Weighted Multisteps Adaptive Autoregression for Seismic Image Denoising

We devised a new filtering technique for random noise attenuation by weighted multistep adaptive autoregression (WMAAR). We first obtain a series of denoised results by means of different steps adaptive AR, and then we sum these results with different weights. The adaptive AR coefficients are obtained by solving a global regularized least squares problem, in which regularization is used to control the smoothness of these coefficients. The adaptive AR can estimate seismic events with varying slopes since AR coefficients have temporal and spatial variabilities. We derive the weights from the normalized power of local similarity by comparing the result of the nearest step with the ones of other steps. The application of these weights makes the proposed algorithm more effective in fault information conservation. The proposed WMAAR can be implemented both in the frequency–space and in time–space domains. Multidimensional synthetic and field seismic data examples demonstrate that, compared with conventional methods in frequency–space or time–space domain, multistep adaptive AR is more effective in suppressing random noise and preserving effective signals, especially for complex geological structure (e.g., faults).