基于L<sub>1-2</sub>范数约束的叠前多分量地震数据直接反演纵横波速度比方法

doi:10.11720/wtyht.2025.1365

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Abstract

The ratio of compressional to shear wave velocities(hereafter referred to as the P-to-S-wave velocity ratio) is an essential parameter for lithology discrimination,reservoir characterization,and gas reservoir identification.Direct inversion of PP-wave seismic data to derive the P- and S-wave velocities has been a well-established technique.However,calculating the P-to-S-wave velocity ratio using the P- and S-wave velocities obtained through individual inversion may lead to cumulative errors.In contrast,since PS-wave data inherently contain S-wave velocity information,the joint inversion of PS-wave data can significantly improve the accuracy of the P-to-S-wave velocity ratio.This study employed the L_1-2 norm to enhance the resolution of inversion results.Compared to the L₁ and L₂ norms,the L_1-2 norm yielded sparser solutions with higher resolution.First,this study derived and assessed the accuracy of linearized forward modeling approximate formulas for PP- and PS-waves.Second,based on Bayesian theory,this study incorporated the L_1-2 norm to construct an objective function for the direct inversion of the P-to-S-wave velocity ratio.Third,the objective function was solved to obtain the inversion result for the P-to-S-wave velocity ratio.The quantitative comparison of the correlation coefficients demonstrates that the inversion results based on the L_1-2 norm outperform those based on the L₁ or L₂ norm,direct inversion is superior to indirect inversion,and joint inversion provides better results than individual inversion.Finally, the effectiveness and feasibility of the proposed method in this study were validated through inversions of synthetic and field data.

Key words： P-to-S-wave velocity ratio L_1-2 norm multi-wave multi-component seismic data direct inversion

Received: 25 October 2024 Published: 22 July 2025

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	Lei HAN
	Jing-Ye LI
	Wei-Heng GENG
	Yong-Ping WANG
	Qi-Yu YANG
	Yu-Ning ZHANG

Cite this article:

Lei HAN,Jing-Ye LI,Wei-Heng GENG, et al. A method for calculating the P-to-S-wave velocity ratio through direct inversion of prestack multi-component seismic data based on the L_1-2 norm constraint[J]. Geophysical and Geochemical Exploration, 2025, 49(3): 620-630.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2025.1365 OR https://www.wutanyuhuatan.com/EN/Y2025/V49/I3/620

Direct inversion of P-wave velocity (a), S-wave velocity (b) and density (c) by PP and PP-PS wave

Correlation coefficients of inversion results of different data types m/s

The first type of typical AVO model

The second type of typical AVO model

The third type of typical AVO model

Comparison of PP wave reflection coefficients of three typical AVO models

Comparison of PS wave reflection coefficients of three typical AVO models

Noise-free forward-modeled PP-wave(a) and PS-wave(b) seismic records

Comparison of one-dimensional probability density functions with different distributions

Two-dimensional images of L₀ norm (a), L₁ norm (b), L₂ norm (c), and L_1-2 norm (d)

Noise-free data inversion results
a—PP only inversion;b—PP+PS joint inversion

Forward modeling synthetic seismic record with SNR=10
a—PP wave seismic record;b—PS wave seismic record

SNR=10 data inversion results
a—PP only inversion;b—PP+PS joint inversion

Forward modeling synthetic seismic record with SNR=4
a—PP wave seismic record;b—PS wave seismic record

Comparison of correlation coefficients of inversion results

SNR=4 data inversion results
a—PP only inversion;b—PP+PS joint inversion

PP only inversion results with SNR=10(a) and SNR=4(b) data

Part-stack seismic profile of PP waves(a) and PS waves(b)

Comparison between offset well log inversion results inversion results of PP waves alone(a) joint inversion results of PP-PS waves(b)

Direct inversion of P-to-S wave velocity ratio using L_1-2 norm constraint for single PP waves seismic data

Direct inversion of P-to-S wave velocity ratio using L_1-2 norm constraint for joint PP waves and PS waves seismic data

Comparison of correlation coefficients of inversion results

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