二阶声波方程频域PML边界条件及频域变网格步长并行计算

研究了二阶声波方程频域PML边界条件和频域变网格并行计算技术。PML边界是一种较为理想的吸收边界方法，多用在求解时域应力速度方程中，但对于频域声波正演，二阶位移方程更常用。从一阶声波方程PML吸收边界条件导出频域二阶位移方程PML边界条件，模拟算例得到的频率切片、时间切片和地震记录对比都说明该边界条件吸收效果很好。频域单炮正演不同频率间是独立的，据此低频部分采用大网格计算，高频采用小网格，实现变网格步长计算技术，这是较时间域正演的一个优势，在保证模拟质量的同时，减少计算量和内存消耗。

PML Boundary Conditions for Second-Order Acoustic Wave Equations and Variable Grid Parallel Computation in Frequency-Domain Modeling

With the development of the computer, full-waveform inversion based on frequency-domain modeling attracts researchers’ attentions again, accordingly, PML boundary conditions for second-order acoustic wave equations and variable grid parallel computation in frequency-domain modeling are studied. PML boundary conditions is a relatively ideal absorbing boundary method and is usually used in solving the stress-velocity equations in time domain, however, for frequency acoustic wave modeling, second order displacement equation is more commonly used. We derived frequency domain second-order displacement equation PML boundary conditions from the first order acoustic wave equation PML boundary conditions and present satisfactory results of simulation examples. A single shot frequency domain modeling is implemented by solving a number of linear equations followed by an inverse Fourier transform on the records, so the frequency domain parallel computing can be performed either in different shots or in different frequencies. According to the frequency dependent character, we study the variable grid spacing computing method, using large grids in low frequencies, and small grids in high frequencies, which is one of the advantages compared to time domain modeling, and reduce the number of computation and memory consumption in the premise of ensuring the quality of simulation.