Multi-Dimensional Deconvolution with Stochastic Gradient Descent

Abstract

Multi-Dimensional Deconvolution (MDD) is a versatile technique used in seismic processing and imaging to create ideal datasets deprived of overburden effects. Whilst, the forward problem is well defined for a single source, stable inversion of the MDD equations relies on the availability of a large number of sources, this being independent on the domain where the problem is solved, frequency or time. In this work, we reinterpret the cost function of time-domain MDD as a finite-sum functional, and solve the associated problem by means of stochastic gradient descent algorithms, where gradients at each step 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. Therefore, it represents a novel, efficient, and robust approach to deconvolve seismic wavefields in a multi-dimensional fashion.