True Amplitude-Versus-Offset Green's Function Retrieval Using Augmented Marchenko Focusing

Abstract

Summary The Marchenko focusing method enables the retrieval of Green's functions between virtual sources in the subsurface and receivers at the surface using surface reflection data and the direct arrival of the inverse transmission response of the overburden as input. The latter is the initial down-going focusing function and is conventionally approximated via modeling in an estimated smooth medium as the detailed velocity field is usually unknown. The characteristic of the focus and, hence, the radiation pattern of the virtual source is determined by the initial down-going focusing function. Approximating this input by the time reversed direct arrival modelled in a kinematically correct smooth medium results in dynamically erroneous redatumed Green's functions, with overall and angle-dependent amplitude errors. We show that, using an augmented Marchenko algorithm, we can accurately correct for the angle-dependent amplitude error in a laterally-invariant medium, yielding a true Green's function up to a single scale factor. Accurately retrieved Green's functions subsequently could open the way for target- oriented analysis methods, such as reflection full-waveform inversion with virtual sources.