Accurate 3D frequency-domain seismic wave modeling with the wavelength-adaptive 27-point finite-difference stencil: a tool for full waveform inversion

Description

Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset node data can be performed with a few frequencies. The seismic response of these frequencies can be computed with compact finite-difference stencils on regular Cartesian grid with direct or hybrid direct/iterative methods. Compactness, which is necessary to mitigate the fill-in induced by the Lower-Upper (LU) factorization, is implemented with second-order stencils while accuracy is achieved by building a consistent mass matrix and a compound stiffness matrix with optimal weights so that the stencil covers the eight cells surrounding the central point, leading to a 27-point stencil. Classical approaches estimate constant weights by jointly minimizing numerical dispersion in homogeneous media for several numbers of grid points per wavelength ( G). Then, the impedance matrix is built by using these constant weights at each central point covering the heterogeneous subsurface model, leading to non-uniform wavefield accuracy. Instead, we estimate G-dependent weights once and for all by minimizing dispersion separately for each value of 1/ G in a range found in FWI applications. Then, we build the impedance matrix without computational overhead by selecting at each central point the weights corresponding to the local 1/ G, hence leading to a wavelength-adaptive stencil. This separate approach with adaptive weights makes wavefield accuracy uniform.We benchmark wavefields, which are computed in several 3D large-scale subsurface models with a sparse multifrontal direct solver and the non-adaptive/adaptive stencils, against analytical solutions when available and the highly accurate discretization-free convergent Born series (CBS) method. Each benchmark reveals the higher accuracy of the adaptive stencil relative to the non-adaptive one. In the presence of sharp contrasts, the adaptive stencil is also more accurate than a classical O(Δ t 2 ,Δ h 8 ) finite-different time-domain staggered-grid stencil. The relevance of the adaptive stencil is finally illustrated with a 3D FWI case study in the 3.5–13 Hz frequency ba

Abstract

International audience

Additional details