Adjoint-state traveltime tomography for azimuthally anisotropic media in spherical coordinates

Abstract

Summary Tong (2021) has proposed an adjoint-state traveltime tomography method to determine velocity heterogeneity and azimuthal anisotropy. This method, however, ignores the Earth’s curvature when deriving the eikonal equation for azimuthally anisotropic media. Thus, further coordinate transformation or approximation is required to ensure the accuracy of traveltime prediction in large-scale tomography. To address this problem, we derive the eikonal equation for azimuthally anisotropic media in spherical coordinates, which naturally considers the Earth’s curvature. Another key ingredient is the forward modeling algorithm, whose accuracy and efficiency dominate the numerical error and computational cost of the inversion. In this study, we apply a modified fast sweeping method to solve the eikonal equation in spherical coordinates. Two approaches, including the third-order weighted essentially nonoscillatory approximation and multiplicative factorization technique, are applied to improve the accuracy. According to the numerical experiments, this new eikonal solver achieves a second-order accuracy and is about two orders of magnitude more accurate than the commonly used first-order fast sweeping method with similar runtime. Taking advantage of the two improvements, we develop a novel eikonal equation-based adjoint-state traveltime tomography method for azimuthally anisotropic media in spherical coordinates. This method is applicable for large-scale tomography, and its performance is verified by a synthetic checkerboard test and a practical seismic tomographic inversion in central California near Parkfield.

Adjoint‐State Teleseismic Traveltime Tomography: Method and Application to Thailand in Indochina Peninsula

“…In all, this restriction is similar to adding a damping parameter, which has been verified by previous studies (J. Chen et al, 2023;Liu et al, 2019;Tong, 2021aTong, , 2021b.…”

“…Note that the upper bounds for the perturbations decrease once the objective function increases, ensuring the convergence of iteration (J. Chen et al., 2023). In all, this restriction is similar to adding a damping parameter, which has been verified by previous studies (J. Chen et al., 2023; Liu et al., 2019; Tong, 2021a, 2021b).…”

“…The perturbations in the relative slowness and station correction terms are along the negative gradient direction, but their amplitudes are limited to less than 1% and 0.01 s at each iteration, respectively. Note that the upper bounds for the perturbations decrease once the objective function increases, ensuring the convergence of iteration (J. Chen et al., 2023). In all, this restriction is similar to adding a damping parameter, which has been verified by previous studies (J. Chen et al., 2023; Liu et al., 2019; Tong, 2021a, 2021b).…”

Topography‐Incorporated Adjoint‐State Surface Wave Traveltime Tomography: Method and a Case Study in Hawaii

“…The adjoint‐state method has been introduced to solve various seismic inverse problems based on eikonal equations, including local earthquake tomography (e.g., Leung & Qian, 2006; Taillandier et al., 2009; Tong, 2021a), body‐wave differential arrival time tomography (e.g., Tavakoli et al., 2017; Tong et al., 2024) and seismic anisotropy tomography (Tong, 2021b). It is also feasible for teleseismic traveltime tomography (Chen et al., 2023). In this study, we develop a novel approach called adjoint‐state surface wave traveltime tomography, which enables the inversion of surface wave traveltimes while inherently accounting for the topography effects.…”