刘延利^1,,
李振春^1,,,
孙苗苗¹,
王姣²,
刘强¹
1. 中国石油大学(华东)地球科学与技术学院, 山东青岛 266580
2. 青岛黄海学院智能制造学院, 山东青岛 266427

基金项目: 国家自然科学基金"深水区非规则多次波分离与成像方法研究"（41974145）和中石油重大专项"塔里木盆地深层复杂高陡构造与碳酸盐岩储层地震速度建模及成像关键技术研究"（ZD2019-183-003）联合资助


详细信息

作者简介: 刘延利, 女, 1988年生, 在读博士, 主要从事地震波传播与成像方面的研究.E-mail:746573860@qq.com

通讯作者: 李振春, 1963年生, 男, 教授(博士生导师), 主要从地震波传播与成像等方面的研究.E-mail:leonli@upc.edu.cn

中图分类号: P631

收稿日期:2020-05-11
修回日期:2020-11-16
上线日期:2021-01-10

High precision simulation in frequency domain based on improved acoustic equation and MCPML boundary

LIU YanLi^1,,
LI ZhenChun^1,,,
SUN MiaoMiao¹,
WANG Jiao²,
LIU Qiang¹
1. School of Geosciences in China University of Petroleum, Qingdao Shandong 266580, China
2. Intelligence and Manufacture College, Qingdao Huanghai University, Qingdao Shandong 266427, China


More Information

Corresponding author: LI ZhenChun,E-mail:leonli@upc.edu.cn

MSC: P631

--> Received Date: 11 May 2020
Revised Date: 16 November 2020
Available Online: 10 January 2021


摘要
摘要:数值频散和边界反射是频率域模拟时需要解决的两个重要问题.然而，受计算效率和分解阻抗矩阵时的内存占用量的制约，提高有限差分算子长度或增加有限差分网格数目均不是提高频率域模拟精度的最优解决方案.本文首先分析了数值频散产生的理论机制，在此基础上，推导了一种"波数补偿"的声波方程表达式来压制数值频散，并给出其物理意义，有效地改善了数值频散问题，提高了模拟精度；在边界问题上，本文采用多轴卷积完全匹配层（MCPML）边界条件代替传统的完全匹配层（PML）边界条件，快速吸收边界内的残余能量，压制边界反射.结合改进声波方程和MCPML边界条件，给出了一种高精度的频率域声波方程有限差分格式.数值模拟结果表明，在不增加计算量和内存占用量的前提下，本文研究的方法、正演精度高、波场模拟清晰、无干扰反射，是一种可靠高效的频率域模拟方法.
关键词: 数值频散/
波数补偿/
MCPML边界/
高精度/
频率域模拟

Abstract:Numerical dispersion and boundary reflection are two important problems affecting the simulation results in frequency domain. However,restricted by the computational efficiency and memory consumption of impedance matrix decomposition,increasing the length of finite-difference operators or the number of finite-difference grids are not the optimal solution to improve the simulation accuracy. Firstly,the theoretical mechanism of numerical dispersion is analyzed. On this basis,an improved acoustic equation expression with "wave number compensation" is derived and its physical significance is elaborated,which could effectively suppress numerical dispersion and improve simulation accuracy; On the boundary reflection problem,instead of perfectly matched layer (PML) boundary,the multi-axial convolution perfectly matched layer (MCPML) boundary is used to rapidly absorb the residual energy and eliminate the boundary reflection. Combined with the improved acoustic equation and MCPML boundary,a high-precision expression of acoustic equation in frequency domain is studied. The numerical simulations demonstrate that the proposed method in this paper is a high-precision simulation method in frequency domain,with high simulated accuracy and efficiency,clear simulated wave fields and without increasing the calculation amount and memory consumption.
Key words:Numerical dispersion/
Wave number compensation/
MCPML boundary/
High precision/
Frequency domain simulation



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