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.

Imaging Near-surface Heterogeneities by Natural Migration of Back-scattered Surface Waves

“…The typical strategy is to (1) linearize the relation between the scattered data d and the model perturbation m (i.e. heterogeneities map) under the Born approximation d = Lm, and then (2) find the approximate solution by either an iterative optimization method (Riyanti 2005;Campman & Riyanti 2007;Kaslilar 2007) or by applying the adjoint (Snieder 1986;Blonk et al 1995;Campman et al 2005;Yu et al 2014) of the modeling operator L † to the scattered data d to get the migration image m mig = L † d. In all cases, the two key assumptions are that the velocity model (typically, just the smooth component of the surface wave velocity distribution) is known and the weak-scattering approximation is invoked. For many practical applications, the background velocity model is assumed to be a layered medium.…”

“…For many practical applications, the background velocity model is assumed to be a layered medium. This methodology has found a growing number of uses in earthquake, exploration and engineering seismology (Snieder 1986;Blonk et al 1995;Wijk 2003;Campman et al 2005;Riyanti 2005;Campman & Riyanti 2007;Kaslilar 2007).…”

Estimating the Location of Scatterers by Seismic Interferometry of Scattered Surface Waves

“…Several authors used scattered surface waves for imaging cavities, buried objects, or shallow water reservoirs (Snieder, 1987;Herman et al, 2000;Campman and Riyanti, 2007;Kaslilar and Herman, 2006;Kaslilar, 2007). The scattered surface waves are studied in detail in terms of seismic interferometry by Halliday and Curtis (2009).…”

Surface‐wave eikonal tomography in a scattering environment

“…Surface-waves are of increasing interest in seismic prospecting, as they provide information about shallow structures (e.g., Campman and Riyanti, 2007;Socco and Boiero, 2008). They are usually processed using linearized (asymptotic) traveltime tomography, to obtain per-frequency phase-or group-velocity maps first, which are then inverted into a S-and P-wave velocity model at shallow depth.…”