Stochastic Multi-Dimensional Deconvolution

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