An interferometric interpretation of Marchenko redatuming

Abstract

Recently, an iterative scheme was introduced to retrieve up- and downgoing Green’s functions at an arbitrary location F in the subsurface. The scheme uses the reflection data as acquired at the surface as input, together with an estimate of the direct arrival from the surface to location F, which is referred to as the initial focusing function. We interpret the overall action of the scheme as the successive actions of various linear filters, acting on the initial focusing function. These filters involve multidimensional crosscorrelations with the reflection response, time reversals and truncations in time. Inspired by literature on seismic interferometry, we interpret multidimensional crosscorrelation in terms of the subtraction of traveltimes along stationary raypaths. The scheme has been designed for layered media with smooth interfaces. Our interferometric interpretation reveals some of the scheme’s limitations when it is applied to more complex configurations. It can be concluded that (downgoing or upgoing) internal multiples that arrive at F with a particular angle can be retrieved only if the initial focusing function (i.e., the direct wave) has visited F with this angle. Consequently, shadow zones that cannot be imaged with primary reflections can theoretically also not be imaged with internal multiples, when the current iterative scheme is used for their retrieval. Finally, we observe that the current scheme does not yet optimally perform in media with point scatterers, since an underlying assumption (generally referred to as the ansatz) is not perfectly obeyed in this case. It is envisioned that this can be improved if truncations in time that are implemented after each iteration are replaced by more advanced filtering methods.