Controlled-source Seismic Interferometry by Multi-dimensional Deconvolution Applied to a Laterally Varying Elastic Model

In controlled-source seismic interferometry (SI), one typical aim is to redatum an array of sources to a receiver location. In cross-correlation (CC) based SI this goal is achieved by cross-correlating registrations at two receiver locations and summation over sources. Although a closed boundary of multi-component sources surrounding the receiver array is required, applications generally involve one-sided illumination and single source types only, which can result in spurious artifacts, erroneous kinematics and incorrect amplitudes. Therefore it can be helpful in some cases to replace cross-correlation by multi-dimensional deconvolution (MDD). In MDD based SI the reflection response is retrieved by inverting a general integral equation, which we implement in a least-squares sense. Additional advantages include improved radiation characteristics of the retrieved (virtual) sources and a relaxation of some assumptions, including the absence of loss terms and knowledge of the source wavelet. Disadvantages include the need for accurate wavefield decomposition and instabilities that might occur in the matrix inversion that forms the core of MDD. We apply SI by both MDD and CC to an elastic model with lateral variations and report slight improvements of MDD compared to CC.