Random noise reduction using Bayesian inversion

Enlightened by the classical total variation (TV) model, we present a novel random noise reduction method for seismic data based on Bayesian inversion, called Bayesian inversion filtering. The method regards 2D 'clean' seismic data as model parameters, and the noise reduction is equivalent to inverting these parameters from the observed data. The inversion is implemented by maximizing a posterior distribution, which is replaced by the product of a priori distribution and a likelihood function. The performance of this method mainly depends on the choice of a priori information. Based on statistical knowledge or assumption that coherent events oscillate slightly and random noise strongly, TV is used as the prior information to control the noise reduction. A variety of synthetic and real data examples show that the method can clarify amplitude, phase and frequency variations in the spatial direction. Moreover, the geometrical properties of the events, such as the curvature and slope, can be retained. In particular, this method preserves the edges of discontinuous events, which usually correspond to important geologic features.