Stochastic Multi-Dimensional Deconvolution

Geophysical measurements such as seismic datasets contain valuable information that originate from areas of interest in the subsurface; these seismic reflections are, however, inevitably contaminated by other events created by waves reverberating in the overburden. Multidimensional deconvolution (MDD) is a powerful technique used at various stages of the seismic processing sequence to create ideal datasets deprived of such overburden effects. While the underlying forward problem holds for a single source, a successful inversion of the MDD equations requires the availability of a large number of sources alongside prior information, possibly introduced in the form of physical constraints (e.g., reciprocity and causality). In this work, we present a novel formulation of time-domain MDD based on a finite-sum functional. The associated inverse problem is then solved by means of stochastic gradient descent algorithms, where the gradients at each iteration are computed using a small subset of randomly selected sources. Through synthetic and field data examples, we show that the proposed method converges more stably than the conventional approach based on full gradients. Stochastic MDD represents a novel, efficient, and robust strategy to deconvolve seismic wavefields in a multidimensional fashion.