Kirchhoff elastic wave migration for the case noncoincident source and receiver

In taking into account both compressional (P) and shear (S) waves, more geologic information can likely be extracted from the seismic data. The presence of shear and converted shear waves in both land and marine seismic data recordings calls for the development of elastic wave-migration methods. The migration method presently developed consists of simultaneous migration of P- and S-waves for offset seismic data based on the Kirchhoff-Helmholtz type integrals for elastic waves. A new principle of simultaneously migrating both P- and S-waves is introduced.The present method, named the Kirchhoff elastic wave migration, has been tested using the 2-D synthetic surface data calculated from several elastic models of a dipping layer (including a horizontal layer), a composite dipping and horizontal layer, and two layers over a half-space. The results of these tests not only assure the feasibility of this migration scheme, but also demonstrate that enhanced images in the migrated sections are well formed. Moreover, the signal-to-noise ratio increases in the migrated seismic section by this elastic wave migration, as compared with that using the Kirchhoff acoustic (P-) wave migration alone. This migration scheme has about the same order of sensitivity of migration velocity variations, if V p and V s vary concordantly, to the recovery of the reflector as that of the Kirchhoff acoustic (P-) wave migration. In addition, the sensitivity of image quality to the perturbation of V s /V p has also been tested by varying either V s or V p . For varying V s (with V p fixed), the migrated images are virtually unaffected on the u z depth section while they are affected on the u y depth section. For varying V p (with V s fixed), the migrated images are affected on both the u z and u y depth sections.