Blind deconvolution of seismic signals with non-white reflectivities

Abstract

Seismic deconvolution technology is important in seismic data processing. We propose a new blind deconvolution algorithm for simultaneous wavelet estimation and deconvolution of seismic data. Optimal seismic deconvolution can be achieved by the combined application of a non-white reflectivity model and the blind deconvolution method. We incorporate a scaled Gaussian noise (SGN) model of seismic reflection coefficients into the seismic blind deconvolution method. The SGN model has the property of scale invariance. We present a framework to generalise the conventional deconvolution procedure to handle reflection coefficients that do not follow the white-noise model. Reflection coefficients are assumed to have an autocorrelation function with a power spectrum roughly proportional to some power of frequency.

The seismic blind deconvolution method consists of three steps: (1) selection of initial reflectivities, (2) determination of the hyper parameters of the problem, and (3) an iterative procedure to solve the resulting equations until a tolerance criterion is satisfied. The alternative relaxation solution and pre-conditioned conjugate gradient algorithm are employed for practical numerical implementation. Seismic blind deconvolution not only can better realise the simultaneous evaluation of the seismic wavelet and the reflection coefficients, but also has advantages of stable algorithm and fast convergence. The test shows that the method is an effective tool of improving the resolution of seismic data that can effectively broaden the useful band of records.