Summary

With the acoustic single-sided Marchenko method it is possible to retrieve the Green’s function of a virtual source in the subsurface from the single-sided reflection response of the medium and an estimate of the first arrival of the Green’s function. Important ingredients of the Marchenko method are the so-called focusing functions. One of the underlying ideas of the acoustic Marchenko method is that the Green’s functions and focusing functions reside in different time intervals in the time domain. We call this the causality condition. The only overlap of the Green’s functions and focusing functions occurs at one time instant, namely at the time of the direct arrival of the Green’s function. In this paper we analyze the causality condition for the elastodynamic extension of the single-sided Marchenko method. It appears that the overlap of the elastodynamic Green’s functions and focusing functions occurs in an extended time interval. The parts of the focusing functions that overlap with the Green’s functions cannot be retrieved with the Marchenko method, and must therefore be specified separately. It appears that these overlapping parts are defined as the inverse of the forward-scattered part of the transmission response of the medium