Elastic Extrapolation of Primary Seismic P‐ and S‐waves1

A bstract The elastic Kirchhoff‐Helmholtz integral expresses the components of the monochromatic displacement vector at any point A in terms of the displacement field and the stress field at any closed surface surrounding A. By introducing Green's functions for P‐ and S‐waves, the elastic Kirchhoff‐Helmholtz integral is modified such that it expresses either the P‐wave or the S‐wave at A in terms of the elastic wavefield at the closed surface. This modified elastic Kirchhoff‐Helmholtz integral is transformed into one‐way elastic Rayleigh‐type integrals for forward extrapolation of downgoing and upgoing P‐ and S‐waves. We also derive one‐way elastic Rayleigh‐type integrals for inverse extrapolation of downgoing and upgoing P‐ and S‐waves. The one‐way elastic extrapolation operators derived in this paper are the basis for a new prestack migration scheme for elastic data.