Reflecting boundary conditions for interferometry by multidimensional deconvolution

Abstract

Seismic interferometry (SI) takes advantage of existing (ambient) wavefield recordings by turning receivers into so-called “virtual-sources.” The medium’s response to these virtual sources can be harnessed to image that medium. Applications of SI include surface-wave imaging of the Earth’s shallow subsurface and medical imaging. Most interferometric applications, however, suffer from the fact that the retrieved virtual-source responses deviate from the true medium responses. The accrued artifacts are often predominantly due to a non-isotropic illumination of the medium of interest, and prohibit accurate interferometric imaging. Recently, it has been shown that illumination-related artifacts can be removed by means of a so-called multidimensional deconvolution (MDD) process. However, The current MDD formulation, and hence method, relies on separation of waves traveling inward and outward through the boundary of the medium of interest. As a consequence, it is predominantly useful when receivers are illuminated from one side only. This puts constraints on the applicability of the current MDD formulation to omnidirectional wavefields. We present a modification of the formulation of the theory underlying SI by MDD. This modification eliminates the requirement to separate inward-and outward propagating wavefields and, consequently, holds promise for the application of MDD to non-isotropic, omnidirectional wavefields