基于分段采样和MCA的地震数据重建

doi:10.11720/wtyht.2022.1458

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Abstract

Data reconstruction is a critical preliminary work in the processing of seismic data.Compressed sensing (CS) has been well applied in data reconstruction.The key to CS is random sampling,which converts the mutual coherent alias caused by regular under-sampling into lower-amplitude incoherent noise. But traditional sampling methods lack constraints on sampling points, resulting in excessive noise interference. The segmented random sampling (SRS) method can effectively control the distance between sampling points. Furthermore, a single mathematical transformation will lead to incomplete sparse representation and impact data reconstruction. The morphological component analysis (MCA) can decompose a signal into several components with outstanding morphological features to approximate the complex internal structure of data. A new dictionary combination (Shearlet+DCT) has been found under the MCA framework, and the block coordinate relaxation (BCR) algorithm has been used to get the optimal solution to obtain desired reconstruction results. Tests of real data have proven that the proposed method can produce good effects when used to reconstruct the SRS data.

Key words： compressed sensing segmented random sampling morphological component analysis data reconstruction

Received: 25 November 2021 Published: 03 January 2023

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	Articles by authors
	De-Ying WANG
	Kai ZHANG
	Zhen-Chun LI
	Yi-Kui ZHANG
	Xin XU

Cite this article:

De-Ying WANG,Kai ZHANG,Zhen-Chun LI, et al. Seismic data reconstruction based on segmented random sampling and MCA[J]. Geophysical and Geochemical Exploration, 2022, 46(5): 1214-1224.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2022.1458 OR https://www.wutanyuhuatan.com/EN/Y2022/V46/I5/1214

Schematic diagram of segmented random sampling

Sampled data and spectrum
a—synthetic seismic record;b—spectrum of synthetic seismic record wavenumber;c—synthetic seismic data after regular sampling;d—spectrum of synthetic seismic data after regular sampling wavenumber;e—synthetic seismic data after random sampling;f—spectrum of synthetic seismic data after random sampling wavenumber;g—synthesized seismic record after SRS;h—spectrum of synthesized seismic record after SRS

Original data, sampling matrix and missing data
a—original data;b—Random sampling matrix;c—Jitter sampling matrix;d—segmented random sampling matrix;e—missing data after random sampling;f—missing data after Jitter sampling;g—missing data after segmented random sampling

Reconstruction results and difference profiles of DCT dictionary
a—DCT reconstruction result of random sampling;b—DCT reconstruction result of Jitter sampling;c—DCT reconstruction result of segmented random sampling;d—DCT reconstruction result of segmented random sampling;e—DCT difference profile of Jitter sampling;f—DCT difference profile of segmented random sampling

Reconstruction results and differences profile of Shearlet dictionary
a—Shearlet reconstruction result of random sampling;b—Shearlet reconstruction result of Jitter sampling;c—Shearlet reconstruction result of segmented random sampling;d—Shearlet reconstruction result of segmented random sampling;e—Shearlet difference profile of Jitter sampling;f—Shearlet difference profile of segmented random sampling

Reconstruction results and difference profiles of Dictionary Combination
a—Shearlet+DCT reconstruction result of random sampling;b—Shearlet+DCT reconstruction result of Jitter sampling;c—Shearlet+DCT reconstruction result of segmented random sampling;d—Shearlet+DCT reconstruction result of segmented random sampling;e—Shearlet+DCT difference profile of Jitter sampling;f—Shearlet+DCT difference profile of segmented random sampling

Evaluation parameters of reconstruction results

Lagrangian multiplier and number of iterations and reconstruction signal-to-noise ratio

Under sampling of noise synthetic seismic data
a—original noise data;b—50% missing data

Three reconstruction results
a—DCT reconstruction result;b—Shearlet reconstruction result;c—Shearlet+DCT reconstruction result

Evaluation parameters of reconstruction results

Original profile

Shearlet+DCT reconstruction of 11 consecutive missing
a—11 consecutive missing images;b—reconstruction result;c—absolute error

Shearlet+DCT reconstruction of 22 consecutive missing
a—22 consecutive missing images;b—reconstruction result;c—absolute error

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