A number of boundary value problems, relevant to the modelling of the electrical response of bodies of interest to the exploration geophysicist, are formally posed. Electromagnetic excitation by both time-harmonic and time-invariant sources is considered for model types that can be characterized as three-dimensional (3-D), two-dimensional (2-D), and two-and-a-half dimensional (21/2-D), the last representing the case of a 2-D body excited by a confined source. The method of surface integral equations is used to present a detailed theoretical development of the solutions to these boundary value problems. For the cases involving time-harmonic excitation, consideration is given to their asymptotic forms at low frequency.
A numerical strategy for the solution of the 21/2-D time-harmonic electromagnetic boundary value problem is proposed, and is theoretically justified. The method is applied to a suite of 21/2-D models including conductive, resistive and permeable targets in both a full-space find a (layered) half-space. A model consisting of a local step in the depth to resistive basement is also considered. For all cases, the numerical results are documented in some detail, and inferences are drawn on the general behaviour of the surface integral equation technique in the 21/2-D context. The results are most encouraging, but two weaknesses in performance are apparent, viz. the system becomes ill-conditioned at low frequencies and large cpu times are required to compute a target response using the present numerical solution strategy.
The digital filter method for numerical Fourier transformation is discussed and new sets of filter weights are presented for the sins and cosine transforms. These compare most favourably with those already in existence.