Theoretical discussion on signal modeling and noise suppression in seismic data processing

Noises in land seismic data, which can be classified into linear and nonlinear coherent noises, incoherent noises, and random noises, may come from near-surface formations, externally sourced wavefield, and other sources. The basic idea of noise suppression is to establish a model to predict signals or coherent noises and then remove coherent, random, and incoherent noises from seismic data. Some high-precision imaging methods, such as full waveform inversion and least-squares reverse time migration, should be accomplished using seismic data with high signal to noise ratios. This paper presents an overview of denoising theories and techniques, and develops a conceptual model of seismic data to show that signals or coherent noises with linear and/or nonlinear structures float in random noises that satisfy a certain probability distribution. Based on the conceptual model, various denoising methods are discussed, including AR model predictor, linear Radon transform, K-L transform, and Hankel matrix for the prediction of linear signals or coherent noises and Radon transform and polynomial fitting for the prediction of nonlinear (hyperbolic) signals or coherent noises. The fundamental point of denoising is optimal signal modeling, which is the basic idea for most denoising methods in commercial processing systems. The comparative analysis in this paper provides further insights on denoising theories to improve the effect of data processing.