Summary Some conventional noise attenuation methods in seismic data processing often need assume that coherent events are piecewise-stationary, piecewise-linear and regularly sampled along spatial direction. In this paper, without any spatial assumptions about coherent signal, a noise attenuation method using Bayesian inversion is presented. Its essential idea is to directly invert the “clean” data, regarded as model parameter, from observed seismic data by maximizing a posterior distribution, which is made up of prior distribution and likelihood function. Whether this method can reduce noise is dependent on the choice of prior information. Based on a statistical knowledge that coherent data oscillates slightly and random noise strongly, the minimization of L1 norm of model parameters’ difference quotient, also called as total variation, is used as prior information. What advantage of this method is that it can enhance nonstationary and nonlinear seismic events. Moreover, the de-noised effect neither strongly relies on the size and layout of time windows nor depends on whether traces are sampled regularly. Especially, this method has good ability for preserving edges of discontinuous events, which often correspond to important geologic features, and deblurring amplitude’s variation along spatial direction, which is probably AVO response. A model data and a real data are used to test its validity.
Introduction The structural feature and physical property of subsurface reflectors can be reflected in seismic section. That’s just what geophysicists make use of to explore oil and gas. Unfortunately, besides effective response from reflectors, some random disturbance is also recorded in seismic sections, which compromises our ability for describing the underground medium. Generally speaking, conventional random noise attenuation methods can be classified into two categories: (1) prediction filtering method in the frequency-space (f-x) domain, mainly including f-x deconvolution (Canales, 1984), and (2) eigen-decomposition-and-reconstruction method, mainly including (local) singular value decomposition (SVD) filtering (Ulrych et al., 1988; Bekara and van der Baan, 2007) and (partial) Karhunen-Loeve transform filtering (Jones and Levy, 1987; Al-Yahya, 1991). Both this two methods are based on the fact that coherent events and noise can be separated in certain domain. However, this separability is strictly limited by some conditions or assumptions. For prediction filtering, we need assume that coherent events are linear and stationary, and the trace interval is equal. For eigen-decomposition-andreconstruction, we need assume that coherent events are horizontal (dipping events should be flattened by dip steering), the amplitude of one trace for any event is proportional to that of any other traces, the phase is invariant among traces, and there are no conflicting events in the section. However, real data does not satisfy all assumptions of every method, thus the de-noised result is often not as ideal as we expect. Even if some techniques, such as sliding time windows and dip steering, are applied to try to make seismic data meet those geometry assumptions, they will make noise-reduction process complicated and bring other new problems. In this paper, noise attenuation using Bayesian inversion is proposed, which does not need any spatial assumptions about coherent events.