Frequency-domain finite-difference one-way full-wavefield modeling

Abstract

Seismic modelling plays an important role in the estimation of subsurface parameters by waveform inversion. Modelling methods based on a two-way wave equation are well known for their high accuracy, however by using them explicitly when solving inverse problems is very nonlinear, yielding local minima issues. One of the possibilities to overcome this is splitting the governing two-way wave equation into a set of one-way wave equations that define propagation along the preferred (vertical) direction and that are coupled by a special term that includes transmission and reflection functions. In this case, the scattering is mainly driven by the coupling term whereas the velocity model is responsible for the propagation, which simplifies the inversion and also puts more control on the modelling. We demonstrate that this system of equations can be discretized and solved numerically using a frequency-domain finite-difference (FDFD) approach. Numerical examples demonstrate the validity of such modelling as a forward model in full wavefield migration (FWM) – an inversion-based imaging method that includes multiple scattering and transmission effects.