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### Abstract

The Born and Kirchhoff-Helmholtz integrals are the most widely used descriptions of reflected and transmitted wavefields due to smooth interfaces. Although representing basically the same phenomena, the two integrals result from quite independent formulations, and are traditionally kept as completely separate objects. Concerning the model of a single target reflector in a smooth inhomogeneous elastic anisotropic medium, it has been recently shown that the volume Born integral in the region surrounding the reflector, can be transformed into a surface scatter-ing integral on the reflector. This derived surface integral has been called Born-Kirchhoff as it relates very naturally to the Kirchhoff-Helmholtz integral, thus providing the theoretical link between the two approaches. Besides, briefly reviewing the derivation and main properties of the Born-Kirchhoff integral in the acoustic case, we use a simple synthetic example to provide a comparison between the new integral and their classical counterparts.

/content/papers/10.3997/2214-4609-pdb.299.54
1997-11-07
2021-12-02