韩复兴^1,,
孙章庆¹,
陈祥忠^2,,,
高正辉¹,
王瑞兴²,
刘俊成¹,
王丽丽³
1. 吉林大学地球探测科学与技术学院, 长春 130026
2. 北京桔灯地球物理勘探股份有限公司, 北京 102200
3. 吉林油田地球物理勘探研究院, 松原 138006

基金项目: 国家自然科学基金面上项目(42074150)和国家重点研发计划课题"典型矿集区三维地质结构与矿体定位"(2017YFC0601305)联合资助


详细信息

作者简介: 韩复兴, 男, 1981年生, 博士, 现任吉林大学地球探测科学与技术学院教授, 主要从事地震波传播与成像、计算地球物理方面的学习与研究.E-mail: hanfx@jlu.edu.cn

通讯作者: 陈祥忠, 男, 1982年生, 博士, 主要从事物探综合处理方法技术的研究.E-mail: 6447316@163.com

中图分类号: P631

收稿日期:2020-11-02
修回日期:2020-12-28
上线日期:2021-03-10

Directional interpolation of the velocity model based on partial differential equations used in migration imaging

HAN FuXing^1,,
SUN ZhangQing¹,
CHEN XiangZhong^2,,,
GAO ZhengHui¹,
WANG RuiXing²,
LIU JunCheng¹,
WANG LiLi³
1. College for Geoexploration Science Technology, Jilin University, Changchun 130026, China
2. Beijing Orangelamp Geophysical Exploration Company Limited, Beijing 102200, China
3. Geophysical Exploration and Research Institute of Jilin Oilfield, Songyuan 138006, China


More Information

Corresponding author: CHEN XiangZhong,E-mail:6447316@163.com

MSC: P631

--> Received Date: 02 November 2020
Revised Date: 28 December 2020
Available Online: 10 March 2021


摘要
摘要:对于射线类偏移成像来说，求解射线追踪系统中所涉及的属性值不在网格节点上的插值计算问题是一个非常重要的环节，它影响到求解走时、路径和振幅信息的计算效率和精度，进而影响到整个偏移成像的质量和效率.本研究根据速度模型的空间梯度特点，考虑被插值点处速度的梯度在横向和纵向的分布特征，构建基于速度梯度空间变化的偏微分方程算法，将近几年发展起来的基于偏微分方程的定向插值算法引入到射线类偏移成像当中，实现射线追踪当中涉及的属性值不在网格节点上的插值计算.由于偏微分方程法本身固有的特性(局部特征不变性、解的唯一性和线性叠加性)，因此，该算法可以实现不破坏原始速度模型空间梯度结构的非网格节点属性的插值计算.通过在常用的速度模型上的插值计算对比、不同速度模型上射线路径对比分析以及复杂介质模型上最后的偏移成像结果分析可以得出，应用基于速度梯度构建的偏微分方程插值算法在进行插值计算的过程当中可以实现不破坏原始速度模型空间速度梯度结构的属性计算，同时应用该算法可以最终提高射线类偏移成像的质量.
关键词: 偏微分方程/
射线追踪/
模型处理/
定向插值/
偏移成像

Abstract:Interpolation of velocity and velocity derivative at non-grid nodes of velocity model is an important part of ray-type migration imaging,which affects the efficiency and accuracy of ray tracing and the quality and efficiency of whole migration imaging. According to the characteristics of the velocity model and considering the gradient effect of the velocity at interpolated points,partial differential equation algorithm has been constructed based on the minimum velocity gradient of the interpolated points along the x-direction and the z-direction of velocity model. In this work,the directional interpolation algorithm based on such partial differential equations in recent years is introduced into ray type migration imaging to achieve the velocity and velocity derivative interpolation of non-grid nodes. Because the partial differential equation method has linear superposition characteristic,uniqueness of the model solution,the local features of retention,the PDE interpolation algorithm can be used to solve the velocity and velocity derivative interpolation problem of non-grid nodes based on the spatial structure of the original velocity model. Through interpolation of the Marmousi and Sigsbee velocity models and comparison of ray paths,interpolation results and migration imaging results of rough and steep slope rugged seabed velocity models,it can be concluded that the application of partial differential equation interpolation to velocity models can better maintain the edge characteristics of the velocity models and improve the quality of migration imaging.
Key words:Partial differential equation/
Ray tracing/
Processing Model/
Directional Interpolation/
Migration imaging



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