For the modeling of a single-target reflector in a smooth inhomogeneou
s elastic anisotropic medium, it has been recently shown that the volu
me Born integral can be transformed into a surface-scattering integral
on the reflector. This derived surface integral has been called Born-
Kirchhoff as it relates very naturally to the Kirchhoff-Helmholtz inte
gral, thus providing the theoretical link between the two approaches.
Here we specify the derivation and main properties of the Born-Kirchho
ff integral in the acoustic case, and use a simple synthetic example t
o provide a comparison between the new integral and its classical coun
terparts.