Title

Numerical modeling of acoustic wave equations based on convolutional perfectly matched layer absorbing boundary condition

单位

(1.东北石油大学,黑龙江大庆163318;2.黑龙江省普通高校科技创新团队“断层变形、封闭性及与流体运移”,黑龙江大庆163318)

Organization

(1.Northeast Petroleum University,Daqing 163318,China；2.Heilongjiang Province college science and technology innovation team “faults deformation,sealing ability and fluid migration”,Daqing 163318,China)

摘要

完全匹配层(PML)吸收边界条件已广泛应用于地震波场模拟中,但PML吸收边界条件存在一些问题,如对低频和地震波为掠射波时会产生虚假反射等。褶积完全匹配层(CPML)吸收边界条件能够有效地解决PML吸收边界条件存在的问题。推导了带有CPML条件的一阶速度-应力波动方程,并且在方程中引入记忆变量代替复杂褶积项的运算,将CPML与交错网格有限差分算法相结合,发挥了该边界条件节省计算存储空间、易于编程实现等优点。数值模拟结果表明,在不增加计算量的情况下,CPML吸收边界条件有效地提高了波场模拟精度。

Abstract

The perfectly matched layer (PML) absorbing boundary condition has been widely undertaken in numerical modeling of seismic wave fields; however,PML reflects a large amount of spurious energy at grazing incidence or a low frequency at all angles of incidence.The convolutional perfectly matched layer (CPML) absorbing boundary condition can effectively solve the above problem.We deduce a first-order velocity-stress wave equation with CPML,substitute the memory variables for complex convolution operation in the equation,and combine the CPML and a staggered-grid finite difference method in the forward modeling.CPML can save the memory of computers and programs easily from the implementation process.The result of the numerical simulation testing indicated that CPML can improve the precision effectively in the wave field simulation without increasing the computational cost.

关键词：

褶积完全匹配层; 交错网格; 数值模拟; 声波方程; 边界条件;

Keywords:

convolutional perfectly matched layer (CPML),; staggered-grid,; numerical modeling,; acoustic wave equation,; boundary condition;

基金项目

国家自然科学基金(41474118)、黑龙江省杰出青年科学基金项目(JC2016006)、东北石油大学研究生创新科研项目(YJSCX2016-002NEPU)以及大连理工大学海岸和近海工程国家重点实验室开放基金项目(LP1509)联合资助。

DOI

10.3969/j.issn.1000-1441.2017.05.003

基于褶积完全匹配吸收边界的声波方程数值模拟