频率域反射波全波形速度反演

成景旺; 顾汉明; 刘春成; 刘志斌

doi:10.3799/dqkx.2013.038

频率域反射波全波形速度反演

doi: 10.3799/dqkx.2013.038

成景旺^{1, 2,},
顾汉明^{1, 2, ,},
刘春成³,
刘志斌³

1.
中国地质大学地球物理与空间信息学院，湖北武汉 430074
2.
中国地质大学构造与油气资源教育部重点实验室，湖北武汉 430074
3.
中海油研究总院，北京 100027

基金项目:

国家重大科技专项 2011ZX05025-001

详细信息

作者简介:
成景旺(1987-)，男，博士，研究方向为石油地震勘探正反演研究.E-mail：chjw2008@126.com

通讯作者:
顾汉明，E-mail：guhanming@263.net

中图分类号: P631.4
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出版历程
- 收稿日期: 2012-04-15
- 刊出日期: 2013-03-01

Full Waveform Inversion for Velocity Structure from Reflected Wave Seismic Data in the Frequency Domain

1.
Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan430074, China
2.
Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education, China University of Geosciences, Wuhan430074, China
3.
CNOOC Research Center, Beijing100027, China

摘要

摘要: 全波形反演不仅利用相位和振幅信息，还利用波形的细节变化，具有刻画模型精确细节的能力.在对稀疏矩阵直接LU分解求解的基础上，采用梯度预处理方法对声波介质速度模型进行了反射波全波形反演.采用误差反向传播算法计算目标函数梯度以及伪Hessian矩阵的对角线元素来做梯度预处理.数值模型的实验结果表明，利用有效的频率段便能反演出分辨率较高的速度结构，用低频反演出的结果作为高频反演的初始模型，减少了解的非唯一性.二维高斯光滑初始模型提供了有利的低频信息，得到较好的反演结果.伪Hessian矩阵的预处理吸收了高斯牛顿法的二次收敛优势，在不增加计算量的前提下，加快收敛速度.
- 全波形反演 /
- 梯度预处理 /
- 误差反向传播算法 /
- 伪Hessian矩阵
Abstract: Full waveform inversion uses not only phase and amplitude information, but also waveform details, revealing precise details of the model. We use the LU factorization technique directly to solve the forward modeling, and show a preconditioned gradient method to inverse the velocity structure using the reflected wave from low-frequency to high-frequency in this study. The numerical structure of the finite difference method and back-propagation algorithm is exploited to develop an algorithm that explicitly calculates the Jacobin matrix utilizing a forward model solution. Furthermore, the diagonal elements of the false Hessian matrix are used as the preconditioned operator. Numerical tests on simple synthetic models find that a good velocity model can be obtained only by several frequency inversions, and the strategy of using low-frequency inversion result as the starting model in the high-frequency inversion can greatly reduce the non-uniqueness of their solutions. The initial model directly affects the imaging result. The smooth two-dimensional Gaussian model provides favorable low-frequency information for a better inversion result. The fast convergence can be achieved by using of the false Hessian matrix without any increase in the premise of computation.
- full waveform inversion /
- preconditioned gradient /
- back-propagation algorithm /
- false Hessian matrix

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图 1 不同频率的反演结果(其中b~i为2~16 Hz的反演结果)

Fig. 1. The inverted model at different frequencies

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图 2 复杂模型

a.理论模型；b.初始模型；c.反演速度模型

Fig. 2. The complex model

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图 3 合成记录对比

a.理论模型合成记录；b.反演结果合成记录；c.两者残差

Fig. 3. Comparison of the synthetic seismograms

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图 4 Marmous模型及反演结果

a.理论模型；b.初始模型；c.未进行预处理反演结果；d.预处理反演结果

Fig. 4. The Marmous model and the inverted velocity model

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图 5 模型合成记录以及残差

a.理论模型合成记录；b.未进行预处理反演结果合成记录；c.预处理反演结果合成记录；d.初始模型合成记；e.记录b和记录a残差；f.记录c和记录a残差

Fig. 5. The synthetic seismograms and the residual

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图 6 横向不同位置速度曲线

a.4 000 m处；b.5 600 m处；c.6 875 m处

Fig. 6. The velocity curves at different horizontal positions

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图 7 迭代误差曲线

a.预条件梯度法迭代曲线；b.未进行预处理迭代曲线

Fig. 7. The relative error as a function of iteration number

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