Modeling and inversion in acoustic-elastic coupled media using energy-stable summation-by-parts operators

Abstract

Seismic data acquired at the seafloor are valuable in characterizing the subsurface and monitoring producing hydrocarbons fields. To fully use such data, a stable, accurate, and efficient numerical scheme is needed that accounts for acoustic and elastic wave propagation, their interaction at the seafloor interface, and for sources and receivers placed on either side of that interface. Existing methods either make incorrect assumptions or have high implementation and computational costs. We have developed a high-order finite-difference summation-by-parts framework for the acoustic-elastic wave equations in second-order form (in terms of displacements in the solid and an extension of velocity potential in the fluid). Our modified discretization of the elastic operator overcomes the dispersion errors known to plague displacement-based schemes in the high VP/ VS limit. We weakly impose boundary and interface conditions using simultaneous approximation terms, leading to an energy-stable numerical scheme that rigorously handles point injection and extraction. The fully discrete system is self-adjoint after a time reversal and a sign flip and is furthermore a high-order accurate discretization of the continuous problem. The self-adjointness ensures that forward and adjoint wavefields are computed with similar accuracy and simplify gradient computation for inversion purposes. We find that our numerical scheme achieves accuracy comparable to a more computationally expensive spectral-element method and determine its application to a full-waveform inversion using the Marmousi2 model.