Singular-value decomposition analysis for seismic interferometry by multidimensional deconvolution

Multidimensional deconvolution (MDD) is an alternative method for seismic interferometry which retrieves new wavefield with desired source-receiver configuration from observed wavefield without source information. Because this method involves inverse problems to estimate new wavefield, we apply singular-value decomposition (SVD) to evaluate pseudo-inverse solution. Introducing SVD into MDD opens the way of interpreting the effect of the source-receiver configuration in the inversion procedure by linear mapping theory. We numerically simulate the wavefield with two-dimensional homogeneous model and investigate the rank of the data kernel of inverse problem for MDD. The sparse source distribution and the dense source distribution show almost same number of rank and also retrieve same wavefield when the spatial distribution is identical. Therefore analyzing the rank of the data kernel of inverse problem can be used for the determination of optimum source distribution. Furthermore, we show that the ambiguity of the wavefield which is inferred from the model resolution matrix constructed by the matrices from SVD showed the same trend with the discrepancy of the inverted wavefield from true wavefield. Therefore the evaluation of the reliability of the inverted wavefield could be possible by evaluating the model resolution matrix.