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

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