Representations for the Marchenko Method for imperfectly sampled data

Abstract

The Marchenko method is based on two integral representations for focusing functions and Green’s functions. In practice the integrals are replaced by finite summations. This works well for regularly sampled data, but the quality of the results degrades in case of imperfect sampling. We reformulate the integral representations into summation representations which properly account for imperfectly sampled data and we illustrate these representations with numerical examples. We indicate how these representations may be used to modify the Marchenko method to account for imperfect sampling.