Inversion for magnetic anomalies of arbitrary three-dimensional bodies

Two-dimensional (profile) inversion techniques for magnetic anomalies are widely used in exploration geophysics; but, until now, the three-dimensional (3-D) methods available have been restricted in their geologic applicability, dependent upon good initial values or limited by the capabilities of existing computers. We have developed a fully 3-D inversion algorithm intended for routine application to large data sets.The algorithm, based on a Fourier transform expression for the magnetic field of homogeneous polyhedral bodies (Hansen and Wang, 1988), is a 3-D generalization of CompuDepth (O'Brien, 1972). Like CompuDepth, the new inversion algorithm employs the spatial equivalent of frequency-domain autoregression to determine a series of coefficients from which the depths and locations of polyhedral vertices are calculated by solving complex polynomials. These vertices are used to build a 3-D geologic model. Application to the Medicine Lake Volcano aeromagnetic anomaly resulted in a geologically reasonable model of the source.