基于虚拟波场的可控源三维电磁法正演

Forward modeling of a controllable-source 3Delectromagnetic method based on fictitious wave field

根据扩散场和虚拟波场的变换关系,将频率域电磁扩散方程转换成虚拟域的波动方程,实现了虚拟波场的电磁场数值计算。在边界的处理上,通过引入复频率完全匹配层吸收边界条件,降低了内存的存储量。将空气层包含在计算域中,避免了地—空界面的复杂处理。通过与均匀半空间解析解对比,其相对误差在3.5%以内,验证了算法的有效性和正确性。最后通过典型地电模型的数值模拟表明:通过一次正演可以获得多个频率的三维电磁响应,提高了计算效率。虚拟波场计算的视电阻率对场源效应不敏感且对异常体的边界具有较好的识别能力。

This study converted the frequency-domain electromagnetic diffusion equation into the wave equation in the fictitious domain based on the transformation relationship between the diffusion field and the fictitious wave field,achieving the numerical calculation of the electromagnetic field in the fictitious wave field.By introducing the complex frequency shifted perfectly matched layer(CFPML)boundary condition,the storage capacity of the computer memory decreased.Furthermore,by encompassing the air layer in the calculation domain,the complex processing of the ground-air interfaces was avoided.Compared to the uniform half-space analytical solution,the algorithm proposed in this study had relative errors of less than 3.5%and thus is effective and correct.Finally,the numerical simulation of a typical geoelectric model indicated that the 3D electromagnetic responses of multiple frequencies can be obtained through single forward modeling,suggesting an elevated calculation efficiency.The numerical simulation results also exhibit that the apparent resistivity calculated based on the fictitious wave field is insensitive to the field source effect and thus can effectively identify anomaly boundaries.