Computationally efficient three-dimensional acoustic finite-difference frequency-domain seismic modeling in vertical transversely isotropic media with sparse direct solver

Abstract

The computational burden of frequency-domain full-waveform inversion (FWI) of wide-aperture fixed-spread data is conventionally reduced by limiting the inversion to a few discrete frequencies. In this framework, frequency-domain seismic modeling is performed efficiently for multiple sources by solving the linear system resulting from the discretization of the time-harmonic wave equation with the massively parallel sparse direct solver. Frequency-domain seismic modeling based on the sparse direct solver (DSFDM) requires specific design finite-difference stencils of compact support to minimize the computational cost of the lower-upper decomposition of the impedance matrix in terms of memory demand and floating-point operations. A straightforward adaptation of such finite-difference stencil, originally developed for the (isotropic) acoustic-wave equation, is proposed to introduce vertical transverse isotropy (VTI) in the modeling without any extra computational cost. The method relies on a fourth-order wave equation, which is decomposed as the sum of a secondorder elliptic-wave equation plus an anellipticity correction term. The stiffness matrix of the elliptic-wave equation is easily built from the isotropic stiffness matrix by multiplying its coefficients with factors that depend on Thomsen's parameters, whereas the anelliptic term is discretized with a parsimonious second-order staggered-grid stencil. Validation of DSFDM against finite-difference time-domain modeling performed in various synthetic models shows that a discretization rule of four grid points per minimum wavelength provides accurate DSFDM solutions. Moreover, comparison between real data from the Valhall field and DSFDM solutions computed in a smooth VTI subsurface model supports that the method can be used as a fast and accurate modeling engine to perform multiparameter VTI FWI of fixedspread data in the viscoacoustic approximation.

ADMM-based multiparameter wavefield reconstruction inversion in VTI acoustic media with TV regularization

“…We first consider the frequency-domain first-order velocitystress wave equation in 2D VTI acoustic media (Duveneck et al, 2008;Duveneck and Bakker, 2011;Operto et al, 2014) −îωv…”

“…The wave equation operator in equation C-4 has been broken down into an elliptic wave equation operator and anelliptic correction term (the term of A z related to diag(m − m 2 δ ), equation C-4). The former can be accurately discretized with the 9-point finite-difference method of Chen et al (2013), while the anelliptic term can be discretized with a basic second-order accurate 5-point stencil without generating significant inaccuracies in the modelling (Operto et al, 2014).…”

Forward Modeling of VTI Media in the Frequency‐Space Domain Based on an Average‐Derivative Optimal Method

“…Grini et al (2007) and Operto et al (2007Operto et al ( , 2009) studied mixed-grid FDFDM of viscoacoustic TTI media by the form of first-order equation. Operto et al (2014) proposed a new 3D VTI media FDFDM method which decomposes the 3D VTI fourth-order wave equation as the sum of a second-order elliptic-wave equation plus an anellipticity correction term.…”

Waveform inversion for acoustic VTI media in frequency domain

“…Pseudo-acoustic VTI wave propagation can be described by the following coupled partial differential equations (Duveneck and Bakker (2011);Zhang et al (2011);Chu and Stoffa (2012); Operto et al (2014)):…”