Laplace-domain Waveform Inversion for the 3D Acoustic-elastic Coupled Media

In the marine streamer survey, the sources and receivers are located in the homogeneous acoustic media; however, the media below the sea bottom, which is the target area, has highly heterogeneous 3D elastic properties. Thus, the hydrophone pressure data contain various elastic effects, such as shear wave effects, mode converted waves and amplitude offset variation, and these effects impact the Laplace-transformed wavefield. Therefore, it is not possible to perfectly reduce the misfit between modelled and observed data using only acoustic wave equations. In this study, we developed a Laplace-domain waveform inversion algorithm for 3D acoustic-elastic coupled media. We can precisely simulate the environment of a conventional streamer marine survey by coupling the 3D acoustic and elastic wave equations using a proper boundary condition at the solid-fluid interface. Also, for the matrix solver, we suggest using the parallel sparse direct solver library, which was developed by the MUltifrontal Massively Parallel Solver (MUMPS) team. Because this is a direct matrix solver, we do net lose the main advantage of implicit modeling (e.g., frequency or Laplace domain modeling) over the explicit time-domain modelling when we solve the wave field for a number of shots.