valley, California (2008) — Z. Lawrence et al. — Bulletin of the Seismological Society of America
• Investigation of the robustness of time reversal acoustics in solid media through the reconstruction of temporally symmetric sources (2008) — M Griffa et al. — Journal of Physics D: Applied Physics
• Nonlinear ultrasound can detect accumulated damage in human bone (2008) — M. Muller et al. — Journal of Biomechanics
• Numerical modeling of the effects of finite size transducers for time reversal acoustics in solid media (2008) — Michele Griffa, Brian E. Anderson, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Time Reversal Acoustics (TRA) has been shown to be very robust not only in fluids but also in solid bounded media. The most relevant limitations to the Time Reversal Process (TRP) in solid specimens are the co-existence of several propagation modes, mode conversion at each interface (inhomogeneities or boundaries), attenuation mechanisms and the multidimensional nature of the propagating wave fields. Additional limitations arise in practical applications, for example for Non Destructive Evaluation purposes, when the Time Reversal Mirror (TRM) piezoelectric transducers are usually attached to the surface of the solid. We have investigated the role of the finite size of the TRM transducers and their sensitivity to only certain components of the incident wave fields in the TRP when they are attached to the surface of the sample under study. We have developed a theoretical analysis and performed numerical simulations and laboratory experiments in order to examine the robustness of TRA in solid media, including where the TRM is composed of finite size elements attached to the specimen surface. The results lead to useful information about the efficiency of the TRP as well as the optimization of the TRM setup in terms of transducer size.
• Observations and models of dynamic earthquake triggering (2008) — Joan Gomberg, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Seismologists have long accepted the idea that step-function perturbations to the deformation field acting on a fault can change its likelihood of, or 'trigger', failure as fault slip. We review the observations that have lead to the very recent recognition that transient perturbations (e.g., associated with seismic waves) also affect failure probabilities, and more broadly, observations of the spatial and temporal variations in both triggering deformations and triggered responses. Many of these cannot be explained by conventional models of earthquake nucleation, requiring consideration of ideas developed in other disciplines, such as those describing and explaining nonlinear dynamic elasticity from rock-mechanics. In addition to the scientific challenges, these observations and models significantly impact earthquake forecasts and hazard assessments. We focus on observations of natural earthquakes and from the rock-mechanics laboratory, and some of the explanatory models that we and others have proposed. While many of these observations and models are just being vetted now, even newer ones related to slow aseismic fault slip and non-volcanic tremor (seismic radiation that scales very differently from that from earthquakes) may lead to substantive modifications and advances. We conclude with a few tantalizing examples as a prelude to a companion presentation.
• SELECTIVE SOURCE REDUCTION TO IDENTIFY MASKED SMALLER SOURCES USING TIME REVERSED ACOUSTICS (TRA) (2008) — Brian E. Anderson et al. — REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION: 34th Annual Review of Progress in Quantitative Nondestructive Evaluation
• Selective source reduction to identify masked sources using time reversal acoustics (2008) — M Scalerandi et al. — Journal of Physics D: Applied Physics
• The effect of acoustic waves on stick-slip behaviour in sheared granular media, with implications to earthquake processes (2008) — Paul A. Johnson et al. — The Journal of the Acoustical Society of America
  Abstract

  We are studying the effects of acoustic waves on sheared granular material, with two goals in mind: one is to understand the intriguing physics that arises in this experimental system, and the other is to see if such experiments offer insight into earthquake processes, in particular the phenomenon where one earthquake triggers another nearby, or distant, earthquake ('dynamic earthquake triggering'). We conducted laboratory experiments of stick-slip in granular media using a double-direct, shear apparatus, while applying low amplitude vibration as well as pulsed waves. We find that vibration and pulses significantly perturb the shearing behaviour of the granular material, and that the manifestation of vibration is extremely complex, including strong material memory of the acoustic perturbation, that persists. We note that the wave disturbance must take place near the critical point, where the granular material is near failure, otherwise no effect is observed. Also, horizontal loads on the system can eliminate the effect if they arelarge (⩾4-5 MPa).
• The effects of transducers on the time reversal process in solids (2008) — Brian E. Anderson, Michele Griffa, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Every experimental implementation of Time Reversal (TR) involves the use of transducers to convert wave motion, whether mechanical or acoustical, into electrical signals, and vice versa. Practical considerations of transducers are not included in the basic theory of time reversal, which is based on idealized point-like sources. These considerations include temporal ring down at a narrowband transducer resonance, the finite size of the transducer giving rise to directivity, and the impedance contrast between the transducer and the medium. The effects of these considerations on the TR process will be characterized by presenting data from various TR experiments.
• Time reversal and non-linear elastic wave spectroscopy (TR NEWS) techniques (2008) — T.J. Ulrich et al. — International Journal of Non-Linear Mechanics
• Time reversal use in detection of buried cracks (2008) — Pierre-Yves Le Bas et al. — The Journal of the Acoustical Society of America
  Abstract

  Time reversal has the potential to become a powerful tool in nondestructive evaluation. Coupled with nonlinear properties of cracks in a technique known as time reverse nonlinear elastic wave spectroscopy (TRNEWS), it provides the means to detect defects in complex structures. This experimental study explores the capabilities of TR to focus energy inside a 3D medium in order to activate nonlinear features or defects. Special attention is given to buried cracks. The current challenge is introducing sufficient energy in order to excite the buried feature and produce nonlinear scattering. We will provide an overview of the problem.
• Transitional nonlinear elastic behaviour in dense granular media (2008) — Thomas Brunet, Xiaoping Jia, Paul A. Johnson — Geophysical Research Letters
  Abstract

  Nonlinear sound propagation in a stressed glass bead pack is investigated via amplitude measurements of harmonic generation. We evidence two distinct regimes of sound‐matter interaction: reversible and irreversible, as a function of the ratio r s between dynamic strain and static one. In the reversible regime, the higher harmonics generated agree well with a mean‐field model based on the Hertz contact theory, and the coefficient of nonlinearity β deduced from the measured amplitude of second‐harmonic is consistent with that deduced from the acoustoelastic measurement. Beyond a certain threshold ( r s &gt; 3%), the interaction of sound wave with granular matter becomes irreversible, accompanied by a small compaction of the medium.
• Application of nonlinear dynamics to monitoring progressive fatigue damage in human cortical bone (2007) — T. J. Ulrich et al. — Applied Physics Letters
  Abstract

  In this work, the results of applying nonlinear dynamics to study progressive material fatigue in human bone are described. Material nonlinear dynamical response has been shown to be associated with mechanical damage. The progressive mechanical damage experiments were conducted in cortical bone extracted from a human femur. After each damage step, the material dynamical nonlinear response was measured by applying wave modulation and extracting a nonlinear parameter proportional to the sideband amplitude. The nonlinear parameter increases rapidly with damage step, indicating increased damage after the initial cycling procedure, while the quasistatic stiffness taken from the cycling experiments shows little change.
• Applying nonlinear resonant ultrasound spectroscopy to improving thermal damage assessment in concrete (2007) — C. Payan et al. — The Journal of the Acoustical Society of America
  Abstract

  Nonlinear resonant ultrasound spectroscopy (NRUS) consists of evaluating one or more resonant frequency peak shifts while increasing excitation amplitude. NRUS exhibits high sensitivity to global damage in a large group of materials. Most studies conducted to date are aimed at interrogating the mechanical damage influence on the nonlinear response, applying bending, or longitudinal modes. The sensitivity of NRUS using longitudinal modes and the comparison of the results with a classical linear method to monitor progressive thermal damage (isotropic) of concrete are studied in this paper. In addition, feasibility and sensitivity of applying shear modes for the NRUS method are explored.
• Complex source imaging using time-reversal (TR): experimental studies of spatial and temporal resolution limits (2007) — Brian E. Anderson et al. — The Journal of the Acoustical Society of America
  Abstract

  Large earthquakes are composed of a complex succession of slip events that are nearly indistinguishable on a seismogram. The question, how does an earthquake work? remains largely unsolved. The slip events on the fault plane(s) generally take place at different spatial locations and at different times. TR wave physics can be advantageously exploited to recreate, from measured signals, a spatially and/or temporally complex sound/seismic source. An experimental study is conducted to determine the spatial and temporal resolution limitations in imaging a complex source in solids, as part of our goal to understand earthquake source complexity. TR experiments are conducted on solid blocks of different materials, such as Berea sandstone and aluminum. Arrays of piezoelectric transducers are bonded to the samples for the creation of complex spatial-temporal sources, as well as to record signals. The experimental spatial and temporal resolution limits for complex source imaging will be presented as a function of material physical characteristics (e.g., Q, modulus), as well as source signal characteristics such as pulse width, frequency and repetition rate. [This work was supported by Institutional Support (LDRD) at Los Alamos National Laboratory.]
• Imaging and Characterizing Damage Using Time Reversed Acoustics (2007) — T. J. Ulrich, A. M. Sutin, P. A. Johnson — REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION
• Interaction Dynamics of Elastic Waves with a Complex Nonlinear Scatterer through the Use of a Time Reversal Mirror (2007) — T. J. Ulrich, Paul A. Johnson, Robert A. Guyer — Physical Review Letters
• Nonlinear dynamics and time reversed acoustic imaging in damaged solids (2007) — T. J. Ulrich et al. — The Journal of the Acoustical Society of America
  Abstract

  Our ultimate goal is locating and imaging nonlinear scatterers in solids (e.g., cracks) without a priori knowledge of their existence. Toward that goal, two methods have been devised that combine the spatial and temporal focusing abilities of TRA with nonlinear elastic wave spectroscopy’s (NEWS) sensitivity to mechanical damage. The first method uses TRA to create large amplitude signals and induce a nonlinear response in a highly localized region on a sample surface. Repeating the process in a step-scan approach provides the means to image the sample surface/near-surface with high resolution, distinguishing nonlinear features (cracks) from the linear background (undamaged material). The second method takes advantage of TRA to focus acoustic energy from two input frequencies onto an unknown, but nonlinear, scattering source, creating nonlinear wave modulation. The time reversal mirror (TRM) array records the primary and scattering source waveforms. Filtering the recorded signals for a modulation sideband, time reversing, and rebroadcasting through the TRM focuses the filtered signal onto the source of the modulation—the crack. Experimental results demonstrating each technique will be presented. [This work was supported by Institutional Support (LDRD) at Los Alamos National Laboratory.]
• Selective source reduction to identify masked sources using time-reversed acoustics (2007) — Brian E. Anderson et al. — The Journal of the Acoustical Society of America
  Abstract

  This paper describes a time-reversed acoustics (TRA) method of spatially illuminating a source signal, which has been masked by another source signal. The selective source reduction (SSR-TRA) method employs a subtraction technique where one focus is selectively reduced to illuminate the masked focus. In this paper, numerical and experimental results are presented to demonstrate to what degree the SSR-TRA method is successful. The SSR-TRA method is demonstrated for two elastic wave pulses emitted simultaneously from two spatially separated sources of differing amplitudes. Results are presented from experiments conducted with two different solid samples: Aluminum and doped silica glass. Applying the SSR-TRA method, a stronger source, up to 13 times stronger than a weaker one, may be reduced to reveal information about the weaker source. Spatial and/or temporal characteristics of multiple close proximity sources can be resolved with the use of the SSR-TRA method. The results show that the SSR-TRA methods’ limitations are chiefly due to imperfect reconstruction of the source function in the time-reversed focal signal. [This work was supported by Institutional Support (LDRD) at Los Alamos National Laboratory.]
• Strong Unique Continuation Properties of Generalized Baouendi–Grushin Operators (2007) — Nicola Garofalo, Dimiter Vassilev — Communications in Partial Differential Equations
• The 24 hr product: from concept to interactive model in less than a day (2007) — Paul Johnson, R. Griffiths, Steve Gill — International Journal of Design Engineering
• Existence of solutions and regularity near the characteristic boundary for sub-Laplacian equations on Carnot groups (2006) — Dimiter Vassilev — Pacific Journal of Mathematics
• Fatigue damage in cortical bone detected using nonlinear ultrasound (2006) — M. Muller et al. — Journal of Biomechanics
• Imaging nonlinear scatterers applying the time reversal mirror (2006) — T. J. Ulrich, P. A. Johnson, A. Sutin — The Journal of the Acoustical Society of America
  Abstract

  Nonlinear elastic wave spectroscopy (NEWS) has been shown to exhibit a high degree of sensitivity to both distributed and isolated nonlinear scatterers in solids. In the case of an isolated nonlinear scatterer such as a crack, by combining the elastic energy localization of the time reversal mirror with NEWS, it is shown here that one can isolate surfacial nonlinear scatterers in solids. The experiments presented here are conducted in a doped glass block applying two different fixed frequency time-reversed signals at each focal point and scanning over a localized nonlinear scatterer (a complex crack). The results show a distinct increase in nonlinear response, via intermodulation distortion, over the damaged area. The techniques described herein provide the means to discriminate between linear and nonlinear scatterers, and thus to ultimately image and characterize damaged regions.
• Nonclassical Nonlinear Acoustics in Solids: Methods, Applications, and the State of the Art (2006) — Paul A. Johnson — INNOVATIONS IN NONLINEAR ACOUSTICS: ISNA17 - 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum
• Nonlinear Elastic Wave Experiments: Learning About the Behaviour of Rocks and Geomaterials (2006) — J. A. TenCate, T. J. Shankland, P. A. Johnson — Universality of Nonclassical Nonlinearity
• P3F-2 Nonlinear Resonant Ultrasound Spectroscopy for Micro Damage Assessment in Human Bone (2006) — P. Laugier et al. — 2006 IEEE Ultrasonics Symposium
• A note on the stability of local zeta functions (2005) — Dimiter Vassilev — Proceedings of the American Mathematical Society
  Abstract

  We show the existence of an interval of stability under small perturbations of local zeta functions corresponding to non-trivial local solutions of an elliptic equation with Lipschitz coefficients. Résumé. Nous démontrons l’existence d’un intervalle de stabilité pour la fonction zêta associée à une équation uniformément elliptique du second ordre à coefficients lipschitziens.
• Dynamic triggering of earthquakes (2005) — Joan Gomberg, Paul Johnson — Nature
• Nonlinear dynamics, granular media and dynamic earthquake triggering (2005) — Paul A. Johnson, Xiaoping Jia — Nature
• Nonlinear Elastic Wave NDE I. Nonlinear Resonant Ultrasound Spectroscopy and Slow Dynamics Diagnostics (2005) — P. A. Johnson — REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION
• Overdetermined Boundary Value Problems, Quadrature Domains and Applications (2005) — Dmitry Khavinson, Alexander Yu. Solynin, Dimiter Vassilev — Computational Methods and Function Theory
• Slow dynamics and anomalous nonlinear fast dynamics in diverse solids (2005) — Paul Johnson, Alexander Sutin — The Journal of the Acoustical Society of America
  Abstract

  Results are reported of the first systematic study of anomalous nonlinear fast dynamics and slow dynamics in a number of solids. Observations are presented from seven diverse materials showing that anomalous nonlinear fast dynamics (ANFD) and slow dynamics (SD) occur together, significantly expanding the nonlinear mesoscopic elasticity class. The materials include samples of gray iron, alumina ceramic, quartzite, cracked Pyrex, marble, sintered metal, and perovskite ceramic. In addition, it is shown that materials which exhibit ANFD have very similar ratios of amplitude-dependent internal-friction to the resonance-frequency shift with strain amplitude. The ratios range between 0.28 and 0.63, except for cracked Pyrex glass, which exhibits a ratio of 1.1, and the ratio appears to be a material characteristic. The ratio of internal friction to resonance frequency shift as a function of time during SD is time independent, ranging from 0.23 to 0.43 for the materials studied.
• Strong Unique Continuation for Generalized Baouendi-Grushin Operators (2005) — Nicola Garofalo, Dimiter Vassilev — Proceedings of the 4th International ISAAC Congress
• Time reversal acousto-seismic method for land mine detection (2005) — Alexander Sutin et al. — Defense and Security
• Dynamic measurements of the nonlinear elastic parameter α in rock under varying conditions (2004) — Paul A. Johnson et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  Since the exhaustive work by Adams and Coker at the Carnegie Institute in the early 1900s and the work of F. Birch's group at Harvard University conducted in the 1940s–1950s, it has been well documented that the quasi‐static stress‐strain behavior of rock is nonlinear and hysteretic. Over the past 20 years, there has been an increasing body of evidence suggesting that rocks are highly elastically nonlinear and hysteretic in their dynamic stress‐strain response as well, even at extremely small strain amplitudes that are typical of laboratory measurements. In this work we present a compendium of measurements of the nonlinear elastic parameter α extracted from longitudinal (Young's mode) and flexural‐mode resonance experiments in eight different rock types under a variety of saturation and thermal conditions. The nonlinear modulus α represents a measure of the dynamic hysteresis in the wave pressure‐strain behavior. We believe that hysteresis is the primary cause of nonclassical nonlinear dynamics in rock, just as it is responsible for elastic nonlinear behavior in quasi‐static observations. In dynamics, α is proportional to the wave speed and modulus reduction as a function of wave strain amplitude due to the hysteresis, based on our current model. The rocks tested include pure quartz sandstone (Fontainebleau), two sandstones that contain clay and other secondary mineralization (Berea and Meule), marble (Asian White), chalk, and three limestones (St. Pantaleon, Estaillades, and Lavoux). The values of α range from ∼500 to &gt;100,000, depending on the rock type, damage, and/or water saturation state. Damaged samples exhibit significantly larger α than intact samples (hysteresis increases with damage quantity), and water saturation has an enormous influence on α from 0 to 15–30% water saturation.
• Land mine detection by time reversal acousto-seismic method (2004) — Alexander Sutin et al. — The Journal of the Acoustical Society of America
  Abstract

  We present a concept and results of a pilot study on land mine detection based on the use of time reversal acoustics (TRA). TRA provides a possibility of highly effective concentrating of seismic wave energy in time and space in complex heterogeneous media. TRA focusing of seismic waves on a land mine increases the detection abilities of conventional linear and nonlinear acousto-seismic methods. Such factors as medium inhomogeneities, presence of reflecting boundaries, which could critically limit conventional acoustic approaches, do not affect TRA based method. The TRA mine detection system comprises several air borne or seismic sources and a noncontact (laser vibrometer) device for remote measurements of the surface vibration. The TRA system focuses a seismic wave at a surface point where the vibration is measured. The focusing point is scanned across the search area. The amplitude and frequency dependence of the signal from the seismic wave focusing point and nonlinear acoustic effects are analyzed to assess probability of the mine presence. Preliminary experiments confirmed high focusing ability of the TRA seismo-acoustic system in complex conditions (a laboratory tank with sand) and demonstrated a significant increase in the surface vibration in the presence of mine imitator. [Work supported by DoD grant.]
• Linear and nonlinear acoustic control of accumulated fatigue damage in steel (2004) — Alexander Sutin, Yulian Kin, Paul Johnson — The Journal of the Acoustical Society of America
  Abstract

  We present results of linear and nonlinear acoustic testing of steel samples with different levels of fatigue damage. The steel specimens were tested under programed cyclic loading on a fatigue testing machine and accumulated different levels of fatigue damage. No visible surface-crack formations during fatigue cycling were observed. In other words, the emphasis was placed on the characterization of continued but physically invisible in service life conditions damage in different materials and structures. Both linear and nonlinear acoustic techniques were used to assess damage accumulation. (1) Impulse resonant acoustic spectroscopy (IRAS) is based on analysis of the free-sample vibration after impact excitation. It demonstrated the increasing of the resonance frequencies and Q factor with damage accumulation. (2) Nonlinear resonant acoustic spectroscopy (NRAS) is based on measurement of the resonance response for different levels of acoustic excitation. The amplitude-dependent frequency shift for damaged steel was observed to increased with damage accumulation. (3) Nonlinear wave modulation spectroscopy (NWMS) implies the modulation of ultrasound wave by lower frequency vibration. High level of the side-band components for damaged samples were observed. The comparison of different methods is given.
• Nonlinear and Nonequilibrium Dynamics in Geomaterials (2004) — James A. TenCate et al. — Physical Review Letters
• Single-channel time reversal in elastic solids (2004) — Alexander M. Sutin, James A. TenCate, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Reverberant volume time reversal in 3D elastic solids (doped glass and Berea sandstone) using a single channel are presented. In spite of large numbers of mode conversions (compressional to shear wave conversions at the walls), time reversal works extremely well, providing very good spatial and time focusing of elastic waves. Ceramics were bonded to the surface as sources (100–700 kHz); a broadband laser vibrometer (dc—1.5 MHz) was used as detector. Temporal and spatial time-reversal focusing are frequency dependent and depend on the dissipation characteristics of the medium. Doped glass (inverse dissipation Q between 2000 to 3000) shows time-reversed spatial focal resolution at about half of the shear wavelength. The Berea sandstone (Q=50) yields a wider focusing width (a bit more than the shear wavelength) due to its lower Q. Focusing in the doped glass is better because the time-reversal (virtual) array created by wave reflections is larger than in the highly attenuating sandstone. These are the first results reported in granular media, and are a first step toward geophysical and field applications.
• Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids (2003) — Marco Scalerandi et al. — The Journal of the Acoustical Society of America
  Abstract

  Recent studies show that a broad category of materials share “nonclassical” nonlinear elastic behavior much different from “classical” (Landau-type) nonlinearity. Manifestations of “nonclassical” nonlinearity include stress–strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft “bond” elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.
• Performance of miniature piezocones in thinly layered soils (2003) — C. C. Hird, P. Johnson, G. C. Sills — Géotechnique
• Resonant acoustic spectroscopy at low Q factors (2003) — A. V. Lebedev et al. — Acoustical Physics
• Stress induced conditioning and thermal relaxation in the simulation of quasi-static compression experiments (2003) — M Scalerandi, P P Delsanto, P A Johnson — Journal of Physics D: Applied Physics
• Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means (2003) — Jean-Christoph Lacouture, Paul A. Johnson, Frederic Cohen-Tenoudji — The Journal of the Acoustical Society of America
  Abstract

  The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.
• LISA simulations of time-reversed acoustic and elastic wave experiments (2002) — P P Delsanto et al. — Journal of Physics D: Applied Physics
• Resonance acoustic spectroscopy of lossy materials (2002) — Lev A. Ostrovsky et al. — The Journal of the Acoustical Society of America
  Abstract

  Resonance acoustic spectroscopy (RAS) is known as an efficient tool for determining the elastic and dissipative parameters of materials. However, its use for diagnostics of a variety of materials with a low quality factor (including materials with defects) is often impeded by overlapping of resonance responses at different modes. Here, a method of processing experimental data is suggested which enables one to determine resonance frequencies and Q-factors in cases of broad and overlapping resonances. In experiments, both undamaged and cracked samples were studied. A swept-frequency excitation was used for polycarbonate samples, whereas an impulse method with impact excitation was used for concrete samples. Signal processing was performed with the use of the suggested algorithm. In particular, the decrease of the Q-factor and splitting of resonance frequencies due to crack formation were registered. This method, which demonstrates a high efficiency even at a significant resonance overlapping, can be used for nondestructive testing of a broad class of materials.
• Sensitive imaging of an elastic nonlinear wave-scattering source in a solid (2002) — Vyacheslav V. Kazakov, Alexander Sutin, Paul A. Johnson — Applied Physics Letters
  Abstract

  We have developed an imaging method for locating isolated nonlinear scattering source(s) in solids. It relies on extracting the nonlinear response of a solid by modulation of a high by a low-frequency wave, and employing moving-window, synchronous detection. The resulting image consists of nonlinear wave reflection profiles with remarkable sensitivity to an isolated elastic nonlinear source(s). In creating the image, we can distinguish between a nonlinear scattering source and other wave scatterers in the material. The method should work equally well for imaging the relative nonlinearity of different regions within a volume.
• Crack location using nonlinear means applying modulation of ultrasonic pulses by cw vibration (2001) — Vyacheslav V. Kazakov, Alexander M. Sutin, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  Nonlinear wave modulation spectroscopy (NWMS) was recently introduced as a new tool in NDE. This technique employs the nonlinear interaction of ultrasound and vibration in the presence of defects. Vibration changes the contact area within a defect effectively modulating an ultrasonic wave sensing the defect. NWMS has high sensitivity to the presence of cracks and can be a very good tool for a ‘‘pass–fail’’ test but cannot provide the crack location. A new method for locating defects or cracks in a material, presented in this paper, is based on the modulation of ultrasonic pulses by vibration. The cw vibration induces modulation of the signal reflected from cracks. Measurements of the spatial distribution of the modulation level are the basis of nonlinear acoustic imaging. Experimental verification of the method has been conducted in steel plates containing a circular hole and a fatigue crack. The high-frequency (carrier) impulse was about 3 MHz, and the modulating vibration frequency was 5–15 Hz. This technique images a crack very well while a hole was not detected. As the location of damage is the next important issue in NWMS, this work represents an important step. [This work was partially supported by International Science Technical Center, Grant No. 1369.]
• Dynamic nonlinear elasticity in geomaterials (2001) — L. A. Ostrovsky, P. A. Johnson — La Rivista del Nuovo Cimento
• Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS) (2001) — Koen E-A. Van Den Abeele et al. — NDT &amp; E International
• Nonlinear Dynamics of Rock: Hysteretic Behavior (2001) — L. A. Ostrovsky, P. A. Johnson — Radiophysics and Quantum Electronics
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type (2001) — Nicola Garofalo, Dimiter Vassilev — Duke Mathematical Journal
• A nonlinear mesoscopic elastic class of materials (2000) — Paul A. Johnson — 15th international symposium on nonlinear acoustics: Nonlinear acoustics at the turn of the millennium
• Acoustically induced slow dynamics in nonlinear mesoscopic elastic materials (2000) — Alexander M. Sutin, Paul A. Johnson, James A. TenCate — The Journal of the Acoustical Society of America
  Abstract

  We have known about slow dynamics in rock due to continuous wave excitation drive for several years (http://www.ees4.lanl.gov/nonlinear). TenCate, Smith, and Guyer (see abstract, this meeting) have recently discovered that both the elastic modulus and the wave dissipation display log time recovery in granular solids, and that it may be thermally or mechanically induced. Much to our surprise, we have discovered that a CW or broad-frequency band acoustic source can also induce slow dynamical response. This response was observed as a variation of the ultrasonic probe wave amplitude, the resonance frequency, and Q factor after the action of a pump wave. The slow time recovery took place in materials such as powdered metals, damaged materials, concrete, and rocks as well. The variations of material properties due to the action of pump waves lead to transient amplification and an obscuration of CW probe waves. The observed behavior may be more universal than was first thought. The results have potential implications to many topics, including laboratory wave studies, earthquake strong ground motion, elastic waves emanating from a point source, damage detection, and manufacturing processes. [Work supported by Stevens and by the Department of Energy: Office of Basic Energy Sciences.]
• Amplitude variation of resonant frequencies and Q-factor in impulse acoustic resonant spectroscopy (2000) — Alexander M. Sutin, Robert A. Guyer, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  One of the oldest and simplest nondestructive tests of the quality of an object is to tap it and listen to the radiated sound. The translation of this test into a modern instrumentation system leads to impulse acoustic resonance spectroscopy, IARS. The processing of the acoustic time train after impulse excitation (tap) allows one to follow Q and resonance frequencies as a function of time. Examination of the time train can reveal important properties of this elastic state and of the state of the object. IARS will be illustrated with data on a suite of automobile brake drums made of powdered aluminum. The time evolution of Q and a resonance frequency will be described. Typically Q is of order one-half of its late time (equilibrium) value at short times whereas a resonance frequency shifts by of order 0.2% from early (0.2 s) to late (5 s) time. These qualitative properties have two possible explanations: (1) amplitude-dependent internal friction or (2) the ‘‘slow dynamics’’ that is characteristic of elastic systems inhabited by hysteretic elastic elements. [Work supported by Stevens and by the Department of Energy: Office of Basic Energy Sciences.]
• Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS) (2000) — K. E. -A. Van Den Abeele, P. A. Johnson, A. Sutin — Research in Nondestructive Evaluation
• Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part II: Single-Mode Nonlinear Resonance Acoustic Spectroscopy (2000) — K. E. -A. Van Den Abeele et al. — Research in Nondestructive Evaluation
• Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups (2000) — Nicola Garofalo, Dimiter Vassilev — Mathematische Annalen
• Hysteresis and the Dynamic Elasticity of Consolidated Granular Materials (1999) — R. A. Guyer, James TenCate, Paul Johnson — Physical Review Letters
• Nonlinear Mesoscopic Elasticity: Evidence for a New Class of Materials (1999) — Robert A. Guyer, Paul A. Johnson — Physics Today
  Abstract

  A squash ball almost doesn't bounce; a Superball bounces first left then right, seeming to have a mind of its own. Remarkable and complex elastic behavior isn't confined to sports equipment and toys. Indeed, it can be found in some surprising places. When the elastic behavior of a rock is probed, for instance, it shows extreme nonlinearity hysteresis and discrete memory (the Flint-stones could have had a computer that used a sandstone for random-access memory). Rocks are an example of a class of unusual elastic materials that includes sand. soil, cement, concrete, ceramics and, it turns out, damaged materials, Many members of this class are the blue-collar materials of daily life: They are in the bridges we cross on the way to work, the roofs over our heads and the ground beneath our cities—such as the Los Angeles basin (home to many earthquakes). The elastic behavior of these materials is of more than academic interest.
• The nonlinear mesoscopic elasticity class of materials (1999) — Paul A. Johnson, Robert A. Guyer — The Journal of the Acoustical Society of America
  Abstract

  It is becoming clear that the elastic properties of rock are shared by numerous other materials (sand, soil, some ceramics, concrete, etc.). These materials have one or more of the following properties in common: strong nonlinearity, hysteresis in stress–strain relation, and discrete memory. Primarily, it is the material’s compliance, the mesoscopic linkages between the rigid components, that give these materials their unusual elastic properties. It can be said that these materials have nonlinear mesoscopic elasticity and encompass a broad class of materials. Materials with nonlinear mesoscopic elasticity stand in contrast to liquids and crystalline solids whose elasticity is due to contributions of atomic level forces, i.e., materials with atomic elasticity. Atomic elastic materials are well described by the traditional (Landau) theory of elasticity; however, mesoscopic elastic materials are not. Mesoscopic materials are well described by the P–M (Preisach–Mayergoyz) model of nonlinear elasticity developed by Guyer and McCall. A sequence of experiments on numerous materials illustrates the evidence of nonlinear mesoscopic elastic behavior. In experimental analysis a surprising discovery was made: damaged atomic elastic materials behave as mesoscopic elastic materials. It is significant that the nonlinear mechanism(s) in mesoscopic elastic materials remains a mystery.
• Acoustic nonlinearities in earth solids (1998) — Lev A. Ostrovsky, Paul Johnson — The Journal of the Acoustical Society of America
  Abstract

  Nonlinear elastic response in earth solids is a robust and representative physical characteristic. In this lecture the evidence leading to this conclusion is presented by providing an overview of theoretical and experimental developments in the domain. Illustrated measurements include those of nonlinear response in rock from a variety of dynamical wave experiments. The evidence leads to a pattern of unifying behavior. Nonlinear elasticity in earth solids is large relative to most materials; hysteresis and ‘‘discrete’’ memory play an important role in nonlinear properties of earth solids; nonlinear response is evident over a large frequency interval (dc to several MHz at least); and nonlinear response is significant, as is commonly appreciated, at large static and dynamic strain levels, but also at small strains where this behavior and the manifestations of this behavior are commonly disregarded. Recently, the methodology for extracting the nonlinear coefficients for a material have been proposed. Some theoretical models of structural nonlinearity of solid media and of wave propagation in such media are also described.
• Application of resonant ultrasound spectroscopy to geomaterials (1998) — Alexander L. Matveyev et al. — The Journal of the Acoustical Society of America
  Abstract

  Our objective is to apply resonant ultrasound spectroscopy (RUS) for obtaining the full elastic tensor of geomaterials. To our knowledge, RUS has never been successfully applied to complex materials such as rock: materials that are anisotropic and often inhomogeneous, and that contain grain-to-grain contacts, microcracks, etc. The fundamental problem with applying RUS to rock is high dissipation in the material, and the problem of coupling into all possible modes. The high dissipation limits the frequency band, and coupling into all modes controls the outcome of whether or not the full elastic tensor can be obtained. Our current experiment is operable in the frequency band of 3–30 kHz. Numerous sensor positions were tested in order to excite and detect different resonant modes. To date, the method has been applied to a rectangular brick sample. The comparison with theoretical calculation demonstrates that all modes (eigenfrequencies) of the sample were detected with high accuracy. Preliminary testing on cylindrical sandstone samples was also carried out. Duplicating the result from the brick in the rock sample is in progress. [This work is supported by the United States Industry Coalition, with the US DOE Contract W-7405-ENG-36, through the University of California.]
• Correcting regional seismic discriminants for path effects in western China (1998) — H. E. Hartse, R. A. Flores, P. A. Johnson — Bulletin of the Seismological Society of America
  Abstract

  Abstract The effect of path on regional seismic wave propagation can be significant. In an effort to improve discriminant performance, we explore the effect of path upon Pg/Lg ratios. Our primary objective is to find path corrections that reduce scatter within earthquake and explosion ratio populations, while at the same time increasing the separation between the two populations. We emphasize the 1.5- to 3-Hz and 2- to 4-Hz bands, as Pg and Lg in these bands can often be observed at smaller magnitudes and greater distances than higher-frequency bands, which have previously been shown to be reliable discriminants. For data, we use 271 earthquakes from northwest China, 25 nuclear explosions from the Kazakh test site (KTS), and one nuclear explosion from the Lop Nor test site recorded at station WMQ. We also use 185 earthquakes from the same region and seven nuclear explosion from the Lop Nor test site recorded at station AAK. Event-station distances range from 200 to 1400 km, earthquake magnitudes range between mb 2.5 and 6.2, and explosion magnitudes range between mb 4.5 and 6.5. In addition to ratio-distance trends, we examine Pg/Lg ratio-parameter trends related to topography, basin thickness, and crustal thickness. The parameters we consider are mean, roughness, gradient mean, and gradient roughness of the topography, basin thickness, and crustal thickness along each event-station path. We also consider the same parameters after weighting by path length. Through linear regressions, we found path corrections that reduce scatter within event populations, and we also found path corrections that increase the separation between earthquakes and KTS explosions recorded at WMQ. We obtained the best improvement in discrimination performance at WMQ by removing the trends of topography roughness, mean topography, and the gradient of basin thickness after weighting the parameters by path length. For AAK, we found that removing the trends of mean topography and the basement roughness improved discrimination performance over the uncorrected case. However, unlike WMQ, weighting these parameters by path length degraded discriminant performance. Because we see no predictable or repeatable trends for “adjacent” central Asian stations and overlapping regions of interest, we recommend an even more empirical approach to correcting for the effect of path. Where earthquakes are abundant, such as the Tian Shan, contouring a grid of ratio residuals (for each band of interest) may be a simpler method of finding appropriate path corrections.
• Direct and inverse problems of linear resonant ultrasound spectroscopy (1998) — Andrey V. Lebedev et al. — The Journal of the Acoustical Society of America
  Abstract

  The model approach of linear resonance ultrasound spectroscopy (LRUS) is described: obtaining the elastic moduli and Q values from resonance spectral measurements at frequencies ranging from several kHz to tens of kHz on complex solids such as rock. In the direct (forward) problem, LRUS is based on the variational principle, that of determining the eigenvalues from resonance spectral peaks of samples (complex in the general case). By minimizing the difference between the measured and calculated resonant modes for a given geometry of the sample, the linear properties of the sample (inverse problem) can be determined. The method was tested by comparing theoretical and experimental results obtained by Demarest [H. Demarest, J. Acoust. Soc. Am. 49, 768–775 (1971)] and data obtained from experiments carried out in IAP RAS on rectangular bricks at audio frequencies. Comparison of measured and calculated data showed that the difference may be as low as 0.6%. [This work is supported by the United States Industry Coalition, with the U.S. DOE, Contract No. W-7405-ENG-36, through the University of California.]
• Magnitude of nonlinear sediment response in Los Angeles basin during the 1994 Northridge, California, earthquake (1998) — Igor A. Beresnev et al. — Bulletin of the Seismological Society of America
  Abstract

  Abstract The study of nonlinear site response has practical difficulties due to large ambiguities in isolating local response from other competing effects. We chose a sedimentary site LF6 in Los Angeles basin that (1) has the closest reference rock sites available, compared to other stations, allowing an accurate estimation of local amplification, and (2) illustrates clear resonance in the near surface. In our opinion, this case represents the least ambiguity in the identification of possible nonlinearity. The site responses during the Northridge, the 1987 Whittier Narrows events and the Northridge aftershocks are compared. The station shows a fundamental resonance-frequency change between the higher- and lower-amplitude motions in the entire ensemble of 17 events used. The net shear-modulus reduction during the Northridge event is a factor of 1.3 to 1.4 compared to the Whittier Narrows event and is a factor of 1.7 compared to the aftershocks. This result provides guidance of what to expect at other sites in the basin, where the nonlinear response is less easy to characterize.
• Nonlinear sediment response during the 1994 Northridge earthquake: Observations and finite source simulations (1998) — Edward H. Field et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  We have addressed the long‐standing question regarding nonlinear sediment response in the Los Angeles region by testing whether sediment amplification was similar between the Northridge earthquake and its aftershocks. Comparing the weak‐ and strong‐motion site response at 15 sediment sites, we find that amplification factors were significantly less for the main shock implying systematic nonlinearity. The difference is largest between 2 and 4 Hz (a factor of 2), and is significant at the 99% confidence level between 0.8 and 5.5 Hz. The inference of nonlinearity is robust with respect to the removal of possibly anomalous sediment sites and how the reference‐site motion is defined. Furthermore, theoretical ground‐motion simulations show no evidence of any bias from finite source effects during the main shock. Nonlinearity is also suggested by the fact that the four sediment sites that contain a clear fundamental resonance for the weak motion exhibit a conspicuous absence of the peak in the strong motion. Although we have taken the first step of establishing the presence of nonlinearity, it remains to define the physics of nonlinear response and to test the methodologies presently applied routinely in engineering practice. The inference of nonlinearity implies that care must be exercised in using sediment site data to study large earthquakes or predict strong ground motion.
• Nonlinear Site Response: Where We're At (A report from a SCEC/PEER seminar and workshop) (1998) — E. H. Field et al. — Seismological Research Letters
• Nuclear Wastes in the Arctic Ocean. the Consequences of Past Dumping and Opportunities for Future Prevention (1998) — P. A. Johnson — Chemistry and Ecology
• Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California, earthquake. II. Widespread Nonlinear response at soil sites (1998) — Igor A. Beresnev et al. — Bulletin of the Seismological Society of America
  Abstract

  Abstract On average, soil sites behaved nonlinearly during the M 6.7 1994 Northridge, California, earthquake. This conclusion follows from an analysis that combines elements of two independent lines of investigation. First, we apply the stochastic finite-fault simulation method, calibrated with 28 rock-site recordings of the Northridge mainshock, to the simulation of the input motions to the soil sites that recorded this event. The calibrated model has a near-zero average bias in reproducing ground motions at rock sites in the frequency range from 0.1 to 12.5 Hz. The soil sites selected are those where there is colocation of strong-motion accelerographs and temporary instruments from the Northridge aftershock observation network. At these sites, weak-motion amplification functions based on numerous aftershock records have been empirically determined, in three separate investigations reported in the literature. These empirical weak-motion amplification factors can be applied to the simulated input rock motions, at each soil site, to determine the expected motions during the mainshock (i.e., neglecting nonlinearity). These expected motions can then be compared to the actual recordings during the mainshock. This analysis shows that the recorded strong-motion spectra are significantly over-estimated if weak-motion amplifications are used. The null hypothesis, stating that the inferred differences between weak- and strong-motion amplifications are statistically insignificant, is rejected with 95% confidence in the frequency range from approximately 2.2 to 10 Hz. On average, the difference between weak- and strong-motion amplifications is a factor of 2. Nonlinear response at those soil stations for which the input peak acceleration exceeded 150 to 200 cm/sec2 contributes most to this observed average difference. These findings suggest a significant nonlinear response at soil stations in the Los Angeles urban area during the Northridge mainshock. The effect is consistent with the increase in damping of shear waves at high levels of strain, which is well known from geotechnical studies of soil properties.
• Influence of change in physical state on elastic nonlinear response in rock: Significance of effective pressure and water saturation (1997) — Bernard Zinszner, Paul A. Johnson, Patrick N. J. Rasolofosaon — Journal of Geophysical Research: Solid Earth
  Abstract

  We describe Young's mode resonant bar results obtained under effective pressure at two saturation states: dry and water saturated. We monitor primary manifestations of nonlinear response in these experiments: the harmonic content, the source extinction intensity, and fundamental resonant frequency shift. In addition, we describe the hysteretic behavior of the static pressure response, the linear modulus, and Q . Because we currently lack a complete theoretical description of nonlinear behavior under resonance at pressure, we provide relative measures of nonlinear response rather than absolute values. The rocks include Fontainebleau and Meule sandstones and Lavoux limestone. Dynamic strain levels range from 10 −8 to 10 −5 and frequencies range from 1 to 10 kHz. The elastic nonlinear response of each of the rocks is markedly different over the range of physical property states explored. The different responses are related to differences in mechanical response resulting from rock type, grain cement type, etc. In all of the samples studied, the change in resonant frequency as a function of excitation intensity is not measurable above approximately 10 MPa; however, harmonics are observed at larger effective pressure levels. Hysteresis in velocity and Q versus pressure vary considerably between the rocks. The effect of Q on the experiments is marked. When Q is low (&lt;10) as for some saturated samples, relative excitations must be large in order to induce equivalent dry sample strains.
• Interaction of acoustical waves in concretes with cracks (1997) — Igor N. Didenkulov et al. — The Journal of the Acoustical Society of America
  Abstract

  Two separate experiments conducted with concrete samples containing cracks illustrate that acoustical methods have promise in damage detec- tion. Samples of concrete were 2.6 m×19 cm×12 cm and 1.7 m×20 cm×20 cm for the first and the second experiments, correspondingly. Cracks were located near sample centers and had dimensions of sample sections. In one experiment, high-frequency (5.3-kHz) longitudinal or rotational waves were modulated by low frequency (3 to 200-Hz) flexural vibrations. The relative amplitude of the modulation signal was about −20 dB. When the crack was filled by water, the modulation amplitude decreased in amplitude by approximately 3–4 dB. This result is expected because fluid should diminish the nonlinearity on the crack contact. In an uncracked sample, no modulation should be observed. In the second experiment, small explosive sources (less than 100 kg/cm2) were used to study the interaction of a large amplitude, broad-band frequency pulse, with a weak impulse from small explosive source. It was first observed that the weak pulse did not propagate through the crack. The weak signal passed through the crack when a stronger explosion pulse was simulteneously applied to the bulk, transiently closing the crack. The results are two of many experiments that indicate linear and nonlinear wave methods may be applied to characterize damage in concrete. [Work supported by INCAS, Nizhny Novgorod and by RFBR Grant 97-02-17524.]
• Nonlinear ground-motion amplification by sediments during the 1994 Northridge earthquake (1997) — Edward H. Field et al. — Nature
• On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation (1997) — Koen E-A Van Den Abeele et al. — The Journal of the Acoustical Society of America
  Abstract

  Microscopic features and their hysteretic behavior can be used to predict the macroscopic response of materials in dynamic experiments. Preisach modeling of hysteresis provides a refined procedure to obtain the stress–strain relation under arbitrary conditions, depending on the pressure history of the material. For hysteretic materials, the modulus is discontinuous at each stress–strain reversal which leads to difficulties in obtaining an analytic solution to the wave equation. Numerical implementation of the integral Preisach formulation is complicated as well. Under certain conditions an analytic expression of the modulus can be deduced from the Preisach model and an elementary description of elastic wave propagation in the presence of hysteresis can be obtained. This approach results in a second-order partial differential equation with discontinuous coefficients. Classical nonlinear representations used in acoustics can be found as limiting cases. The differential equation is solved in the frequency domain by application of Green’s function theory and perturbation methods. Limitations of this quasi-analytic approach are discussed in detail. Model examples are provided illustrating the influence of hysteresis on wave propagation and are compared to simulations derived from classical nonlinear theory. Special attention is given to the role of hysteresis in nonlinear attenuation. In addition guidance is provided for inverting a set of experimental data that fall within the validity region of this theory. This work will lead to a new type of NDT characterization of materials using their nonlinear response.
• Physical properties and mantle dynamics (1997) — T.J. Shankland, P.A. Johnson, K.R. McCall — Los Alamos National Lab.(LANL), Los Alamos, NM (United States), 1997
• Propagation des ondes élastiques dans les matériaux non linéaires Aperçu des résultats de laboratoire obtenus sur les roches et des applications possibles en géophysique (1997) — P. Rasolofosaon, B. Zinszner, P. A. Johnson — Revue de l'Institut Français du Pétrole
• Elastic pulsed wave propagation in media with second- or higher-order nonlinearity. Part II. Simulation of experimental measurements on Berea sandstone (1996) — Koen E-A Van Den Abeele, Paul A. Johnson — The Journal of the Acoustical Society of America
  Abstract

  The theoretical 1-D wave propagation model described in Part I is applied to laboratory data from dynamic propagating wave experiments on a 2-m-long cylindrical rod of Berea sandstone as previously reported by Meegan et al. [J. Acoust. Soc. Am. 94, 3387–3391 (1993)]. Using the iterative procedure, good agreement is obtained limiting model parameters up to cubic anharmonicity (i.e., two nonlinear terms proportional to β and δ in the stress-strain polynomial expansion). Both the data and simulations illustrate that nonlinear response is likely to occur even at extremely small strains (order 10−7). As generally expected for disordered materials, the resulting values for the nonlinear parameters are several orders of magnitude larger than those for intact (uncracked, noncompliant) materials. The values obtained for the dynamic nonlinearity parameters are discussed in relation to commonly obtained static and resonance results which suggest the need to include more complicated phenomena such as hysteresis in the theory.
• Evaluating hysteresis in earth materials under dynamic resonance (1996) — Abraham Kadish, Paul A. Johnson, Bernard Zinszner — Journal of Geophysical Research: Solid Earth
  Abstract

  A lumped parameter model is derived for studying hysteretic effects in resonant bar experiments on rock. The model uses equations of state obtained by approximating closed hysteresis loops in the stress‐strain plane by parallelograms. The associated approximate nonlinear state relations have a sound speed (modulus) that takes two values. Assuming hysteresis and discrete memory to be the primary nonlinear mechanisms, periodic solutions corresponding to these equations of state are obtained analytically for single‐frequency continuous wave drivers, and their frequency spectral densities are analyzed. In this simple approximation, if hysteretic contributions to the signal speed are a correction to the linear elastic signal speed (i.e., the parallelogram is narrow), the model predicts that the spectral density at even multiples of the source frequency is zero, and an approximate “pairing” of amplitudes is predicted for odd harmonic multiples. Comparison of the model spectrum with experimental data shows the model to be qualitatively correct. We conclude that hysteresis is an important mechanism in rocks. We consider the model to be a prototype.
• Laboratory study of linear and nonlinear elastic pulse propagation in sandstone (1996) — James A. TenCate et al. — The Journal of the Acoustical Society of America
  Abstract

  Linear and nonlinear elastic wave pulse propagation experiments were performed in sandstone rods, both at ambient conditions and in vacuum. The purpose of these experiments was to obtain a quantitative measure of the extremely large nonlinear response found in microcracked (i.e., micro-inhomogeneous) media like rock. Two rods were used, (1) a 2-m-long, 5-cm-diam rod of Berea sandstone (with embedded detectors) used in previously published experiments and (2) a somewhat smaller 1.8-m-long, 3.8-cm-diam rod. In the earlier experiments, wave scattering from the embedded detectors was a critical problem. In most of the experiments reported here, this problem was avoided by mounting accelerometers directly to the outside surface of the rod. Linear results show out of vacuum attenuations varied from 1.7 Np/m at 15 kHz (Q=10) for the large rod to 0.4 Np/m at 15 kHz (Q=55) for the small rod; attenuations for the small rod in vacuum were much less, typically about 0.15 Np/m at 15 kHz (Q=150). Wave velocities ranged from 1900 to 2600 m/s. The nonlinear results illustrate growth of the second and third harmonics and accompanying decay of the fundamental. These nonlinear results compare well with a numerical model. Although the results here were performed at peak strain amplitudes as low as 5×10−7, they still show the pronounced nonlinearity characteristic of rock, in agreement with static and resonance studies using the same rock type.
• Manifestation of nonlinear elasticity in rock: convincing evidence over large frequency and strain intervals from laboratory studies (1996) — P. A. Johnson, P. N. J. Rasolofosaon — Nonlinear Processes in Geophysics
  Abstract

  Abstract. Nonlinear elastic response in rock is established as a robust and representative characteristic rock rather than a curiosity. We show measurements of this behaviour from a variety of experiments on rock taken over many orders of magnitude in strain and frequency. The evidence leads to a pattern of unifying behaviour in rock: (1) Nonlinear response in rock is ubiquitous. (2) The response takes place over a large frequency interval (dc to 105 kHz at least). (3) The response not only occurs, as is commonly appreciated, large strains but also at small strains where this behaviour and the manifestations of this behaviour are commonly disregarded.
• Observations of nonlinearity with slow dynamics in rocks (1996) — James A. TenCate et al. — The Journal of the Acoustical Society of America
  Abstract

  A typical resonance curve—measured acceleration versus drive frequency—made on a thin bar of rock shows peak bending with a softening (nonlinear) modulus as drive levels are increased. Previous work showed the shapes of these nonlinear resonance curves depend on sweep rate, i.e., the ‘‘slow dynamics.’’ Slow dynamics in a 0.3-m-long, 50-mm-diam bar of Berea sandstone under ambient conditions have been documented for the first time. Peak strain levels during the experiments ranged from 10−11 to 10−5 at a fundamental bar resonance frequency near 4 kHz. Slow dynamics begin to appear at strain amplitudes above 10−6 at ambient conditions and at the onset of nonlinear peak bending. Higher strains condition the rock, altering its response for minutes to hours after the drive has been turned off. Other rocks show similar results. Physical origins of the slow dynamics lie in nonlinear effects at the microstructural level of cracks, pores, and interstitial clays. Further work examines environmental effects on conditioning and recovery as a means of relating them to physical properties and microtexture of the rock. [Work supported by OBES/DOE through the University of California.]
• Resonance and elastic nonlinear phenomena in rock (1996) — Paul A. Johnson, Bernard Zinszner, Patrick N. J. Rasolofosaon — Journal of Geophysical Research: Solid Earth
  Abstract

  In a great variety of laboratory experiments over large intervals in stress, strain, and frequency, rocks display pronounced nonlinear elastic behavior. Here we describe nonlinear response in rock from resonance experiments. Two important features of nonlinear resonant behavior are a shift in resonant frequency away from the linear resonant frequency as the amplitude of the disturbance is increased and the harmonics in the time signal that accompany this shift. We have conducted Young's mode resonance experiments using bars of a variety of rock types (limestone, sandstone, marble, chalk) and of varying diameters and lengths. Typically, samples with resonant frequencies of approximately 0.5–1.5 kHz display resonant frequency shifts of 10% or more, over strain intervals of 10 −7 to 10 −6 and under a variety of saturation conditions and ambient pressure conditions. Correspondingly rich harmonic spectra measured from the time signal progressively develop with increasing drive level. In our experiments to date, the resonant peak is observed to always shift downward (if indeed the peak shifts), indicating a net softening of the modulus with drive level. This observation is in agreement with our pulse mode and static test observations, and those of other researchers. Resonant peak shift is not always observed, even at large drive levels; however, harmonics are always observed even in the absence of peak shift when detected strain levels exceed 10 −7 or so. This is an unexpected result. Important implications for the classical perturbation model approach to resonance results from this work. Observations imply that stress‐strain hysteresis and discrete memory may play an important role in dynamic measurements and should be included in modeling. This work also illustrates that measurement of linear modulus and Q must be undertaken with great caution when using resonance.
• Elastic nonlinearity in rock: On the relative importance between higher-order elastic constants and hysteresis (1995) — Koen Van Den Abeele, Paul Johnson, James Ten Cate — The Journal of the Acoustical Society of America
  Abstract

  Rocks are extremely elastically nonlinear, even at strain as low as 10−7. Recent simulations of dynamic elastic pulsed wave experiments and comparison with static and resonance test predictions revealed that the physical mechanism for nonlinearity in rocks cannot be attributed to higher-order nonlinear coefficients alone. Static stress-strain tests and resonance measurements show in addition an undeniable hysteretic behavior of stress and modulus versus strain. Therefore, hysteresis has been introduced into the dynamic nonlinear wave equation by means of a discontinuous term in the modulus. The new theoretical model is based on four parameters: the first and second nonlinearity constants, attenuation, and hysteresis strength. In doing so, rich harmonic spectra and nonlinear waveforms observed in dynamic pulse mode experiments can be simulated using realistic values of higher-order elastic constants and hysteresis. Furthermore, the model provides characterization criteria for rock types depending on the relative importance of hysteresis and nonlinearity parameters. Chalk, for instance, can have large first and second nonlinearity parameters, because it shows a rich harmonic spectrum but no hysteresis. On the other hand, the nonlinear spectra of several sandstones can be attributed almost entirely to the first nonlinear coefficient and to hysteresis. [Work supported by DOE/OBES/UCal.]
• Observation and implications of nonlinear elastic wave response in rock (1994) — P. A. Johnson, K. R. McCall — Geophysical Research Letters
  Abstract

  Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural discontinuities in rock such as microcracks and grain boundaries. The magnitude of the harmonics created by nonlinear interactions grows linearly with propagation distance in one‐dimensional systems. In the earth, a large nonlinear response may be responsible for significant spectral alteration of a seismic wave at amplitudes and distances currently considered to be within the linear elastic regime. We argue, based on observations at ultrasonic frequencies, that the effect of nonlinear elasticity on seismic wave propagation may be large, and should be considered in modeling.
• Seismological studies at Parkfield III: microearthquake clusters in the study of fault-zone dynamics (1994) — R. Nadeau et al. — International Journal of Rock Mechanics and Mining Sciences &amp; Geomechanics Abstracts
• Elastic wave attenuation and velocity of Berea Sandstone measured in the frequency domain (1993) — T. J. Shankland, P. A. Johnson, T. M. Hopson — Geophysical Research Letters
  Abstract

  Using measurements in the frequency domain we have measured quality factor Q and travel times of direct and side‐reflected elastic waves in a 1.8 m long sample of Berea sandstone. The frequency domain travel time (FDTT) method produces the continuous‐wave (cw) response of a propagating wave by stepwise sweeping frequency of a driving source and detecting amplitude and phase of the received signal in reference to the source. Each separate travel path yields a characteristic repetition cycle in frequency space as its wave vector‐distance product is stepped; an inverse fast Fourier transform (IFFT) reveals the corresponding travel time at the group velocity. Because arrival times of direct and reflected elastic waves appear as spikes along the time axis, travel times can be obtained precisely, and different arrivals can be clearly separated. Q can be determined from the amplitude vs. frequency response of each peak as obtained from a moving window IFFT of the frequency‐domain signal. In this sample at ambient conditions compressional velocity V P is 2380 m/s and Q P is 55.
• Nonlinear elasticity and stress‐induced anisotropy in rocks: reflections on experimental results (1993) — Paul A. Johnson, Patrick N. J. Rasolofosaon — SEG Technical Program Expanded Abstracts 1993
• Nonlinear Waves in Rocks (1993) — Katherine R. McCall, Paul A. Johnson, G. Douglas Meegan — Review of Progress in Quantitative Nondestructive Evaluation
• Observations of nonlinear elastic wave behavior in sandstone (1993) — G. Douglas Meegan et al. — The Journal of the Acoustical Society of America
  Abstract

  An experimental investigation of nonlinear elastic wave behavior was conducted using a 2-m-long cylindrical rod of Berea sandstone in order to study the strong elastic nonlinearity that is characteristic of microcracked materials. Measurements of the displacement field at distance x from the source show rich harmonic content with harmonic amplitudes depending on x, source frequency, and source amplitude. The amplitude of the 2ω harmonic is found to grow linearly with x and as the square of both the source frequency ω and the source amplitude U. This behavior is in agreement with the predictions of nonlinear elasticity theory for a system with cubic anharmonicity. From the measured amplitude of the 2ω harmonic the parameter ‖β‖, a measure of the strength of the cubic anharmonicity, is found to be of order 104 (7.0×103±25%). This value is orders of magnitude greater than that found in ordinary uncracked materials. These results suggest that wave distortion effects due to nonlinear elasticity can be large in seismic wave propagation and significantly influence the relationship of seismic signal to seismic source.
• Finite amplitude wave studies in earth materials. (1992) — P. A. Johnson et al. — The Journal of the Acoustical Society of America
  Abstract

  The highly nonlinear elastic behavior of rock may enable new means of interrogating earth structure, of measuring physical properties, and of modeling the seismic source. Compared to uncracked materials, rocks have a large nonlinear response because they contain numerous microcracks that readily compress under applied stress causing large changes of elastic moduli with pressure. Thus nonlinear effects in rocks can be two orders of magnitude greater than those of the uncracked materials typically studied in nonlinear acoustics. Several areas of nonlinear research are currently being undertaken in these laboratories. First, low-frequency (0.1–100 Hz) attenuation studies using a torsional oscillator show that nonlinear coefficients can be greatly increased by inducing additional microcracks in Sierra White granite. Second, ultrasonic parametric array studies demonstrate that strong difference frequency signal generation can take place inside rock samples. Lastly, energy redistribution of finite amplitude waves may produce progressive changes in observed spectra with distance. If a significant amount of energy is redistributed as a function of distance, then source models (based on assuming linear elastic wave propagation) may be in error. This theoretical and experimental work demonstrates that energy redistribution does indeed take place in rock.
• Frequency-domain travel time (FDTT) measurement of ultrasonic waves by use of linear and nonlinear sources (1992) — Paul A. Johnson, Thomas M. Hopson, Thomas J. Shankland — The Journal of the Acoustical Society of America
  Abstract

  This paper describes a frequency-domain travel time (FDTT) method for measurement of direct and reflected travel times of sound waves based on the change in phase with frequency between a reference signal and a transmitted wave. An ordinary (linear) source can be used for measuring delays over shorter path lengths, and a parametric array (nonlinear) source can be used for measuring delays over longer path lengths. In the ordinary source measurement a reference signal is electronically multiplied with a signal that is time delayed by propagation through a sample. As frequency is incremented stepwise, the relative phase difference generates a corresponding stepwise dc output from the multiplier. For any travel path within the sample, there is a characteristic period of the dc signal whose reciprocal is proportional to the group time delay along the path. If more than one arrival exists, characteristic periods are superposed. An inverse Fourier transform of the frequency signal gives the discrete arrival times for each path. In the parametric measurement, a second electronic multiplier is used to create an electronic difference frequency signal for phase comparison with a wave at the difference frequency created by nonlinear elastic interaction in the material. The FDTT method should be applicable to ultrasonic investigation of material properties, nondestructive evaluation, seismology, sonar, and architectural acoustics.
• Continuous wave phase detection for probing nonlinear elastic wave interactions in rocks (1991) — Paul A. Johnson, Albert Migliori, Thomas J. Shankland — The Journal of the Acoustical Society of America
  Abstract

  A new method that uses nonlinear elastic wave generation to produce a continuous wave (cw) phase measurement from which dimensions or velocities of a body can be obtained is described. Like the technique of standing wave resonance for obtaining sound velocities, this method takes advantage of the high accuracy characteristic of frequency measurements. In the experiment, two intersecting, high-frequency primary signals f1 and f2 are mixed inside a sample, creating a directional beam at the difference frequency Δf=f1−f2. An externally generated, low-pass-filtered Δf signal is electronically mixed with the signal obtained from the sample. As either primary frequency is swept, the dc component from the mixer varies between relative maximum and minimum values at characteristic frequency intervals depending on the phase differences. The resulting interference signal can be used to calculate the distance from the mixing volume in the sample to the detector and to the two primary signal transmitters, providing that a single characteristic distance and wave velocities are known. The reverse experiment is determining velocities from known dimensions.
• Comparison of audible sound transmission with ultrasound in screening for congenital dislocation of the hip (1990) — M.H. Stone et al. — The Lancet
• Cross-borehole compressional wave imaging of unconsolidated sediments (1990) — T.H. Larkin et al. — IEEE Transactions on Geoscience and Remote Sensing
• Determination of fault planes at Coalinga, California, by analysis of patterns in aftershock locations (1989) — Michael Fehler, Paul Johnson — Journal of Geophysical Research: Solid Earth
  Abstract

  The May 2, 1983, Coalinga, California, earthquake was not anticipated because it took place along a previously unrecognized fault concealed beneath an anticline, in a region that had little historic seismicity. The main shock hypocenter was at 10 km depth, and faulting did not break the surface. There has been considerable controversy about which of the nodal planes from the main shock fault plane solution was the slip plane. Conflicting results from geodetic, geologic, and aftershock data imply that slip occurred along one or the other or both nodal planes. The aftershock zone is large; several planar features within the aftershock zone indicate that faulting was complex. To delineate the planes of slip, we applied the three‐point method, a statistical technique by which event planes can be determined from aftershock locations. We obtained several important results from our study. First, we identified a number of planes using locations of aftershocks, some of which have not been previously identified from visual inspection of the aftershock locations. Second, the method allows us to choose slip planes by associating three‐point planes with fault plane solutions based on proximity and similar orientation. Finally, three of the planes identified by the method intersect near the main shock hypocenter, making it difficult to determine which plane is the main shock slip plane. Nevertheless, aftershocks during the first 24 hours after the main shock clearly define the high‐angle NE dipping nodal plane, whereas few aftershocks were located along the conjugate plane. Assuming that the aftershocks took place along the rupture zone, we conclude that slip during the main shock occurred predominantly along the high‐angle NE dipping plane from the fault plane solution for this event.
• Conversion of borehole stoneley waves to channel waves in coal (1987) — Paul A. Johnson, James N. Albright — SEG Technical Program Expanded Abstracts 1987
• Fisher Folk: Two Communities on Chesapeake Bay (1987) — Paula Johnson, Carolyn Ellis — The Journal of American Folklore
• In‐situ measurement of weak transverse isotropy within the mesa verde formation (1987) — W. Scott Phillips, Paul A. Johnson — SEG Technical Program Expanded Abstracts 1987
• Nonlinear generation of elastic waves in crystalline rock (1987) — Paul A. Johnson et al. — Journal of Geophysical Research: Solid Earth
  Abstract

  The nonlinear interaction of two elastic waves at frequencies ƒ 1 and ƒ 2 in an elastically nonlinear material can give rise to a collimated wave at the difference frequency ƒ 1 ‐ ƒ 2 . Because the amplitude of a difference frequency beam is proportional to the degree of elastic nonlinearity of the material through which it passes, amplitude should be higher in a material containing microcracks such as rock than it is in uncracked materials such as metals, single crystals, or water in which nonlinear elastic interactions have previously been observed. The “nonlinear signal” is important for investigating the nonlinear properties of rocks. Such a beam has already proved useful as a low‐frequency acoustic source in water and may ultimately be useful in geophysical exploration. In this paper, our observations of nonlinear signal generation in experiments with crystalline rocks are presented. Three criteria must be fulfilled in such experiments to establish that nonlinear interactions take place in the rock and not in the associated experimental apparatus: (1) The frequency of the observed nonlinear signal must precisely equal the difference frequency Δƒ = ƒ 1 ‐ ƒ 2 , (2) the amplitude of the nonlinear signal must be proportional to the product of the amplitudes of the primary beams, and (3) the trajectory of the nonlinear signal, which is a function of the input trajectories, wave types, frequencies, and rock velocities, must match that predicted by theory. We observed signals that satisfy the above three criteria in the frequency range from 0.1 to 1.0 MHz.
• In-Situ Physical Properties Using Crosswell Acoustic Data (1985) — P. A. Johnson, J. N. Albright — SPE/DOE Low Permeability Gas Reservoirs Symposium
  Abstract

  Abstract Crosswell acoustic surveys enable the in situ measurements of elastic moduli, Poisson's ratio, porosity, and apparent seismic Q of gas-bearing low-permeability formations represented at the Department of Energy Multi-Well Experiment (MWX) site near Rifle, Colorado. These measurements, except for Q, are compared with laboratory measurements on core taken from the same depths at which the crosswell measurements are made. Seismic Q determined in situ is compared to average values for sandstone. Porosity was determined from crosswell data using the empirical relationship between acoustic velocity, porosity, and effective pressure developed by Domenico. in situ porosities are significantly greater than the core-derived values. Sources of the discrepancy may arise from (i) the underestimation of porosity that can result when Boyle's Law measurements are made on low-permeability core and (ii) the application of Dominico's relationship, which is developed for clean sands, to the mixed sandstone and shale lithologies represented at the MWX site. Values for Young's modulus and Poisson's ratio derived from crosswell measurements are comparable to values obtained from core. Apparent seismic Q measured in situ between wells is lower than Q measured on core and clearly shows the heterogeneity of sandstone deposited in a fluvial environment.
• Effects of long-term exposure of tuffs to high-level nuclear waste-repository conditions. Preliminary report (1982) — J. Blacic et al. — Los Alamos National Lab., NM (USA), 1982
• Seismic velocity and Q‐structure of the upper mantle lid and low velocity zone for the Eastern Great Basin (1980) — K. H. Olsen, L. W. Braile, P. A. Johnson — Geophysical Research Letters
  Abstract

  A 100‐km‐long record section of NTS explosions recorded in the eastern Snake River Plains lpar;7°&lt;Δ&lt;8°) shows the cusp of critical refractions from the steepened P velocity gradient at the bottom of the upper mantle LVZ. Synthetic seismograms calculated with a modified reflectivity program have been used to derive a regional velocity model of the upper mantle beneath the eastern Great Basin. The model suggests that observed very weak P n arrivals are due to a slight negative velocity gradient below the Moho and that no high velocity mantle lid exists in this region.
• Palaeomagnetic Studies of the Caerfai Series and the Skomer Volcanic Group (Lower Palaeozoic, Wales) (1971) — J. C. Briden, J. Irons, P. A. Johnson — Geophysical Journal International