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Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multistage Training
The recent development of neural operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this article, we use the Fourier neural operator (FNO) model to directly solve the 3D Helmholtz wave equation for fast seismic ground-motion simulations on different frequencies and show the frequency bias of the FNO model, that is, it learns the lower frequencies better comparing to the higher frequencies. To reduce the frequency bias, we adopt the multistage FNO training, that is, after training a stage 1 FNO model for estimating the ground motion, we use a second FNO model as the stage 2 to learn from the residual, which greatly reduced the errors on the higher frequencies. By adopting this multistage training, the FNO models show reduced biases on higher frequencies, which enhanced the overall results of the ground-motion simulations. Thus the multistage training FNO improves the accuracy and realism of the ground-motion simulations.
Seismic Elastic Double-Beam Characterization of Faults and Fractures for CO₂ Storage Site Selection
Site characterization for underground injection and storage of gigatonne-scale CO₂ requires reliable and cost-effective methods to detect and characterize faults and fractures and to assess their stress state and fault activation potential. This is critical, as wastewater injection and disposal have been shown to activate faults and induce earthquakes, and CO₂ leakage remains a key concern for long-term storage. In this project, we developed seismic methods to detect and characterize large-scale sedimentary and crystalline basement faults and associated small-scale fractures below conventional seismic imaging resolution using multicomponent (9C) surface seismic data. Machine learning was used to automatically interpret large-scale faults, providing key information for estimating the maximum magnitude of potential induced earthquakes. High-fidelity imaging was achieved by exploiting redundancy across multiple elastic wave modes, where independent images from different modes and frequencies cross-validate each other. We also used our nonlinear signal comparison (NLSC) method for ground roll removal, improving data quality in complex near-surface conditions. The methods were validated using field data acquired in central Montana. Results show that basement faults extend into the sedimentary section and that small-scale fractures are widespread above the basement. The inferred stress orientation is consistent with regional stress data, and the estimated maximum induced earthquake magnitude is small (Mw ~2.3). The developed workflow provides a practical approach for fault and fracture characterization and for assessing induced seismicity and leakage risk. It is directly applicable to CO₂ storage site selection and to other subsurface systems.
Ultrasonic waveguide for improved ultrasonic thermometry
An improved ultrasonic waveguide for an ultrasonic thermometry system is provided. The waveguide includes a series of sensing zones, each of which is tuned to a specific narrow frequency band. The waveguide is acoustically coupled to a transducer, which launches a longitudinal elastic wave of desired waveform and frequency. The wave propagates down the waveguide, and is reflected from the sensing zone that is tuned to that frequency. Each sensing zone is designed to be highly reflective to a narrow frequency band while being transparent to other frequencies.
Low-phase-noise surface-acoustic-wave oscillator using an edge mode of a phononic band gap
Low-phase-noise microwave-frequency integrated oscillators provide compact solutions for various applications in signal processing, communications, and sensing. Surface acoustic waves (SAWs), featuring orders-of-magnitude shorter wavelength than electromagnetic waves at the same frequency, enable integrated microwave-frequency systems with much smaller footprint on chip. SAW devices also allow higher-quality (Q) factors than electronic components at room temperature. Here, we demonstrate a low-phase-noise gigahertz-frequency SAW oscillator on 128°Y-cut lithium niobate, where the SAW resonator occupies a footprint of 0.05 mm 2 . Leveraging phononic crystal band-gap-edge modes to balance between Q factors and insertion losses, our 1-GHz SAW oscillator features a low phase noise of -132.5 dBc/Hz at a 10-kHz offset frequency and an overlapping Hadamard deviation of 6.5 × 10 -10 at an analysis time of 64 ms. The SAW resonator-based oscillator holds high potential in developing low-noise sensors and acousto-optic integrated circuits.
Thermal modulation of nonlinear ultrasonic waves for nondestructive evaluation of elastic materials
Temperature variation is often considered an undesirable factor in ultrasonic testing, as wave velocity is highly sensitive to thermal fluctuations. However, completely eliminating the temperature effect is difficult, particularly in tests requiring precise velocity measurements. Recently, a method called Thermal Modulation of Nonlinear Ultrasonics (TMNL) has been developed. Instead of eliminating the thermal effect, the TMNL method leverages the temperature variation as a driving force to stimulate the nonlinear response of the medium and modulate the ultrasonic waves propagating in it. These modulated waves can then be used to evaluate the nonlinear behaviours of the test medium. This paper presents a focused review of the TMNL technique, including its theoretical foundations, particularly the conceptual challenges in integrating thermal effects into classical acoustoelastic theory, and recent applications in non-destructive evaluation (NDE). Three case studies are presented to demonstrate TMNL’s application in detecting microcracking in concrete, assessing ageing in polymer materials, and enabling temperature compensation in acoustoelastic tests. In conclusion, the review also summarises related studies, including photothermal crack modulation, and discusses current limitations and future directions of TMNL in elastic media.
Evaluating Physics-Informed Neural Network Performance for Seismic Discrimination between Earthquakes and Explosions
In this article, we evaluate adding a weak physics constraint, that is, a physics‐based empirical relationship, to the loss function with a physics‐informed manner in local distance explosion discrimination in the hope of improving the generalization capability of the machine learning (ML) model. We compare the proposed model with the two‐branch model we previously developed, as well as with a pure data‐driven model. Unexpectedly, the proposed model did not consistently outperform the pure data‐driven model. By varying the level of inconsistency in the training data, we find this approach is modulated by the strength of the physics relationship. In conclusion, this result has important implications for how to best incorporate physical constraints in ML models.
Denoising Seismograms in the Time Domain Using a Deep Learning Model
Deep learning has emerged as a transformative tool for enhancing the extraction of reliable information from seismograms, addressing the increasing demand for precise and efficient seismic data analysis. We introduce an innovative encoder–decoder deep learning model, named WaveDenoiser, designed for noise reduction in the time domain, thereby eliminating the need for spectrogram computations that have been used for existing deep learning tools and significantly improving processing speed. Utilizing the benchmark dataset that is Stanford Earthquake Dataset, we developed three models of varying sizes: base, medium, and large. Notably, the large (referred to as WaveDenoiser) model demonstrated superior performance, achieving a median signal‐to‐noise ratio improvement of 8.8 dB on in‐distribution unseen data (in the same geographic region) and 7.7 dB on out‐distribution unseen data (in a new geographic region), outpacing both the base and medium models. Further evaluation of the WaveDenoiser model revealed a reduction in median arrival‐time errors by 0.02 s for P waves and 0.01 s for S waves when processing waveforms prior to phase picking using PhaseNet on in‐distribution unseen data. When tested on out‐distribution unseen data, the model also effectively reduced the P‐wave median arrival‐time error by 0.02 and 0.01 s in median arrival‐time error for S waves. Importantly, the application of WaveDenoiser resulted in a significant reduction of phase picking outliers by 1.1% to 3.6% for both P and S waves. In addition, we achieved over five times acceleration in processing speed compared with the seisBench implementation of DeepDenoiser. Our findings underscore the potential of WaveDenoiser as a powerful tool for improving seismic data analysis and processing efficiency.
Evaluation of Station Performance of the Idaho National Laboratory Seismic Monitoring Network Using Network Detection Thresholds
The Idaho National Laboratory (INL) Seismic Monitoring Network is located in eastern Idaho and monitors a portion of the intermountain seismic belt. It has been in place for 50 yr and has undergone several major changes, the most recent of which has been the transition to the Antelope real‐time acquisition system and the implementation of automatic phase picking algorithms to aid in analysis. This study discusses the efforts to evaluate the performance of the INL seismic monitoring network (and other surrounding stations) using the new real‐time acquisition system. The method outlined by Wilson et al. (2021) is used to develop an empirical relationship between the observability of local earthquakes as a function of magnitude and distance. This relationship is used to produce detection thresholds for Pwaves for all stations of interest. The INL seismic network has two main goals: monitor tectonic‐and volcanic‐related events and measure ground motions for input into seismic hazard analysis. Because of these two overall objectives, several seismic stations have been installed near critical facilities and, therefore, are not as quiet as stations that are used primarily for earthquake detection. This is reflected in their detection thresholds, which are much smaller for stations away from facilities. This study shows that the INL Seismic Monitoring Network is able to detect earthquakes near INL facilities with M L > 1.2, with redundancies built in to ensure this sensitivity even if data became unavailable from some stations. This study also shows “holes” in the monitoring network where the detection of smaller earthquakes is highly dependent on sparsely placed seismic stations. In conclusion, the results of this study will be used to govern plans for expansion of earthquake monitoring in Idaho and the surrounding region and to fine‐tune the detection thresholds for individual stations.
Isochoric Phase Transitions in Tin
Any sufficiently rapid physical process, such as a phase transition, proceeds isochorically (at constant density) because elastic relaxation is not instanta neous; it takes a finite time for an elastic relaxation wave to cross a finite specimen. If the post-transition state is less dense than the pre-transition state then the material is left in compression and will relax by expansion. The resulting rarefaction waves will interact and put the sample into tension; it may fracture. A similar process limits the amplitude to which piezoelectrics may be driven without failure, although the elastic state is more complex than isotropic expansion.
Deep Learning for Full Waveform Inversion of Elastic Active-Source Seismic Data to Estimate P-Wave Velocity Models
Seismic imaging methods are critical for Global Security and Energy & Homeland Security missions and activities that rely on subsurface characterization, but traditional methods remain computationally expensive and require significant labor hours and expertise to execute. Within the past few years, machine learning (ML), namely deep learning (DL), has been used to develop data-driven end-to-end full waveform inversion (FWI) methods to estimate 2D P-wave velocity (Vp) models in a fraction of the time as conventional FWI. These methods, however, are trained on simplistic acoustic wave seismic data and Vp models that are not realistic nor representative of real-world observations, leaving a large gap between the state-of-the-art and deployable, feasible, and practical DL FWI methods. Here, we generate a synthetic active-source, 3D, elastic wave seismic data set and a variety of Vp models with realistic geologic structure for training DL FWI methods. We evaluate six different methods that have performed well for acoustic DL FWI or medical imaging tasks using our more realistic dataset. We find that these six trained models do not match the performance of published acoustic end-to-end DL FWI methods, indicating more training data may be needed, physics may need to be incorporated to achieve good accuracy at the sacrifice of the end-to-end advantage, and/or novel methods need to be developed to enable end-to-end DL FWI methods to perform well for real-world seismic data.
Utah FORGE: Direct Shear Test Data for Investigating Seismic Precursors to Shear Failure of Fractures
This dataset includes results of direct shear tests to investigate the mechanical and geophysical response of dry and saturated fractures in Indiana limestone and Sierra White granite. Direct shear tests were performed on tensile-induced fractures in Indiana limestone and Sierra White granite in a custom water-pressurized chamber. The provided Excel files include the representative seismic wave signals and the normalized wave amplitudes of ultrasonic wave transducers. A link to the published journal article presenting the data and describing the experiment in detail is provided as well.
Cyclically symmetric radially self-similar phononic pseudocrystal isolator for broadband, ultrasonic vibration bandstop filtering
A 2D phononic pseudocrystal isolator exhibiting cyclic symmetry and radial self-similarity is measured and demonstrated to block a wide range of ultrasonic vibration. Measurements of longitudinal and shear wave blocking effects are made and compared with computational results. The use of the bandgap edge ratio is recommended for quantifying suppression in very-wide-bandgap materials. In conclusion, the upper-to-lower suppression edge frequency ratios of 3–4 are remarkably large for shear waves and even larger for longitudinal waves upper-to-lower suppression ratio (13 at 5 dB), such that 92.5% of frequencies in that range experience ≥ 5 dB of suppression.
Seafloor Seismic Noise Patterns Across the Pacific Basin
Seismic hazard monitoring and global tomography efforts are improved by recording signals at a variety of distances and azimuths to maximize subsurface sampling. Although seismic networks provide good to excellent coverage on land, seafloor stations are still sparse. Inclusion of ocean-based data would greatly improve the global coverage of seismic networks, but the use of seafloor seismic data to complement land-based detection and characterization of events is complicated by the generally much higher ambient noise level in the ocean compared to that observed on land. This noise is driven primarily by sea surface waves and tides, but how seismic noise levels vary with location in the oceans is not well described. Here, in this work, we analyze the relationship between ocean surface wave height and seismic noise in the 0.4–4 Hz frequency band at ocean-bottom seismometer deployments across the Pacific basin. We find that a noise-to-responsiveness ratio (NRR)—the median noise level at a station divided by its sea surface wave height responsiveness—correlates negatively with detection success for large teleseismic earthquakes. Stations that are close to land, with relatively shallow ocean and low wind speed, often have lower NRR than open-ocean stations, but the connection between geographic location and earthquake detection success is imperfect.
Spatial description of dislocation nucleation in the shock response of single-crystal aluminum
Nonequilibrium molecular dynamics simulations of shock loaded single-crystal Al in the $\langle$100$\rangle$, $\langle$110$\rangle$, $\langle$111$\rangle$, and $\langle$123$\rangle$ orientations are conducted to study elastic and plastic shockwave formation and details associated with dislocation activity. A computer vision-based approach is implemented to capture the presence of dislocations and describe their spatial characteristics in the zone of nucleation behind the propagating shockwave. The methodology developed relies on the sequences of images extracted during shock loading that show dislocation activity within a cross section of the sample. Results reveal that the spacing between activated slip systems is orientation dependent and exhibits a modest reduction for the $\langle$100$\rangle$ and $\langle$111$\rangle$ orientations as shock pressure increases. Comparisons are made to existing theoretical models. Such relationships between shock pressure and dislocation activity, extracted from molecular dynamics simulations, can be used to inform higher length scale simulations or modeling of dislocation-based plasticity during shock.
A limit to strong shock behavior in the dynamic response of matter at pressure
Solids under high pressures experience a series of regimes, where their microstructure adapts to the applied compression and these key transitions are discussed in this paper. As strain increases, new forces emerge at extreme pressures. A previous study introduced the concept of the weak shock limit (WSL), at which the ambient theoretical shear strength is overcome. Above the WSL, further deformation under strong shock conditions results in electrons occupying higher energy levels as strain increases. As pressure rises further, shock melting occurs in the material and at around three times this melting pressure, the strong shock limit is reached where the driving physics under pressure switches, with electrons forced into higher energy states. This leads to significant reduction in their compressibility due to changes in electronic structure and developing electron degeneracy pressures. A derivation for conditions at this state is presented, which indicates that a dependence of the threshold pressure on the free electron number density defines the limit observed. This correlation suggests that ambient material moduli govern material compression up to nearly 50% strain. These observations show that models should account for different behaviors as dominant physics changes in each regime accessed as shock pressure increases.
Revealing Defect-Seeded and Interfacial Generation Mechanisms of Photoinduced Coherent Phonons with 4D Ultrafast Electron Microscopy
Ultrafast photoexcitation of coherent phonons is driven by an impulsive, collective displacement of constituent atoms from their average equilibrium lattice positions [1]. Models describing the generation of coherent acoustic modes typically invoke the creation of an anisotropic strain profile arising from the relatively instantaneous absorption of an ultrafast laser pulse [2]. If the skin depth is shallow relative to the specimen thickness, a steep tensile strain gradient perpendicular to the surface ($\frac{∂ε}{∂z}$) results. Initial relaxation occurs via rapid contraction of the surface layers followed by subsequent coherent oscillations of the lattice and launch of a train of coherent elastic strain waves [i.e., coherent acoustic phonons (CAPs)]. Macroscopically, responses are generally well-described by constitutive relations as gleaned from data gathered using ultrasonic methods or ultrafast spectroscopies. Furthermore, at the atomic to nanoscale level, individual lattice discontinuities and their impact on CAP behaviors can be modeled using multiscale methods [3,4]. Further, average unit-cell level responses on ultrafast timescales can be probed using femtosecond electron and X-ray scattering [5,6].
Geometric Interpretation of the Cluster Location Problem Part I: Theory
We present a new framing of the seismic location problem using principles drawn from differential geometry. Our interpretation relies upon the common assumption that travel times observed across a network are continuous, differentiable functions of source location. In consequence, travel‐time functions constitute a differentiable map between the source region and a Riemannian manifold. The manifold is said to be the image of the source region embedded in a generally high‐dimension travel‐time vector space. A cluster of events in the source region has an image of discrete points on the manifold, that, except in the simplest cases, cannot be viewed directly. However, it is possible to project the image of a cluster into a tangent space of the manifold for direct visualization. The projection operator can be computed directly from the data without a velocity model, but produces a distorted rendering of the cluster geometry. With a model we can predict the distortions and correct them to estimate cluster geometry. We develop these points with the simplest possible example, one for which direct visualization of the manifold is possible, using the example as an introduction to the relevant concepts from differential geometry in a familiar setting. The tangent space, a local linearization of the manifold, plays a key role. We develop a metric to estimate the limits of linearization, that is, to determine when the curvature of the manifold invalidates the linear assumption. We also examine the interplay of model error, inadequate network geometry, and pick error. We then generalize our results from the simple case to the general case of 3D source regions observed by general networks. Although we do suggest a new “project and correct” method for location, we do not develop it into a practical algorithm. In conclusion, our intention rather is to highlight new analytical methods grounded in differential geometry.