基于褶积完全匹配吸收边界的声波方程数值模拟

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

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。

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 prob- lem.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 indi- cated that CPML can improve the precision effectively in the wave field simulation without increasing the computational cost.