arXiv subjects

Robert W. Clayton

Publications and source records attributed to Robert W. Clayton.

11 recordsLinked to original sources

arXiv2026

Enforcing Reciprocity in Operator Learning for Seismic Wave Propagation

Accurate and efficient wavefield modeling underpins seismic structure and source studies. Traditional methods comply with physical laws but are computationally intensive. Data-driven methods, while opening new avenues for advancement, have yet to incorporate strict physical consistency. The principle of reciprocity is one of the most fundamental physical laws in wave propagation. We introduce the Reciprocity-Enforced Neural Operator (RENO), a transformer-based architecture for modeling seismic wave propagation that hard-codes the reciprocity principle. The model leverages the cross-attention mechanism and commutative operations to guarantee invariance under swapping source and receiver positions. Beyond improved physical consistency, the proposed architecture supports simultaneous realizations for multiple sources. This yields an order-of-magnitude inference speedup at a similar memory footprint over a conventional neural operator on a realistic multi-source configuration. We demonstrate the functionality using the reciprocity relation for particle velocity fields under single forces. This architecture is also applicable to pressure fields under dilatational sources and travel-time fields governed by the eikonal equation, paving the way for encoding more complex reciprocity relations.

physics.geo-ph↗

arXiv2026

Receiver Functions in the San Fernando Valley, California: Graph-Regularized Bayesian Approach for Gravity-Informed Mapping

The San Fernando Valley (SFV) in Southern California is a complex sedimentary basin whose shape strongly influences ground shaking. We develop a fully quantitative, probabilistic graph-regularized inference model that integrates both gravity and receiver function (RF) constraints and evaluate its ability to determine the basin's shape. The sediment-basement interface in single-station RFs is often difficult to interpret due to scattering and noise, which can render isolated stations unusable. By using RFs from a dense seismic array and incorporating gravity, we address the issue of non-uniqueness in converting the times of RF phases to layer thickness by comparing the predicted gravity to observations at each station. In areas where the density contrast may change, Bayesian inference with a graph Laplacian allows us to determine the effective density contrast by taking into account its neighbors' picks and densities. This method promotes spatial smoothness between neighboring stations, while preserving sharp contrasts in locations supported by the RF and gravity data. We applied this method to a dataset that was acquired in fall 2023, when 140 nodes were installed in the SFV. Our results show the deep Sylmar sub-basin, the San Fernando sub-basin, and the Leadwell high found in a previous study (Juárez-Zúñiga and Persaud, 2025), and our results also show good agreement with the industry seismic reflection profiles across the valley. This method demonstrates how to incorporate gravity with lateral density variations into receiver function interpretation to better map interfaces in the subsurface.

physics.geo-ph↗

arXiv2025

Ambient Noise Full Waveform Inversion with Neural Operators

Numerical simulations of seismic wave propagation are crucial for investigating velocity structures and improving seismic hazard assessment. However, standard methods such as finite difference or finite element are computationally expensive. Recent studies have shown that a new class of machine learning models, called neural operators, can solve the elastodynamic wave equation orders of magnitude faster than conventional methods. Full waveform inversion is a prime beneficiary of the accelerated simulations. Neural operators, as end-to-end differentiable operators, combined with automatic differentiation, provide an alternative approach to the adjoint-state method. State-of-the-art optimization techniques built into PyTorch provide neural operators with greater flexibility to improve the optimization dynamics of full waveform inversion, thereby mitigating cycle-skipping problems. In this study, we demonstrate the first application of neural operators for full waveform inversion on a real seismic dataset, which consists of several nodal transects collected across the San Gabriel, Chino, and San Bernardino basins in the Los Angeles metropolitan area.

physics.geo-ph↗

arXiv2025

Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multi-Stage 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 paper, 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, i.e. it learns the lower frequencies better comparing to the higher frequencies. To reduce the frequency bias, we adopt the multi-stage FNO training, i.e., after training a 1st stage FNO model for estimating the ground motion, we use a second FNO model as the 2nd stage to learn from the residual, which greatly reduced the errors on the higher frequencies. By adopting this multi-stage training, the FNO models show reduced biases on higher frequencies, which enhanced the overall results of the ground motion simulations. Thus the multi-stage training FNO improves the accuracy and realism of the ground motion simulations.

physics.geo-ph↗

arXiv2024

Imaging the Northern Los Angeles Basins with Autocorrelations

We show reflectivity cross-sections for the San Gabriel, Chino, and San Bernardino basins north of Los Angeles, California determined from autocorrelations of ambient noise and teleseismic earthquake waves. These basins are thought to channel the seismic energy from earthquakes on the San Andreas Fault to Los Angeles and a more accurate model of their depth is important for hazard mitigation. We use the causal side of the autocorrelation function to determine the zero-offset reflection response. To minimize the smoothing effect of the source time function, we remove the common mode from the autocorrelation in order to reveal the zero-offset reflection response. We apply this to 10 temporary nodal lines consisting of a total of 758 geophones with an intraline spacing of 250-300 m. We also show that the autocorrelation function from teleseismic events can provide illumination of subsurface that is consistent with ambient noise. Both autocorrelation results compare favorably to receiver functions.

physics.geo-ph↗

arXiv2023

Imaging urban hidden faults with ambient noise recorded by dense seismic arrays

The identification of preexisting near-surface faults represents a piece of crucial information needed to correctly assess the seismic hazard of any area. The mapping of these structures is particularly challenging in densely populated and heavily urbanized areas. We use ambient seismic noise recorded by a dense array in Seal Beach, California, to image shallow fault lines via a reflected surface wave analysis. Our results highlight the presence of previously unknown shallow faults that correlate remarkably well with shallow seismicity and active survey images.

physics.geo-ph↗

arXiv2023

Deep Neural Helmholtz Operators for 3D Elastic Wave Propagation and Inversion

Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a U-shaped neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.

physics.geo-ph↗

arXiv2023

Rapid Seismic Waveform Modeling and Inversion with Neural Operators

Seismic waveform modeling is a powerful tool for determining earth structure models and unraveling earthquake rupture processes, but it is usually computationally expensive. We introduce a scheme to vastly accelerate these calculations with a recently developed machine learning paradigm called the neural operator. Once trained, these models can simulate a full wavefield at negligible cost. We use a U-shaped neural operator to learn a general solution operator to the 2D elastic wave equation from an ensemble of numerical simulations performed with random velocity models and source locations. We show that full waveform modeling with neural operators is nearly two orders of magnitude faster than conventional numerical methods, and more importantly, the trained model enables accurate simulation for velocity models, source locations, and mesh discretization distinctly different from the training dataset. The method also enables convenient full-waveform inversion with automatic differentiation.

physics.geo-ph↗

arXiv2022

Accelerating Time-Reversal Imaging with Neural Operators for Real-time Earthquake Locations

Earthquake hypocenters form the basis for a wide array of seismological analyses. Pick-based earthquake location workflows rely on the accuracy of phase pickers and may be biased when dealing with complex earthquake sequences in heterogeneous media. Time-reversal imaging of passive seismic sources with the cross-correlation imaging condition has potential for earthquake location with high accuracy and high resolution, but carries a large computational cost. Here we present an alternative deep-learning approach for earthquake location by combining the benefits of neural operators for wave propagation and time reversal imaging with multi-station waveform recordings. A U-shaped neural operator is trained to propagate seismic waves with various source time functions and thus can predict a backpropagated wavefield for each station in negligible time. These wavefields can either be stacked or correlated to locate earthquakes from the resulting source images. Compared with other waveform-based deep-learning location methods, time reversal imaging accounts for physical laws of wave propagation and is expected to achieve accurate earthquake location. We demonstrate the method with the 2D acoustic wave equation on both synthetic and field data. The results show that our method can efficiently obtain high resolution and high accuracy correlation-based time reversal imaging of earthquake sources. Moreover, our approach is adaptable to the number and geometry of seismic stations, which opens new strategies for real-time earthquake location and monitoring with dense seismic networks.

physics.geo-ph↗

arXiv2021

Seismic wave propagation and inversion with Neural Operators

Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations must be performed when the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called Neural Operator. A trained Neural Operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train Neural Operators on an ensemble of simulations performed with random velocity models and source locations. As Neural Operators are grid-free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the method's applicability to seismic tomography, using reverse mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.

physics.geo-ph↗

arXiv2020

Extracting dispersion curves from ambient noise correlations using deep learning

We present a machine-learning approach to classifying the phases of surface wave dispersion curves. Standard FTAN analysis of surfaces observed on an array of receivers is converted to an image, of which, each pixel is classified as fundamental mode, first overtone, or noise. We use a convolutional neural network (U-net) architecture with a supervised learning objective and incorporate transfer learning. The training is initially performed with synthetic data to learn coarse structure, followed by fine-tuning of the network using approximately 10% of the real data based on human classification. The results show that the machine classification is nearly identical to the human picked phases. Expanding the method to process multiple images at once did not improve the performance. The developed technique will faciliate automated processing of large dispersion curve datasets.

cs.LG↗