Sparse multichannel blind deconvolution

Abstract

We developed a sparse multichannel blind deconvolution (SMBD) method. The method is a modification of the multichannel blind deconvolution technique often called Euclid deconvolution, in which the multichannel impulse response of the earth is estimated by solving an homogeneous system of equations. Classical Euclid deconvolution is unstable in the presence of noise and requires the correct estimation of the length of the seismic wavelet. The proposed method, on the other hand, can tolerate moderate levels of noise and does not require a priori knowledge of the length of the wavelet. SMBD solves the homogeneous system of equations arising in Euclid deconvolution by imposing sparsity on the unknown multichannel impulse response. Trivial solutions to the aforementioned homogeneous system of equations are avoided by seeking sparse solutions on the unit sphere. We tested SMBD with synthetic and real data examples. Synthetic examples were used to judge the viability of the method in terms of noise. We found that SMBD gives reasonable estimates of the wavelet and reflectivity series for [Formula: see text]. The results clearly deteriorated when we tried to work on data that were severely contaminated by noise. A real marine data set was also used to test SMBD. In this case, the estimated wavelet was compared with a wavelet estimated by averaging first breaks. The estimated wavelet showed a noticeable resemblance to the average first break with normalized correlation coefficient of 0.92.

A fast algorithm for sparse multichannel blind deconvolution

“…Among other reasons, this happens because of the large similarity between neighboring reflectivities, which makes the problem either numerically unstable or, at worst, ill posed and impossible to solve. To overcome this problem, Kazemi and Sacchi (2014) propose a Bayesian approach in which the hybrid l 1 ∕l 2 -norm loss function is used as a sparsity-promoting regularization function. This technique, called sparse multichannel blind deconvolution (SMBD), presents good results in the synthetic and real data scenarios.…”

“…Thus, one must resort to a body of techniques known as blind deconvolution (Romano et al, 2011). For a thorough account of the several kinds of blind deconvolution methods that have been applied in seismic signal processing, we refer the reader to the "Introduction" section in Kazemi and Sacchi (2014).…”

Skeletonized wave-equation inversion in vertical symmetry axis media without too much math

“…To overcome these limitations, multichannel blind deconvolution algorithms (Xu et al, 1995;Kazemi and Sacchi, 2014) can be used for a more reliable estimation of the source wavelet.…”

Seismic sparse-spike deconvolution via Toeplitz-sparse matrix factorization

“…However, these methods face challenges when being applied to multidimensional data in a trace-by-trace basis: they may show bad lateral continuity and the image quality may be compromised in the presence of noise and wavelet estimation error. Although some scholars have proposed methods to reduce these problems (Wang et al, 2006;Nguyen, 2008;Lu, 2009;Kazemi and Sacchi, 2014;Guitton and Claerbout, 2015;Nose-Filho et al, 2016), the challenges remain for seismic data with complex structure.…”