Elastodynamic Full Wavefield Modelling with Legendre Polynomials

Abstract

Full Wavefield Migration (FWMig) is an inversion-based seismic imaging modality that incorporates multiple reflections via one-way wave propagation. The flexible Full Wavefield Modelling (FWMod) engine that undergirds FWMig can be extended to address both compressional and converted waves. To take care of the angle-dependent nature of reflection and transmission coefficients, a vast number of unknown subsurface parameters has to be estimated in the FWMig process, especially when elastodynamic wave propagation is considered. This can easily result in a significant null space, potentially hampering the underlying inversion procedure. To restrain the number of unknown parameters, we propose an efficient new parameterization for FWMod by expanding reflection and transmission coefficients in Legendre polynomials, providing us with an orthonormal basis that is expected to benefit FWMig. With the aid of a numerical experiment in a two-dimensional layered elastic medium, we show that a relatively small number of only three or four Legendre polynomials per coefficient per gridpoint is sufficient to model pre-critical seismic data. We prospect that our methodology can be extended to include (spatially-varying) reflector dips, so that it might eventually be used for FWMig in laterally-varying two- and three-dimensional elastic media.