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Measurement of gravitational and magnetic fields plays an important role in geophysical exploration. These potential fields can be mathematically transformed from the actual observation point to a fictitious observation point to enhance or reduce features in the data. For example, the effect of near-surface sources can be diminished by upward continuation of the observed values measured on the ground surface to a plane above the surface. On the other hand, if we want to enhance the effect of a shallow source, we perform downward continuation, which determines the fields at some depth below the surface.

In normal magnetic and gravity surveys, only one component of the field is measured. However, other components are often required for interpretation purposes. To derive additional information about the geological structure from the observed data, the derivatives of the field are often used. The conversion of one component of the observed data into other components or the calculation of the derivatives is called field transformation.

There are many methods of field continuation and transformation, but most of them are derived assuming that the data are measured on horizontal profiles or planes. However, if the topography is undulating, numerical methods such as the equivalent source technique (Dampney, 1969; Emilia, 1973; Bhattacharyya and Chan, 1977) and the finite harmonic series (Henderson and Cordell, 1971) are needed to process the data.

In this chapter we apply the BEM to the problem of 2-D and 3-D potential-field continuation and transformation.

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