Ping Tong

A 3-D spectral-element and frequency-wave number hybrid method for high-resolution seismic array imaging

We present a three-dimensional (3-D) hybrid method that interfaces the spectral-element method (SEM) with the frequency-wave number (FK) technique to model the propagation of teleseismic plane waves beneath seismic arrays. The accuracy of the resulting 3-D SEM-FK hybrid method is benchmarked against semianalytical FK solutions for 1-D models. The accuracy of 2.5-D modeling based on 2-D SEM-FK hybrid method is also investigated through comparisons to this 3-D hybrid method. Synthetic examples for structural models of the Alaska subduction zone and the central Tibet crust show that this method is capable of accurately capturing interactions between incident plane waves and local heterogeneities. This hybrid method presents an essential tool for the receiver function and scattering imaging community to verify and further improve their techniques. These numerical examples also show the promising future of the 3-D SEM-FK hybrid method in high-resolution regional seismic imaging based on waveform inversions of converted/scattered waves recorded by seismic array.

A High‐Order Stereo‐Modeling Method for Solving Wave Equations

Abstract In this paper, we propose a high‐order stereo‐modeling method (STEM) to approximate the high‐order spatial derivatives included in the wave equations using simultaneously wave‐field displacements and their gradients and propose a two‐step method for time marching, which is called the two‐step STEM in brief. The two‐step STEM has a higher‐order accuracy in space than conventional finite‐difference (FD) methods when the same number of spatial grid points in a wavelength is used. For example, the stereo‐modeling method that uses five points in one spatial direction can achieve an eighth‐order accuracy in space, whereas other FD methods such as conventional FD methods, Lax–Wendroff correction (LWC) methods, and other methods only have a fourth‐order accuracy. Theoretical properties of the two‐step STEM including stability and errors are analyzed for 1D and 2D cases. The numerical dispersion relationship provided by the two‐step STEM for 1D and 2D cases are also investigated in this study. Meanwhile, we present numerical results computed by the two‐step STEM and compare with the eighth‐order LWC method, the eighth‐order staggered‐grid FD method, and the fourth‐order staggered‐grid method. Numerical results show that the two‐step STEM can effectively suppress numerical dispersion caused by discretizing the wave equations when coarse spatial grids are used or models have strong velocity contrasts between adjacent layers. In contrast to other high‐order FD methods such as the eighth‐order LWC, the eighth‐order staggered‐grid FD, and the fourth‐order staggered‐grid method, the new method has substantially less computational time and requires less memory because large spatial and time increments can be used. Thus, the two‐step STEM can be potentially used to solve large‐scale wave‐propagation problems and seismic tomography.

3D Nearly Analytic Central Difference Method for Computation of Sensitivity Kernels of Wave‐Equation‐Based Seismic Tomography

We propose a numerical method to perform forward‐modeling and sensitivity kernel computation in wave‐equation‐based seismic tomography. This method is an extension of the 2D nearly analytic central difference (NACD) method for solving the 3D acoustic wave equation. The 3D NACD method has fourth‐order accuracies both in time and space with only a three‐point stencil in each axis direction. Theoretical properties such as the stability criterion and the numerical dispersion relation were analyzed in detail. Relative to the fourth‐order Lax–Wendroff correction method and the fourth‐order staggered‐grid finite‐difference method, the 3D NACD method exhibits better performance in suppressing numerical dispersion. This was numerically confirmed by simulation of seismic‐wave propagation in different models. Additionally, the 3D NACD method explicitly calculates the spatial gradients of the propagating wavefield, allowing a direct route to sensitivity kernel calculation. Using this method, waveform kernels and travel‐time kernels for direct arrival, single reflected phase, multiple reflected phase, and headwave are computed in a crust‐over‐mantle model. Numerical examples reveal that sensitivity kernel computation based on solving the full‐wave equation can accurately capture the interactions between wavefields and the Earth’s interior heterogeneous structures, and hence generate high‐accuracy sensitivity kernels for the subsequent tomographic inversion. Overall, the proposed method showed good performances for both forward‐modeling and sensitivity kernel calculation. This suggests that the 3D NACD method could serve as an efficient and accurate forwarding‐modeling tool for wave‐equation‐based seismic tomography.

Time-evolving seismic tomography: The method and its application to the 1989 Loma Prieta and 2014 South Napa earthquake area, California†

We propose a time-evolving approach to conduct traveltime seismic tomography in the 1989 Mw 6.9 Loma Prieta earthquake and 2014 Mw 6.0 South Napa earthquake area, California. The recording period of the chosen seismic data between January 1, 1967 and the day before the 2014 South Napa earthquake is divided into two time windows, separated by the 1989 Loma Prieta earthquake. In each time window the subsurface velocity structure is iteratively updated. Starting from the final model of the first time window, the velocity model has been successively improved throughout iterations in the second time window, indicating that the traveltime data of later time windows have provided extra information to refine the subsurface images. Strong heterogeneities are observed in the final P-wave velocity model. Both of the two large earthquakes occurred at transition zones in between high Vp and low Vp anomalies. In all, this study shows the effectiveness of the time-evolving seismic tomography method.

Wave equation‐based reflection tomography of the 1992 Landers earthquake area

In the framework of a recent wave equation-based traveltime seismic tomography, we show that incorporating Moho-reflected phases (PmP and SmS) in addition to the direct P and S phases can significantly increase tomography resolution in the lower crust and this may provide additional evidence to resolve important tectonic issues. To highlight the resolving power of the new strategy, we apply it in the region around the 1992 Landers earthquake (Mw = 7.3) in Southern California using seismic arrivals from local earthquakes, obtaining 3-D high-resolution P and S wave crustal velocity models and Poisson’s ratio structures. In the upper crust, our method confirmed features that had been previously found. However, in the middle-to-lower crust, we found low-velocity anomalies on the southeastern section of the San Jacinto Fault and high Vp and low Vs structures to the west of the Big Bear earthquake, which may be related to upwelling of partial melt from the mantle.