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

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.