Non-linear inversion of scattered seismic surface waves

Abstract

SUMMARY Seismic surface wave analysis has provided important insight in the Earth’s crustal and upper mantle structure and has recently become a standard tool in geotechnical engineering. Most current surface wave inversion methods are aimed at recovering near-surface (shear) velocity profiles from dispersion curves, assuming a (smoothly varying) horizontally layered Earth. In some cases, however, one is interested in the location, strength or shape of local heterogeneities in the shallow subsurface. In this paper we focus on estimating the strength of near-surface heterogeneity from scattered surface waves. This is a non-linear inversion problem as the wavefield in the scatterer also depends on the contrast. For this reason the inversion is cast as an optimization problem in which we minimize the difference between the observed data and the modelled scattered field. The minimization problem is solved using a conjugate gradient algorithm. To accurately estimate the contrast we account for non-linear interactions such as multiple scattering within the scattering domain in the forward problem. To do so, we use a domain-type integral representation to express the near-surface scattered wavefield, which is solved using the method of moments. The entire inversion is carried out in the frequency domain. This way, we may take advantage of the fact that the decay of surface waves with depth depends on frequency. We study 3-D sensitivity kernels for the given inversion problem and observe that sensitivity of the wavefield with respect to heterogeneity in depth depends on frequency in the same way. We therefore, expect to be able to constrain heterogeneity in depth. A numerical example illustrates this and we conclude that it is in principle possible to reliably resolve heterogeneities and estimate their strengths. We compare the results from our algorithm to a similar but more efficient inversion scheme based on the Born approximation and show that, for the shallowest heterogeneities, this inversion can also recover the contrast well.