基于LSCG法和波数补偿的频率域二维地震正演模拟方法

doi:10.11720/wtyht.2023.2633

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摘要

在地震勘探中,地震正演模拟是非常重要的技术。与时间域正演相比,频率域正演速度快,计算效率高。如何高效准确地完成频率域正演计算是目前该领域的一个重要问题。数值频散问题和如何提高计算效率降低求解分解阻抗内存占用量一直是频率域正演所需要解决的问题。与传统的直接法求解阻抗矩阵的频率域正演方法不同,本文采用最小二乘共轭梯度法(LSCG法)求解阻抗矩阵进行频率域正演,并提出了一种波数补偿的表达式来压制数值频散现象。经过简单模型和复杂模型的数值测试,采用最小二乘共轭梯度法(LSCG法)求解阻抗矩阵进行频率域正演能够有效降低计算时间,且采用波数补偿的频率域正演方法能够有效压制数值频散现象,提高波场模拟精度。

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	张入化
	张洞君
	黄建平
	苟其勇
	周嘉妮

关键词 ：地震勘探, 频率域正演, 最小二乘共轭梯度法, 数值频散, 计算效率

Abstract：

The seismic forward modeling technique is critical to seismic exploration.Moreover,it shows a faster rate and higher calculation efficiency in the frequency domain than in the time domain.Presently,there is a need to complete the forward calculation in the frequency domain efficiently and accurately.The specific problems include the numerical dispersion and the high memory consumption for calculating and decomposing impedance,which should be reduced by improving the calculation efficiency.Different from the conventional direct method,this study adopted the least-squares conjugate gradient (LSCG) method used to determine the impedance matrix for the frequency-domain forward modeling and proposed an expression for wavenumber compensation to suppress the numerical dispersion.The numerical tests of simple and complex models show that the LSCG method can effectively reduce the calculation time and that the frequency-domain forward modeling method based on wavenumber compensation can effectively suppress the numerical dispersion and thus improve the precision of wave field simulation.

Key words： seismic exploration frequency-domain forward modeling least-squares conjugate gradient method numerical dispersion calculation efficiency

收稿日期: 2021-12-25 修回日期: 2022-12-12 出版日期: 2023-04-20

ZTFLH:

P631.4

基金资助:西南油气田科技项目(20210304-02)

引用本文:

张入化, 张洞君, 黄建平, 苟其勇, 周嘉妮. 基于LSCG法和波数补偿的频率域二维地震正演模拟方法[J]. 物探与化探, 2023, 47(2): 384-390.
ZHANG Ru-Hua, ZHANG Dong-Jun, HUANG Jian-Ping, GOU Qi-Yong, ZHOU Jia-Ni. Frequency-domain 2D seismic forward modeling method based on the LSCG method and the wavenumber compensation. Geophysical and Geochemical Exploration, 2023, 47(2): 384-390.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2023.2633 或 https://www.wutanyuhuatan.com/CN/Y2023/V47/I2/384

Fig.1 九点差分格式

Fig.2 频率域正演流程

Fig.3 洼陷模型

Fig.4 洼陷模型正演中频率20 Hz(a)和36 Hz(b)频率切片

Table 1 洼陷模型正演计算效率对比

Fig.5 洼陷模型正演单炮记录
a—采用波数补偿;b—未采用波数补偿

Fig.6 加拿大洛基山脉模型

Fig.7 加拿大洛基山脉模型正演中频率20 Hz(a)和36 Hz(b)频率切片

Fig.8 1.2 s处的波场快照(25 Hz)
a—采用LSCG+波数补偿;b—未采用波数补偿

Fig.9 1.2 s处的波场快照(35 Hz)
a—采用LSCG+波数补偿;b—未采用波数补偿

Table 2 复杂模型正演中4种不同求解阻抗矩阵的正演方法计算效率

Fig.10 加拿大洛基山脉模型正演单炮记录
a—采用波数补偿;b—未采用波数补偿

Fig.11 正演模拟第100道单道对比分析
a—未采用波数补偿;b—采用波数补偿

Fig.12 解析解信号与本文方法接收信号对比

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