Isotropic elastic reverse time migration

In order to obtain the migration imaging results with clear physical meaning and geological interpretation, the current elastic reverse time migration methods require P/S waves decomposition to the extrapolated elastic wavefields in the migration process to eliminate the cross-talk artifacts generated by physically mismatched wave modes in the migration imaging results. Given a smooth model of subsurface media with accurate kinematic characteristics of seismic waves, this paper first proposes a general forward representation for migration as a linear inverse problem of seismic data. Then, by using the isotropic elastic wave equation, the P/S wave decoupled elastic wave equations suitable for the smooth model of elastic media are derived, namely a P wave elastic wave equation and a S wave elastic wave equation. Finally, a new method and new realization for the isotropic elastic reverse time migration are proposed. For the reverse time migration of isotropic elastic wave seismic data excited by the pure P (or S) wave source, a new method is proposed, which does not need the P/S waves decomposition to the extrapolated elastic wavefields and does not appear cross-talk artifacts in the migration imaging results. For the reverse time migration of isotropic elastic wave seismic data excited by P/S waves composite source, a new realization is put forward that even if the P/S waves decomposition is used to the extrapolated elastic wavefields, the cross-talk artifacts still appear in the migration imaging results.