2‐D Analytical P‐to‐S and S‐to‐P Scattered Wave Finite Frequency Kernels. (22nd April 2022) - Harmon, Nicholas; Rychert, Catherine A.; Xie, Yujiang; Bogiatzis, Petros
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. Plain Language Summary: Seismic waves convert from compressional waves to shear waves and vice versa at sharp discontinuities in seismic velocity. These conversions are useful for tightly constraining the structure and properties of the seismic velocity discontinuities, and this can be used to better determine the physical and chemical properties of the Earth. Typical approaches that use the converted phases to constrain discontinuities assume that the discontinuities are relatively flat, and migrate the converted phase energy to depth, stacking the converted phase energy on a grid. However, discontinuities may have significant topography, for instance in subduction zones or beneath hotspots, rifts, or ridges. There are several different approaches to account for such topography with varying degrees of success and also computational cost. One approach is to use the theoretical sensitivity kernels to distribute the converted phase energy in space. Here we present analytical sensitivity kernels for converted phases and assess their ability to recover strong discontinuity topography. The approach is very fast and computationally efficient. The compressional to shear kernel successfully retrieves all shallow discontinuity structures, while the shear to compressional kernel may be useful for constraining discontinuity curvature in certain circumstances. Key Points: We present 2‐D analytical P‐to‐S and S‐to‐P finite frequency sensitivity kernels that are rapidly calculated with low computational cost We demonstrate the validity of the kernels in comparison to kernels calculated using SPECFEM2D Analytical P‐to‐S kernels recover discontinuities with sharp or curved topography, and S‐to‐P kernels may be useful in certain situations