Seismic Wave Propagation and Inversion with Neural Operators

Abstract 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 whenever 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.

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A Smoothing Scheme for Seismic Wave Propagation Simulation with a Mixed FEM of Diffusionized Wave Equation

International Journal of Computational Methods ◽

10.1142/s0219876221500614 ◽

2021 ◽

pp. 2150061

Author(s):

Ryuta Imai ◽

Naoki Kasui ◽

Masayuki Yamada ◽

Koji Hada ◽

Hiroyuki Fujiwara

Keyword(s):

Wave Propagation ◽

Wave Equation ◽

Seismic Wave ◽

Time Integration ◽

Coupled System ◽

Seismic Wave Propagation ◽

Implicit Time ◽

Integration Scheme ◽

Weak Formulation ◽

Mixed Fem

In this paper, we propose a smoothing scheme for seismic wave propagation simulation. The proposed scheme is based on a diffusionized wave equation with the fourth-order spatial derivative term. So, the solution requires higher regularity in the usual weak formulation. Reducing the diffusionized wave equation to a coupled system of diffusion equations yields a mixed FEM to ease the regularity. We mathematically explain how our scheme works for smoothing. We construct a semi-implicit time integration scheme and apply it to the wave equation. This numerical experiment reveals that our scheme is effective for filtering short wavelength components in seismic wave propagation simulation.

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Optimal Third-Order Symplectic Integration Modeling of Seismic Acoustic Wave Propagation

Bulletin of the Seismological Society of America ◽

10.1785/0120190193 ◽

2020 ◽

Vol 110 (2) ◽

pp. 754-762 ◽

Cited By ~ 1

Author(s):

Chuan Li ◽

Jianxin Liu ◽

Bo Chen ◽

Ya Sun

Keyword(s):

Wave Propagation ◽

Wave Equation ◽

Acoustic Wave ◽

Seismic Wave ◽

Truncation Error ◽

Seismic Wave Propagation ◽

Symplectic Integrator ◽

Third Order ◽

The Third ◽

2D And 3D

ABSTRACT Seismic wavefield modeling based on the wave equation is widely used in understanding and predicting the dynamic and kinematic characteristics of seismic wave propagation through media. This article presents an optimal numerical solution for the seismic acoustic wave equation in a Hamiltonian system based on the third-order symplectic integrator method. The least absolute truncation error analysis method is used to determine the optimal coefficients. The analysis of the third-order symplectic integrator shows that the proposed scheme exhibits high stability and minimal truncation error. To illustrate the accuracy of the algorithm, we compare the numerical solutions generated by the proposed method with the theoretical analysis solution for 2D and 3D seismic wave propagation tests. The results show that the proposed method reduced the phase error to the eighth-order magnitude accuracy relative to the exact solution. These simulations also demonstrated that the proposed third-order symplectic method can minimize numerical dispersion and preserve the waveforms during the simulation. In addition, comparing different central frequencies of the source and grid spaces (90, 60, and 20 m) for simulation of seismic wave propagation in 2D and 3D models using symplectic and nearly analytic discretization methods, we deduce that the suitable grid spaces are roughly equivalent to between one-fourth and one-fifth of the wavelength, which can provide a good compromise between accuracy and computational cost.

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Seismic Wave Propagation and Basin Amplification in the Wasatch Front, Utah

Seismological Research Letters ◽

10.1785/0220200449 ◽

2021 ◽

Author(s):

Morgan P. Moschetti ◽

David Churchwell ◽

Eric M. Thompson ◽

John M. Rekoske ◽

Emily Wolin ◽

...

Keyword(s):

Wave Propagation ◽

Ground Motion ◽

Seismic Wave ◽

Seismic Velocity ◽

Site Response ◽

Ground Motions ◽

Seismic Wave Propagation ◽

Velocity Models ◽

Ground Motion Variability ◽

Wasatch Front

Abstract Ground-motion analysis of more than 3000 records from 59 earthquakes, including records from the March 2020 Mw 5.7 Magna earthquake sequence, was carried out to investigate site response and basin amplification in the Wasatch Front, Utah. We compare ground motions with the Bayless and Abrahamson (2019; hereafter, BA18) ground-motion model (GMM) for Fourier amplitude spectra, which was developed on crustal earthquake records from California and other tectonically active regions. The Wasatch Front records show a significantly different near-source rate of distance attenuation than the BA18 model, which we attribute to differences in (apparent) geometric attenuation. Near-source residuals show a period dependence of this effect, with greater attenuation at shorter periods (T<0.5 s) and a correlation between period and the distance over which the discrepancy manifests (∼20–50 km). We adjusted the recorded ground motions for these regional path effects and solved for station site terms using linear mixed-effects regressions, with groupings for events and stations. We analyzed basin amplification by comparing the site terms with the basin geometry and basin depths from two seismic-velocity models for the region. Sites over the deeper parts of the sedimentary basins are amplified by factors of 3–10, relative to sites with thin sedimentary cover, with greater amplification at longer periods (T≳1 s). Average ground-motion variability increases with period, and long-period variability exhibits a slight increase at the basin edges. These results indicate regional seismic wave propagation effects requiring further study, and potentially a regionalized GMM, as well as highlight basin amplification complexities that may be incorporated into seismic hazard assessments.

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A modified wave equation with diffusion effects and its application as a smoothing scheme for seismic wave propagation simulations

International Journal of Computer Mathematics ◽

10.1080/00207160.2018.1463440 ◽

2018 ◽

Vol 96 (5) ◽

pp. 935-949

Author(s):

Ryuta Imai ◽

Kei Takamuku ◽

Hiroyuki Fujiwara

Keyword(s):

Wave Propagation ◽

Wave Equation ◽

Seismic Wave ◽

Seismic Wave Propagation ◽

Diffusion Effects

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Centroid moment tensor inversions of offshore earthquakes using a three-dimensional velocity structure model: slip distributions on the plate boundary along the Nankai Trough

Geophysical Journal International ◽

10.1093/gji/ggaa238 ◽

2020 ◽

Vol 222 (2) ◽

pp. 1109-1125 ◽

Cited By ~ 1

Author(s):

Shunsuke Takemura ◽

Ryo Okuwaki ◽

Tatsuya Kubota ◽

Katsuhiko Shiomi ◽

Takeshi Kimura ◽

...

Keyword(s):

Wave Propagation ◽

Seismic Wave ◽

Velocity Structure ◽

Nankai Trough ◽

Moment Tensor ◽

Plate Boundary ◽

Seismic Wave Propagation ◽

Structure Model ◽

Centroid Moment Tensor ◽

Heterogeneous Distribution

SUMMARY Due to complex 3-D heterogeneous structures, conventional 1-D analysis techniques using onshore seismograms can yield incorrect estimation of earthquake source parameters, especially dip angles and centroid depths of offshore earthquakes. Combining long-term onshore seismic observations and numerical simulations of seismic wave propagation in a 3-D model, we conducted centroid moment tensor (CMT) inversions of earthquakes along the Nankai Trough between April 2004 and August 2019 to evaluate decade-scale seismicity. Green's functions for CMT inversions of earthquakes with moment magnitudes of 4.3–6.5 were evaluated using finite-difference method simulations of seismic wave propagation in the regional 3-D velocity structure model. Significant differences of focal mechanisms and centroid depths between previous 1-D and our 3-D catalogues were found in the solutions of offshore earthquakes. By introducing the 3-D structures of the low-velocity accretionary prism and the Philippine Sea Plate, dip angles and centroid depths for offshore earthquakes were well-constrained. Teleseismic CMT also provides robust solutions, but our regional 3-D CMT could provide better constraints of dip angles. Our 3-D CMT catalogue and published slow earthquake catalogues depicted spatial distributions of slip behaviours on the plate boundary along the Nankai Trough. The regular and slow interplate earthquakes were separately distributed, with these distributions reflecting the heterogeneous distribution of effective strengths along the Nankai Trough plate boundary. By comparing the spatial distribution of seismic slip on the plate boundary with the slip-deficit rate distribution, regions with strong coupling were clearly identified.

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