Adjoint‐State Traveltime Tomography for Azimuthally Anisotropic Media and Insight Into the Crustal Structure of Central California Near Parkfield

Abstract

Seismic anisotropy describes the directional dependence of elastic properties measured at the same place. As widely observed in the crust, the upper mantle, the transition zone, the D" layer, and the inner core (Long & Becker, 2010), seismic anisotropy is a key indicator for the past and present deformation processes in the Earth's interior. The sources for seismic anisotropy vary in different regions. Stress-induced anisotropy caused by local/regional stress field and structure-induced anisotropy due to the presence of faults, sedimentation structures and mineral alignment are the two main types of seismic anisotropy observed in the upper crust (e.g., Boness & Zoback, 2006;Li & Peng, 2017). Seismic anisotropies in the lower crust, upper mantle and mantle transition zone are generally attributed to strain-induced lattice-preferred orientation (LPO) of materials, such as schists, olivine and wadsleyite, that occurs during tectonic and flow deformation (e.g., Kawazoe et al., 2013;Long & Silver, 2008;Porter et al., 2011). In addition to its wide existence, seismic anisotropy has the same level of effect as seismic heterogeneity on traveltime observations (Zhao Abstract Seismic anisotropy provides crucial information on the stress state and geodynamic processes inside the Earth. We develop a novel adjoint-state traveltime tomography method using P-wave traveltime data to simultaneously determine velocity heterogeneity and azimuthal anisotropy of the subsurface. First, an anisotropic eikonal equation is derived to model first-arrival traveltimes in azimuthally anisotropic media. Traveltime tomography is then formulated as an optimization problem constrained by the anisotropic eikonal equation, which is subsequently solved by the adjoint-state method. Ray tracing is not required. Its high accuracy is achieved by solving the anisotropic eikonal equation and the associated adjoint equation with efficient numerical solvers. In addition, an eikonal equationbased earthquake location method for azimuthally anisotropic media is developed to solve the coupled hypocenter-velocity problem. The tomography and earthquake location methods are applied to central California near Parkfield to test their performance in practice. A total of 1,068,850 first P-wave traveltimes clearly maps the velocity heterogeneity and azimuthal anisotropy in the upper and middle crust. The average P-wave velocity model shows a striking velocity contrast across the San Andreas Fault (SAF). In the upper crust, we find structural anisotropy in the SAF zone and stress-induced anisotropy off the SAF zone. In the middle crust, the fast P-wave velocity directions are generally fault-parallel due to the decreased effect of the maximum horizontal compressive stress. In all, the real-data application suggests that the new adjoint-state traveltime tomography method can be reliably used to investigate anisotropic seismic structures.Plain Language Summary This study is a sophisticated extension of the adjointstate traveltime tomography method for isotropic media dis...

Complex Patterns of Past and Ongoing Crustal Deformations in Southern California Revealed by Seismic Azimuthal Anisotropy

“…North of the GF, fast P-wave velocity orientations are generally N-S aligned, with an exception near the Coso geothermal field (CGF) where clear rotations of the fast axes to E-W are observed (Figures 4a-4d). This pattern agrees well with a previous smaller-scale tomographic study which suggests a clockwise rotating crustal block associated with fluids that have possibly led to the nucleation of the 2019 Ridgecrest earthquake (Tong et al, 2021). The Mojave Desert shows nearly uniform NE-SW fast orientations, with the eastern Mojave Desert exhibiting larger anisotropy amplitudes as compared to the west (Figures 4a-c).…”

“…We first conduct several checkerboard tests to assess the resolving ability of our data and the robustness of the tomographic inversion, including one test simultaneously incorporating velocity and anisotropic anomalies and two additional tests incorporating either velocity or anisotropic anomalies for trade-off analysis. The input velocity and anisotropic anomalies are designed based on sinusoidal functions following Tong (2021). Details of the checkerboard resolution tests are given in (Text S1 of Supporting Information S1).…”

“…In the forward calculation, we set up a fine 3‐D forward grid with a size of 1 km × 1 km × 0.5 km and numerically solve the anisotropic eikonal equation using a fast‐sweeping method (Qian et al., 2007). Sensitivity kernels of the objective function with respect to the P ‐wave slowness and anisotropic parameters are calculated based on the traveltime field and an adjoint field that satisfies the transport‐type adjoint equation (Tong, 2021). The inverse problem is handled by a step‐size‐controlled gradient descent method that requires the relative perturbations not to exceed ±2% at each iteration.…”

“…We first perform 40 iterations to generate an anisotropic velocity model for earthquake relocation. Then, we relocate all 74,504 earthquakes with 10 iterations following the algorithm described in Tong (2021) and update the associated P ‐wave arrival times. Finally, starting again with the 3‐D isotropic velocity model, we conduct another 40 iterations using the relocated earthquakes to construct our final model.…”

“…We employ the adjoint‐state traveltime tomography method for azimuthally anisotropic media (Tong, 2021) to iteratively invert for P ‐wave velocity and azimuthal anisotropy (magnitude and fast velocity orientation). In the forward calculation, we set up a fine 3‐D forward grid with a size of 1 km × 1 km × 0.5 km and numerically solve the anisotropic eikonal equation using a fast‐sweeping method (Qian et al., 2007).…”