Seismic wavefield injection based on interface discontinuity: theory and numerical implementation based upon the spectral-element method

SUMMARY In seismology, wavefield injection refers to the propagation of seismic waves generated by remote sources into local domains bounded by enclosed surfaces. The simulations of wavefield injection, primarily focused on the interaction between incoming seismic waves and local structures, are key to earthquake hazard modelling and full-waveform seismic tomography using tele-seismic waves. In this paper, we show that simulating wavefield injection is equivalent to solving the wave equation subject to interface discontinuity conditions. To provide a general framework to study wavefield injection, we formally define the interface discontinuity problem, and discuss its representation theorem and uniqueness. We also develop an efficient interface-discontinuity-based numerical algorithm to solve the wavefield injection problem through implementations of spectral-element methods, and show with numerical examples that wavefield injection can be accurately simulated at different scales with this algorithm. Under this framework, we draw connections with previously proposed wavefield injection algorithms/hybrid methods, and clarify several theoretical questions on wavefield injection from previous research. We demonstrate the efficiency and accuracy of our approach through wavefield injection examples at local and continental scales. Furthermore, we illustrate the applicability of the interface discontinuity approach to performing kinematic fault simulations through a numerical example.