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The resistivity method is a classical geophysical exploration technique that plays important roles in mineral exploration, hydrogeological and geological engineering exploration, and, to a lesser extent, earthquake prediction Analytical methods can be used to generate synthetic results for a few simple forward problems. However, for most forward problems we must use numerical methods. Alfano (1959). Dieter et al. (1969), Lee (1975), Snyder (1976), Oppliger (1984). Eskola et al. (1984), and Kostyanev (1994) use the integral equation method for modeling resistivity and IP responses. Spiegel et al. (1980) simulate the terrain effect on 2-D resistivity surveys using a conformai transformation The use of the finite-element method (FEM) has led to significant improvement in accuracy (Coggon 1971; Rijo 1977; Fox et al 1980 Pridmore et al 1981 Holcombe etal 1984) But for some “problems with complex boundaries such as the 1984 Xu et al., 1988)

This chapter presents the application of the BEM to calculate the electric potential-field due to a point source over 2-D and 3-D geometrical sections.

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