Initial conditions for elastodynamic Green's function retrieval by the Marchenko method

Abstract

With the acoustic Marchenko method it is possible to retrieve the Green’s response to a virtual source in the subsurface from the single-sided reflection response at the surface. The acoustic Marchenko method relies on the separability of the Green’s functions and focusing functions in the time domain. Recently, the first steps have been made towards extending the singlesided Marchenko method to the elastodynamic situation. A complication of the elastodynamic scheme is that the Green’s functions and focusing functions partly overlap each other. The iterative Marchenko method does not retrieve the parts of the focusing functions that overlap with the Green’s functions. Ideally, the overlapping parts of the focusing functions are defined as the initial condition for the iterative Marchenko method. This leads to a perfect retrieval of the elastodynamic Green’s functions. In this paper we investigate the results of the Marchenko method when we use less stringent initial conditions. It appears that using an initial focusing function which contains single events leads to an accurate retrieval of two components of the Green’s matrix, provided the converted reflection responses are included in the Marchenko scheme.