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

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 equation-based 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 discussed in Tong (2021), https://doi. org/10.1029/2021JB021818. An anisotropic eikonal equation is derived to model first-arrival traveltimes in azimuthally anisotropic media. Following that, the adjoint-state traveltime tomography method and eikonal equation-based earthquake location method are developed for azimuthally anisotropic media. Neither ray tracing nor waveform modeling is required. The validity of the new methods is verified in central California near Parkfield, revealing structural anisotropy in the San Andreas Fault zone and stress-induced anisotropy off the fault zone.

Automated summary

The study introduces a novel adjoint-state traveltime tomography method using P-wave traveltime data to determine velocity heterogeneity and azimuthal anisotropy simultaneously. The method was successfully applied to real data in central California, revealing structural anisotropy in the San Andreas Fault zone and stress-induced anisotropy off the fault zone.