Wavefield Injection and Reconstruction in Acoustic and Elastic Reverse Time Migrations

Summary Both acoustic and elastic reverse time migrations reconstruct forward and backward wavefields by solving the full wave equation using recorded data as boundary conditions. The wavefield injection and reconstruction are theoretically based on the Kirchhoff integral for acoustic case, and the representation theorem for elastic case, with which accurate wavefields can be reconstructed by complete boundary conditions on a closed surface. However, in most cases, the recording surface is not closed, nor do the recorded data provide complete information to implement the exact Kirchhoff integral/representation theorem. For reflection seismology, usually only pressure is recorded for the acoustic case and displacements are recorded for elastic case. By using a finite-difference propagator, we uniformly inject boundary values based on exact Kirchhoff integral and representation theorem to reconstruct both source-side and receiver-side wavefields for reverse time migration (RTM). Specifically, boundary values are treated as equivalent sources, providing RTMs with an economic source-side wavefield reconstruction strategy using parsimonious memory, where only single-layer boundary values are required. Receiver-side records are injected and time-reversed propagated with correct phases and amplitudes. To investigate how incomplete data can affect the reconstructed acoustic/elastic wavefields, artefacts from incomplete injections are analyzed. Numerical examples verify the effectiveness of the proposed method.