Beyond the Born Approximation

Abstract

The description of scattered waves in an inhomogeneous elastic medium is frequently treated using the Born formalism. In most previous studies this involved ray tracing through a smooth approximation to the medium under consideration, and the use of the deviation of the true medium from this smooth approximation as the ‘potential’ in the Born scattering integral. A formalism is developed here for describing body waves scattered from parameter gradients in the medium, which obviates the necessity for an approximate smooth medium. The substitution of an asymptotic ray theory (ART) Green's function into the elastodynamic wave equation produces terms due to the error in the ART Green's function. These terms are functions of the velocity and the density gradients of the medium. They are treated as ‘source’ terms and the solution for the scattered waves obtained as an integral over these terms. The expression is similar in form to the Born formalism but is superior in that both the ART Green's function and the scattering integral are calculated using ray tracing through the true medium, not some smooth approximation to it.