Exact wavefield extrapolation for elastic reverse-time migration

A fundamental step of any wave equation migration algorithm is represented by the numerical projection of the recorded data down into the subsurface where reflections occur. The geophysical community refers to this concept as wavefield extrapolation and the extrapolated wavefield is called the receiver wavefield. In elastic reverse-time migration, standard wavefield extrapolation only uses partial information contained in elastic waves, and artificial wave energy is extrapolated as a consequence, polluting seismic images. We propose an exact extrapolation formula, which fully employs the velocity-stress nature of the elastic wavefield to create an improved estimate of the extrapolated receiver wavefield. A synthetic example illustrates the resulting improvements in imaging, providing evidence of the importance of using the full recorded data.