3-D Teleseismic Imaging of Scattered Wavefields Using Both Kirchhoff and Born Approximations

The goal of this study is to compare imaging with scattered teleseismic wavefields using 3-D Kirchhoff- and Born-approximate inversion methods. Kirchhoff and Born-approximate inversions have been well developed in exploration seismology based on the inverse scattering framework (e.g. Beylkin and Burridge, 1990) to image subsurface structure that generates secondary wavefields due to localized heterogeneities. Application of these methods in global seismology has been somewhat limited to 1-D reference models due to high computational cost and the lack of dense receiver arrays (Bostock, 2002, Frederiksen and Revenaugh, 2004; Cao et al., 2010). Due to the deployment of the USArray Transportable and Flexible arrays across the United States and dense array recordings in other countries, we seek to extend teleseismic scattered wavefield imaging with each of these approximations from 2-D to 3-D for both scalar and vector wavefields to resolve the contrast of material parameters in the lowermost crust and the upper mantle. Following Bostock and coworkers (2001, 2002), making each approximation allows us to derive the 3-D multimode (P-to-P, P-to-S etc.) inversion formulae by phrasing the problem in terms of a generalized Radon transform (or its inverse) and then inverting the scattered waves. To demonstrate the relative accuracy of the two different inversions, we examine several synthetic cases with a variety of discontinuity surfaces. In the forward scattering modeling, we extend the method to utilize a 3-D background velocity model by calculating 3-D finite-difference traveltimes and amplitudes, backprojected from the receivers using an eikonal solver. We compare our Kirchhoff- and Born-approximation imaging with the common-conversion point (CCP) stacked receiver function imaging for the synthetic data. We apply these methods to USArray data.