Direct, wave-equation-based modeling of Marchenko-type focusing functions

Abstract

Focusing functions are wavefields that focus at a single point when injected into a source-free volume from its boundary. Focusing functions that are related to the Marchenko equation can be injected from an open part of the boundary only, while vanishing on the remaining boundary. Building on this property, a method for direct, wave-equation-based modeling of Marchenko-type focusing functions in arbitrarily complex media is presented. The method naturally extends conventional frequency-domain modeling. While the numerical examples are for one dimension, a similar concept should, in principle, be applicable to the general three-dimensional case.