Adaptive surface-related multiple subtraction using sparse norm minimization method

Abstract

Multiple attenuation, which is difficult to solve, is an important problem in the seismic data processing especially in the marine case. A strategy for multiple removal consists of estimating a model of the multiples and then adaptively subtracting this model from the data by estimating shaping filters. A classical approach of this strategy is the surface-related multiple elimination (SRME) method. In the SRME process, the subtraction stage plays an important role, because there are amplitude, phase, and frequency distortions in the predicted multiple model. Typically, in this stage the primaries are assumed to have minimum energy (l₂-norm) and the solving method is the least-square errors. Methods using this norm are robust in the presence of noise, but can produce bad results when primaries and multiples interfere. Replacing the l₂-norm, a sparseness constraint is used in our new approach. The sparseness constraint should give better results because the correct subtraction of the predicted multiples should lead to a primary estimation with a minimum number of events. We also develop a fast gradient method for solving the sparse norm minimization problem. The effective results of the new method are illustrated with the synthetic data in the one-dimensional and two-dimensional cases. It is shown that the sparse norm minimization problem with fast gradient solution methods leads to much improved attenuation of the multiples while the minimum energy assumption is violated. The multiples being subtracted fit the multiples well in the data while preserving the energy of primaries.

Keywords:

• seismic data-processing
• multiple elimination
• SRME
• sparseness
• gradient method

AMS Subject Classification:

• 65K10
• 65J15
• 86-08

Acknowledgements

We are quite grateful to reviewers’ helpful comments and suggestions on revision of the paper. This work is supported by National Natural Science Foundation of China under grant number 11271349, Knowledge Innovation Programs of Chinese Academy of Sciences KZCX2-YW-QN107 and the National Science and Technology Major Project 2011zx05057-001-003.