Kirchhoff-approximate inversion of teleseismic wavefields

Abstract

Summary We derive Kirchhoff‐approximate inversion formulae for elastic wavefields that recover the location of discontinuity surfaces and associated material property contrasts in laterally varying, stratified media. The derivation is cast in the context of teleseismic wavefield scattering in a 2‐D medium with allowance made for oblique incidence, although a fully general derivation for 3‐D media follows in straightforward fashion. We exploit a little‐used variant of the isotropic, elastic Kirchhoff‐Helmholtz integral in which individual terms are directly identified with scattered P‐ and S‐wave contributions prior to approximation using ray‐theoretic forms. This approach yields relatively simple formulae for Kirchhoff‐approximate forward modelling that bear a closer resemblance to their acoustic counterpart than standard elastic formulations cast in terms of traction and displacement. Using micro‐local analysis, inversion formulae are readily derived using the generalized Radon transform. Our approach represents an extension of the Kirchhoff‐approximate inversion scheme outlined by Beylkin & Burridge (1990) to S‐waves and conversions. We demonstrate application of the method to field data recorded during the IRIS‐PASSCAL CASC93 experiment.

Equipartitioning is not sufficient for Green’s function extraction

“…In general, the surface waves in the retrieved Green's function are strongest (e.g., Shapiro and Campillo, 2004;. The body waves are usually under-represented, and, with the exception of studies based on teleseismic body waves (Bostock, 2002;Bostock et al, 2002;Kumar and Bostock, 2006;Tonegawa et al, 2009), the number of studies that report extracting body waves is modest Gerstoft et al, 2006;Draganov et al, 2007Draganov et al, , 2009. The reason for the under-representation of body waves is that for the retrieval of the direct surface wave it suffices to have sources anywhere near the Earth surface in a region that straddles a line through the used receivers, as sketched in Figure 3.…”

“…In practice, however, there are insufficient sources in the interior of the Earth to provide the required excitation for field fluctuations on the closed surface surrounding the receivers. This hurdle has been overcome (Bostock, 2002;Bostock et al, 2002;Kumar and Bostock, 2006;Tonegawa et al, 2009) by using teleseismic waves that impinge on the crust from below, as shown in Figure 6. In that case the teleseismic waves propagating through the dashed surface in Figure 6 replace the sources on Figure 6 Teleseismic waves propagating through a bounding surface illuminating the crust from below.…”

Multichannel inversion of scattered teleseismic body waves: Practical considerations and applicability

“…Such anisotropic approaches have already been implemented by Burridge et al [1998] for seismic reflection data, and by Bostock [2002] and Bank and Bostock [2002] for the 1D teleseismic case. The main challenge with generalization to an anisotropic medium lies in the large number of independent parameters that are inverted for.…”

Theory and Observations - Seismology and the Structure of the Earth: Teleseismic Body-Wave Scattering and Receiver-Side Structure

“…Like the 1-D case, these algorithms can be recast to recover singular functions of discontinuity surfaces (vs. Bornapproximate perturbations), thereby accomplishing Kirchhoffapproximate inversion (Beylkin and Burridge, 1990;Bleistein, 1987;Bostock, 2002;de Hoop and Bleistein, 1997). In the teleseismic context, generalized Radon transform inversions have been strictly applied in a limited number of studies on subduction zones (Nicholson et al, 2005;Rondenay et al, 2001), Precambrian mobile belts (Poppeliers and Pavlis, 2003b;Rondenay et al, 2005), and the mantle transition zone (Liu and Pavlis, 2013).…”