One of the parameters derived from field measurements of Sub-Audio Magnetics (SAM) technique is called Total Field Magneto metric Resistivity (TFMMR). In general, SAM is a high resolution technique that obtains subsurface electrical and magnetic properties through measuring total magnetic field including the synthetic geomagnetic field associated with the low frequency (less than 200 Hz) galvanic current flowing in the earth. In a previous paper by one of the authors of this paper, the anomalous TFMMR responses due to simple geometrical targets have been presented in details. However, as was pointed out in that paper, the simple models are ideal models that are rarely exists in nature and hence the need to find the solution for complex structures using numerical methods is inevitable. In this paper, the theoretical basis of the TFMMR parameter and the behavior of the governing electric and magnetic fields over 2-D structures in both spatial and wave number domains are derived first. Next the selection of the proper numerical technique for TFMMR forward modeling over 2-D structures via employing 3-D sources (point source electrodes) is followed by addressing the numerical difficulties encountered in the course of obtaining valid responses including 1) the singularity associated with the source term (current electrode) in the governing partial differential equations, 2) the singularity associated with the inverse Fourier transform and 3) singularities associated with computing different magnetic field components. Finally, some methods for resolving the numerical singularities are presented and the validity and accuracy of the numerical results against the available simple analytical solutions are evaluated.
)