The magnetic and gravitational potentials and fields due to arbitrarily shaped bodies with homogeneous magnetization and uniform density distribution are expressed as a convolution of the source geometry and the Green’s function. The Green’s function depends on the location of the observation point and on either the magnetization vector (in the case of the magnetic field) or the density (in the case of the gravitational attraction). A fast digital convolution algorithm is used for efficiently and accurately calculating anomalies caused by irregular bodies. The shapes of the calculated anomalies faithfully reproduce the exact shapes when the sampling interval selected for digitizing the source geometry and the Green’s function is less than one‐tenth of the depth of the source. In the digital convolution method for computing anomalies, it is unnecessary, for any given structure, to perform analytical integration of the dipolar magnetic field or the gravitational field of a point mass. One of the examples given in the paper deals with the computation of the magnetic anomaly due to the irregularly shaped Round Butte Laccolith, Montana. The results are found to be in satisfactory agreement with the observed aeromagnetic data. A new method is also described for calculating the magnetization vector associated with the laccolith and the datum level of the magnetic observations.
