2‐D Analytical P‐to‐S and S‐to‐P Scattered Wave Finite Frequency Kernels

Abstract

Abstract Scattered wave imaging provides a powerful tool for understanding Earth's structure. The development of finite frequency kernels for scattered waves has the potential for improving the resolution of both the structure and magnitude of discontinuities in S‐wave velocity. Here we present a 2‐D analytical expression for teleseismic P‐to‐S and S‐to‐P scattered wave finite‐frequency kernels for a homogeneous medium. We verify the accuracy of the kernels by comparing to a spectral element method kernel calculated using SPECFEM2D. Finally, we demonstrate the ability of the kernels to recover seismic velocity discontinuities with a variety of shapes including a flat discontinuity, a discontinuity with a sharp step, a discontinuity with a smooth bump, and an undulating discontinuity. We compare the recovery using the kernel approach to expected recovery assuming the classical common conversion point (CCP) stacking approach. We find that the P‐to‐S kernel increases recovery of all discontinuity structures in comparison to CCP stacking especially for the shallowest discontinuity in the model. The S‐to‐P kernel is less successful but can be useful for recovering the curvature of shallow discontinuity undulations. Finally, although we observe some variability in the amplitude of the kernels along the discontinuities, the kernels show some potential for recovering the magnitude of the velocity contrast across a discontinuity.

Keywords

• wave propagation
• wave scattering and diffraction
• numerical approximations and analysis
• numerical modeling
• P‐to‐S and S‐to‐P converted phases
• discontinuity topography