摘要
在瞬变电磁法三维数值模拟中,边界采用Dirichlet条件会导致计算空间过大,耗时过长.对电磁场传播的开域空间进行截断,在截断边界采用CPML吸收边界条件,可以有效减少计算量.从坐标伸缩Maxwell方程可以推导出CPML差分更新方程,通过对空气介质、似稳态条件下大地介质的吸收边界参数进行理论推导,分析了不同频率下的衰减系数和反射系数对吸收效率的影响.根据分析结果对Roden提出的吸收边界参数分布进行改进,使其适合低频条件下的电磁波吸收;分别以无耗空气模型、典型大地介质模型和地下高阻空腔模型为例,计算了CPML吸收边界在不同介质、不同空间大小下的反射误差.计算结果表明,地下模型的边界距离CPML边界在10~15个网格,空气层厚度4~6个网格的空间大小就可以满足计算精度要求.
In the numerical simulation of three-dimensional numerical simulation of Transient Electromagnetic Method（TEM）,when using Dirichlet boundary conditions in the underground border,it is will cause the space too big and takes long time to compute.For the open domain problem of electromagnetic wave propagation,Convolution Perfectly Matched Layer（CPML）absorbing boundary conditions is able to absorb electromagnetic waves without reflection.The CPML truncated the big space to small one and this can effectively reduce the amount of calculation.The CPML differential update equation can be derived from the coordinate modified Maxwell equations.The parameters of CPML are analyzed in the air medium and the earth medium with approximate steady-state conditions.According to the theoretical derivation and the experimental simulation,the parameters of CPML proposed by Roden are improved to match the absorption of low frequency electromagnetic wave.Reflection errors of air model,ground model and cave model are calculated to verify the precision in different size of the space.Based on those results,10~15 grids distance from CPML to underground model border and 4~6 grids thickness of air layer can meet the requirement of accuracy.
出处
《地球物理学进展》
CSCD
北大核心
2017年第4期1705-1710,共6页
Progress in Geophysics
