Adjoint-state reflection traveltime tomography for velocity and interface inversion with its application in central California near Parkfield

Abstract

Traveltime tomography considering reflection arrivals is a promising approach for investigating interface topography and near-interface velocity heterogeneity. In this study, we formulate this inverse problem as an eikonal equation-constrained optimization problem, in which the traveltime field of the reflection wave is accurately described by a two-stage eikonal equation. The novelty lies in deriving the Fréchet derivative with respect to interface topography. By employing the coordinate transformation technique to convert an irregular physical domain with an undulating interface to a regular computational domain, we successfully encode the interface topography into the anisotropic parameters in the eikonal equation. This approach enables us to derive explicit forms of the Fréchet derivatives related to interface topography and velocity based on the adjoint-state method, which is not only computationally efficient but also avoids potential inaccuracy in ray tracing. Several numerical experiments are conducted to verify our new method. Finally, we apply this method to central California near Parkfield by inverting traveltimes of both first-P and Moho-reflected waves (named PmP). The low-velocity anomalies imaged in the lower crust are consistent with the along-strike variations of low-frequency earthquakes (LFEs) beneath the San Andreas Fault (SAF), suggesting the presence of fluids that may influence the occurrence of LFEs in this region.