Retrieving 2D structures from surface-wave data by means of space-varying spatial windowing

Abstract

Surface-wave techniques are mainly used to retrieve 1D subsurface models. However, in 2D environments, the 1D approach usually neglects the presence of lateral variations and because the surface-wave path crosses different materials, the resulting model is a simplified or misleading description of the site. We tested a processing technique to retrieve 2D structures from surface-wave data acquired with a limited number of receivers. Our technique was based on a two-step process. First, we extracted several local dispersion curves along the survey line using a spatial windowing based on a set of Gaussian windows with different shapes; the window maxima span the survey line so that we were able to extract a dispersion curve from the seismic record for every window. This provided a set of local dispersion curves each of them referring to a different subsurface portion. This space varying spatial windowing provided a good compromise between wavenumber resolution and the lateral resolution of the obtained local dispersion curves. In the second step, we inverted the retrieved set of dispersion curves using a laterally constrained inversion scheme. We applied this procedure to the processing of synthetic and real data sets and the method proved to be successful in reconstructing even complex 2D structures in the subsurface.

Skeletonized wave equation of surface wave dispersion inversion

“…The classical method accurately inverts for a 1D S-wave velocity model, but becomes less accurate with increasing lateral heterogeneity in the subsurface velocity model. The 1D assumption is not satisfied for some practical applications, so partial remedies are spatial interpolation of 1D velocity models (Tian et al, 2003) and laterally constrained inversion (Socco et al, 2014;Bergamo et al, 2012).…”

Wave-equation dispersion inversion

“…The classical method accurately inverts for a 1-D S-wave velocity model, but becomes less accurate with increasing lateral heterogeneity in the subsurface. The 1-D assumption is not satisfied for some practical applications, so partial remedies are spatial interpolation of 1-D velocity models (Yamanaka & Ishida 1996;Xia et al 1999;Beaty et al 2002;Tian et al 2003;Dal Moro 2015;Pan et al 2016b) and laterally constrained inversion (Socco et al 2010;Bergamo & Socco 2012). In comparison, full waveform inversion (FWI) can theoretically account for any lateral heterogeneity, but it is computationally expensive and can easily get stuck in local minima associated with the objective function (Tarantola 1984).…”

Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

“…The classical method accurately inverts for a 1D S-wave velocity model, but becomes less accurate with increasing lateral heterogeneity in the subsurface. The 1D assumption is not satisfied for some practical applications, so partial remedies are spatial interpolation of 1D velocity models (Xia et al, 1999) and laterally constrained inversion (Socco et al, 2010;Bergamo et al, 2012). In comparison, full waveform inversion (FWI) can theoretically account for any lateral heterogeneity, but it is computationally expensive and can easily get stuck in local minima associated with the objective function (Tarantola, 1984).…”