A Frequency-domain Seismic Modeling Engine for 3D Visco-acoustic VTI Full Waveform Inversion of Fixed-spread Data

International audienceFrequency-domain full waveform inversion (FWI) of fixed-spread data can be limited to a few discrete frequencies thanks to the redundant control of frequency and scattering angle on the wavenumber coverage. In this framework, 3D finite-difference frequency-domain seismic modeling can be efficiently performed for multiple sources in the visco-acoustic approximation with sparse direct solver. We extend the so-called mixed-grid finite-difference stencil to account for vertical transverse isotropy in visco-acoustic frequency-domain seismic modeling without extra computational cost. The VTI acoustic wave equation is recast as a fourth-order wave equation, which can be decomposed into an elliptic wave equation and an anelliptic term. The discretization of this equation only requires a straightforward adaptation of the existing isotropic stencil. A discretization rule of 4 grid points per minimum wavelength, which is suitable for FWI applications, is used for frequency-domain seismic modeling. We validate our finite-difference frequency-domain method against a finite-difference time-domain method using a smooth VTI acoustic model of the Valhall oil field. Comparison between the real and modeled data for the 7-Hz frequency suggests that our method can provide a suitable modeling engine to perform multi-parameter FWI of fixed-spread data in visco-acoustic VTI media