The moments of a sphere in a uniform field, a versatile model

Abstract

The moments of a sphere in a uniform field can be used to approximately model the moments of a sphere in a dipolar field. The numerical computations are trivial and the approximation is especially good for higher-order moments. The greatest discrepancy is seen on the zeroth-order moment at large radii, however, the zeroth-order moment is not commonly used for interpreting airborne electromagnetic data. The sphere in a uniform field can also be used to approximate the response of a body that has its currents constrained to flow in a specific dip plane. This means that plate-like bodies or anisotropic spheres can also be modelled. The third-order moment of MEGATEMÔ data acquired over the Reid-Mahaffy test site shows an anomalous response than can be modelled by a sphere at 170 m depth with a conductivity of 15 S/m and a radius of 40 m. The currents flowing in the sphere are constrained to flow in a vertical plane. This model is consistent with the geology of the area and a hole drilled to test the anomalous zone.