Extension of the Born Inversion Method to a Depth Dependent Reference Profile

摘要

The purpose of this paper is to describe an extension of the multidimensional Born inversion technique (Cohen and Bleistein, 1979a) for acoustic waves. In that earlier work, a perturbation in reference soundspeed was determined by assuming that the reference or background speed was constant. In this extension, we allow the reference speed to be a function of the depth variable, z, but still require that it be independent of the transverse variables. The output of this method is a high frequency bandlimited reflectivity function of the subsurface. The reflectivity function is an array of bandlimited singular functions scaled by the normal reflection strength. Each singular function is a Dirac delta function of a scalar argument which measures distance normal to a reflecting interface. Thus, the reflectivity function is an indicator map of subsurface reflectors which is equivalent to the map produced by migration. In addition to the assumption of small perturbation, the method requires the assumption that the reflection data reside in the high frequency regime, in a well-defined sense.