Seismic Deconvolution via Total Variation Regularization

The trace-by-trace seismic deconvolution methods for reducing band-limited wavelet interference often cause lateral instability of the estimated reflectivity or impedance, and yield some trails like noodles, corresponding to relatively high wave-number components, when the signal-to-noise ratio of data is low and/or the data include high wave-number noise (or error). In this paper, a modified total variation (TV) regularization by linearly combining the sparseness regularization of model difference along the temporal direction and that along the spatial direction, where spatial regularization can be described as L1 norm of difference model along the interpreted horizontal direction, is introduced to develop a seismic deconvolution method to reduce even overcome these problems. The TV regularization connects the reflectivity at a point with its adjacent points and implicitly with any other points, thus introduces some additional useful information, especially for spatial continuity. In theory, minimizing TV has the ability to preserve edges of model parameters. A synthetic data example and a field data example are adopted to illustrate the performances of the method especially for the inherent role of sparseness regularization of model difference along the temporal and spatial directions.