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

Abstract

Summary P-to-S and S-to-P receiver functions are widely 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 travel time 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 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.

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

“…Our kernels agree with those calculated using SEM both in shape and in amplitude (Figures 2−5). We find agreement in terms of the shapes of our kernels with previous studies that have explicitly calculated and presented P-to-S (Bogiatzis et al, 2022;Hansen & Schmandt, 2017) and S-to-P kernels (Bogiatzis et al, 2022;Hansen & Schmandt, 2017;Mancinelli & Fischer, 2018). The absolute amplitudes of the kernels presented in Figures 2−5) are the same as those in the work of Bogiatzis et al (2022), but 3-5 orders of magnitude smaller than other previous results (Hansen & Schmandt, 2017;Mancinelli & Fischer, 2018).…”

“…Structural recovery using our analytical kernels is similar or worse than that of another study that used the same station and event set‐up and some of the same discontinuity structures (Bogiatzis et al., 2022). For instance, our P‐to‐S and S‐to‐P kernels recover the Gaussian bump just as well as the previous work.…”

“…The work of Bogiatzis et al. (2022) inverted for the magnitude of the velocity contrast and also found recovery that was both smaller and larger than the true model. The work of Mancinelli and Fischer (2018) similarly reported variability of scattering potential, a proxy for amplitude variation based on comparing lithosphere‐asthenosphere amplitudes to overlying Moho amplitudes in a kernel stack.…”

“…These differences are likely because the work of Bogiatzis et al. (2022) used a more sophisticated ray tracing approach to calculate the kernels.…”

“…The work of Bogiatzis et al. (2022) also demonstrated that accounting for heterogeneous structure can lead to up to a 30% improvement in waveform amplitudes in comparison to the assumption of geometric spreading for a homogeneous Earth in a subduction zone setting. The approaches of Hansen and Schmandt (2017) and Mancinelli and Fischer (2018) focused in particular on the imaging problem rather than the recovery of the magnitudes of the velocity discontinuities, and all four studies required moderate amounts of computational cost.…”