Fast calculation of spatial sensitivity kernels for scattered waves in arbitrary heterogeneous media using graph theory

Abstract

SUMMARYP-to-S and S-to-P receiver functions are widely used to constrain the seismic discontinuity structures of the Earth. Typically, receiver functions are projected to the depth and location of conversion assuming a 1-D layered Earth structure. Receiver function finite frequency sensitivity kernels have the potential to increase resolution. Here we present a method for rapidly calculating the P- and S-wave receiver function sensitivity kernels, based upon the shortest path method and Dijkstra's algorithm to calculate the traveltime fields, and accounting for geometrical spreading in heterogeneous media. The validity of the approach is evaluated by comparing with amplitudes derived from a finite difference elastic full waveform simulation in a complex subduction zone geometry. We show P-to-S and S-to-P kernels calculated using our method for three examples cases: a half space, a layer with topography, and a sinusoidal discontinuity. We also demonstrate the kernel recovery of discontinuities with these topographies by inverting synthetic data from SPECFEM2D. We find that P-to-S kernels recover the structure of strong topography better than S-to-P kernels, although S-to-P kernels may be useful in some situations. P-to-S kernels also show better recovery of the amplitude of the discontinuities in comparison to S-to-P, although both typically achieve values within a few percent of the input model. The computational cost of our approach for improved kernel calculation in heterogeneous media is up to a few tens of seconds per station for typical regional scale models on the scale of several 100s of kilometres.