一种基于L<sub>1</sub>-L<sub>1</sub>范数稀疏表示的地震反演方法

doi:10.11720/wtyht.2019.1390

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Abstract

High-resolution seismic inversion is confronted with two problems:First,seismic inversion is an ill-posed problem and has multiplicity of solutions,and second,noise and distortion are generated in the flows of acquisition and processing to reduce the stability of the inversion algorithm.Aimed at solving these two problems, this paper proposes an inversion method of seismic reflectivity based on L₁-L₁-norm sparse representation.Firstly,the L₁-norm regularization term is used to reduce the inversion multiplicity,and then the L₁-norm fitting term is used to enhance the noise robustness.The wavelet is extracted by well logging and seismic data to construct the over-complete wedge wavelet dictionary,and then the seismic signal is sparsely decomposed by the L₁-L₁-norm sparse representation,so as to realize the high-resolution reflectivity inversion.The experimental results of wedge model and actual seismic data show that the inversion algorithm is stable and has good noise robustness,and the inversion results are accurate and credible through logging data calibration.

Key words： sparse representation dipole decomposition reflectivity inversion L₁-norm over-complete wedge wavelet dictionary

Received: 29 October 2018 Published: 15 August 2019

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	Articles by authors
	Zhan-Zhan SHI
	Yan-Qing XIA
	Huai-Lai ZHOU
	Yuan-Jun WANG
	Xiang-Rong TANG

Cite this article:

Zhan-Zhan SHI,Yan-Qing XIA,Huai-Lai ZHOU, et al. Seismic reflectivity inversion based on L₁-L₁-norm sparse representation[J]. Geophysical and Geochemical Exploration, 2019, 43(4): 851-858.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2019.1390 OR https://www.wutanyuhuatan.com/EN/Y2019/V43/I4/851

Wedge geological model
a—reflection coefficient model;b—synthetic seismic section

Comparison of random noise sensitivity
a、b、c、d—inversion results of traditional algorithms;e、f、g、h—inversion results of L₁-L₁ norm sparse representation;random noise intensities from top to bottom are 0%,1%,5% and 10%,respectively

Comparison of outlier sensitivity
a、b、c、d—inversion results of traditional algorithms;e、f、g、h—inversion results of L₁-L₁ norm sparse representation;the number of outliers from top to bottom is 0%,1%,5%,and 10%,respectively

Comparative analysis of inverted reflectivity of wedge model
a—traditional algorithm inversion results under the condition of 1% random noise and 1% outliers;b—L₁-L₁ norm sparse representation inversion results under the condition of 1% random noise and 1% outliers;c—traditional algorithm inversion results under the condition of 5% random noise and 5% outliers;d—L₁-L₁ norm sparse representation inversion results under the condition of 5% random noise and 5% outliers

Vertical section (a) and its amplitude spectrum (b) extracted from a 3D seismic data set intersect well L₁

Comparison of inverted reflectivity section
a—traditional algorithms;b—L₁-L₁ norm system sparse representation

Comparison of inverted impedance sections
a—traditional algorithms;b—L₁-L₁ norm system sparse representation

Zoom of inverted impedance sections
a—traditional algorithms;b—L₁-L₁ norm system sparse representation

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