Parametric level-set full-waveform inversion in the presence of salt bodies

Abstract

SUMMARYFull-waveform inversion attempts to estimate a high-resolution model of the Earth by inverting all the seismic data. This procedure fails if the Earth model contains high-contrast bodies such as salt and if su ciently low frequencies are absent from the data. Salt bodies are important for hydrocarbon exploration because oil or gas reservoirs are often located on their sides or underneath. We represent the shape of the salt body with a level set, constructed from radial basis functions to keep its dimensionality low. We have shown earlier that the salt body can be completely recovered if the sediment structure is already known. In this paper, we propose a strategy to simultaneously reconstruct the sediment and the salt. The sediment is implicitly represented by a bilinear interpolation kernel with a small number of variables. An alternating minimization technique solves the resulting optimization problem. The results on a synthetic model using Gauss-Newton approximation of the Hessian shows the feasibility of the approach.

Shape reconstruction in seismic full waveform inversion using a level set approach and time reversal

“…The specific gradient directions for each of the medium parameters are easily obtained from ( 45) due to the diagonal structure of Γ. We need to calculate the partial derivatives with respect to the three elastic parameters (λ, µ, ρ) which appear in m. We identify in (23) contributions for each of those parameters by explicitly stating the partial derivatives…”

“…In those applications, a shape-based regularization approach has been proposed in the literature for the representation of those anomalous regions. In particular, in the application of imaging ground structure with solid salt domes embedded, different level set based shape reconstruction approaches have been proposed recently in [18,19,20,21,22,23,24,25].…”

A single level set function approach for multiple material-phases applied to full-waveform inversion in the time domain

“…In turn, along the lines originally proposed by Yamada et al (2010) for structural topology optimization, Lanznaster et al (2020) used the LS and an updating procedure based on the reaction-diffusion equation in order to solve the FWI problem. One of the most common approaches for salt body reconstruction problems uses radial basis functions (RBFs) to define a parametric representation of the LS function (Aghasi et al 2011, Kadu et al 2017a, 2017bWu and Dorn 2018, Dahlke et al 2020. Huang et al (2015) apply the level-set method to locate layer interfaces in geothermal reservoirs through shape optimization.…”

“…Liu et al (2019) employ a PLS approach in electrical impedance tomography (EIT) for difference imaging. In geology applications, PLS has been used in seismic FWI, particularly in salt reconstruction problems (Kadu et al 2016(Kadu et al , 2017a(Kadu et al , 2017b.…”