Simultaneous seismic interpolation and denoising based on sparse inversion with a 3D low redundancy curvelet transform
Jingjie Cao 1 3 Jingtao Zhao 2
+ Author Affiliations
- Author Affiliations
1 Hebei GEO University, Shijiazhuang, Hebei 050031, China.
2 State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology (Beijing), Beijing 100083, China.
3 Corresponding author. Email: cao18601861@163.com
Exploration Geophysics 48(4) 422-429 https://doi.org/10.1071/EG15097
Submitted: 8 September 2015 Accepted: 28 April 2016 Published: 9 June 2016
Abstract
The simultaneous seismic interpolation and denoising problem can be solved as a sparse inversion problem by using the sparseness of seismic data in a transformed domain as the a priori information, where the properties of the sparse transform will significantly influence the numerical results and computational efficiency. Curvelet transform has nearly optimal sparse expression for seismic data, thus seismic signal processing based on this transform tends to result in preferable results. However, the redundancy of this transform can be 24–32 for three dimensional data which is not computationally cost efficient. This paper introduces a low redundancy curvelet transform to simultaneously interpolate and denoise. The redundancy of the proposed transform can be reduced to 10 for three dimensional data, and this property will improve the computational efficiency of the curvelet transform-based signal processing. The iterative soft thresholding method was chosen to solve the sparse inversion problem. Some practical principles on how to choose the regularisation parameters are discussed, due to the crucial nature of the regularisation parameter for simultaneous interpolation and denoising. Numerical experiments on synthetic and field data demonstrate that the low redundancy transform can provide reliable results while at the same time improving the computational efficiency.
Key words: curvelet transform, inverse problems, sparse inversion, wavefield interpolation.
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