高静怀^2,3,,
徐文豪^2,3,4,
吴帮玉^1,4,,,
李博⁴,
赵海霞^1,4
1. 西安交通大学数学与统计学院, 西安 710049
2. 西安交通大学电子与信息工程学院, 西安 710049
3. 海洋石油勘探国家工程实验室, 西安 710049
4. 中国石化地球物理重点实验室, 南京 211103

基金项目: 国家自然科学基金项目（41604106，41674123），中国博士后科学基金（2016M600780），中央高校基本科研业务费专项资金（xjj2018260），国家自然科学基金重大项目（41390454）联合资助


详细信息

作者简介: 高静怀, 男, 教授, 博士生导师, 主要从事复杂介质中地震波传播及地震资料处理的理论与方法等研究.E-mail:jhgao@mail.xjtu.edu.cn

通讯作者: 吴帮玉, 男, 1982年生, 西安交通大学数学与统计学院讲师.主要研究方向为波场数值模拟、局域相空间地震波传播、成像以及地震资料处理的理论与方法.E-mail:bangyuwu@xjtu.edu.cn

中图分类号: P631

收稿日期:2018-05-22
修回日期:2018-06-28
上线日期:2018-08-05

Trapezoid grid finite difference seismic wavefield simulation with uniform depth sampling interval

GAO JingHuai^2,3,,
XU WenHao^2,3,4,
WU BangYu^1,4,,,
LI Bo⁴,
ZHAO HaiXia^1,4
1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
2. School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
3. National Engineering Laboratory for Offshore Oil Exploration, Xi'an 710049, China
4. SNOPEC Key Laboratory of Geophysics, Nanjing 211103, China


More Information

Corresponding author: WU BangYu,E-mail:bangyuwu@xjtu.edu.cn

MSC: P631

--> Received Date: 22 May 2018
Revised Date: 28 June 2018
Available Online: 05 August 2018


摘要
摘要:由于重力引起的岩石压实效应，一般来说，地震波传播速度由浅入深整体逐渐增大.梯形坐标系设计可耦合速度由浅入深逐渐增大的变化，该坐标系中均匀网格采样所对应的物理直角坐标系网格由浅入深逐渐增大，也即浅部低速区对应细网格，深部高速区对应粗网格.在梯形坐标系表征波动方程后利用有限差分求解，本文实现一种深度均匀采样、横向采样间隔随深度增加逐渐线性增大的有限差分地震波模拟方法.梯形坐标系波动方程离散后，仍采用常规均匀网格有限差分算法对其求解.由于横向网格大小由浅入深线性增加，本方法可避免不同大小网格区域过渡所产生的虚假反射.梯形坐标系波场模拟浅层精度高，深层横向响应范围广，可有效减少有限差分网格数量.本文提出的方法是在更广义的坐标系下利用有限差分求解波动方程，正交坐标系仅为该梯形坐标系之特例.本文旨在为大速度动态范围深地高效高精度地震波场模拟提供一种思路.
关键词: 有限差分/
变网格/
梯形坐标变换/
波动方程

Abstract:In general, seismic wave propagation speed increases along with depth due to compaction of rocks caused by gravity. Trapezoid coordinate design can incorporate the general increasing trend of velocity. The uniform grid sampling in trapezoid coordinate corresponds to a grid interval increasing along with depth in Cartesian coordinate, that is, fine grid in shallow low velocity region and coarse grid in deep high velocity region. The wave equation is derived in trapezoid coordinate and the traditional uniform grid finite difference can be evoked for the calculation. In this work, we achieve a variable grid finite difference seismic wavefield simulation method with linear increasing for lateral grid interval and uniform sampling along depth. Due to the gradual linear increase of the grid interval, this method avoids the artificial reflections caused by transition of regions with different grid size comparing with the discontinuous variable grid mesh finite difference method. The proposed method achieves high accuracy result in shallow region and covers wider apertures in deep area. The trapezoid coordinate is more general and including Cartesian coordinate as one special case. The proposed method has a potential application for accurate and efficient deep seismic wavefield simulation with wide range velocity variation.
Key words:Finite difference/
Variable grid/
Trapezoid coordinate transform/
Wave equation



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