Wavefield reconstruction inversion modelling of Marchenko focusing functions

Abstract

Marchenko focusing functions are in their essence wavefields that satisfy the wave equation subject to a set of boundary, initial, and focusing conditions. Here, we show how Marchenko focusing functions can be modeled by finding the solution to a wavefield reconstruction inversion problem. Our solution yields all elements of the focusing function including evanescent, refracted, and trapped waves (tunneling). Our examples indicate that focusing function solutions in higher dimensions are however challenging to compute by numerical means due to the appearance of strong evanescent waves.