A representation for Green’s function retrieval by multidimensional deconvolution

Abstract

Green’s function retrieval by crosscorrelation may suffer from irregularities in the source distribution, asymmetric illumination, intrinsic losses, etc. Multidimensional deconvolution (MDD) may overcome these limitations. A unified representation for Green’s function retrieval by MDD is proposed. From this representation, it follows that the traditional crosscorrelation method gives a Green’s function of which the source is smeared in space and time. This smearing is quantified by a space–time point-spread function (PSF), which can be retrieved from measurements at an array of receivers. MDD removes this PSF and thus deblurs and deghosts the source of the Green’s function obtained by correlation.