The Poisson theorem establishes a linear relationship between the gravity and magnetic potentials arising from common dense and magnetized bodies with constant magnetization–density ratio and magnetization direction. For geological formations satisfying such constraints (i.e., the Poisson conditions), this theorem provides suitable relationships between the gravity and magnetic anomalies that are useful in interpreting the related data sets. In such applications, both magnetization–density ratio (MDR) and magnetization direction can be estimated, thus helping the subsurface geological mapping from potential field data acquired on the earth's surface. However, no existing method is fully automatic, which has hampered extensive use in routine applications. Such a drawback follows the adoption of equations that, although obeying the Poisson theorem, relate particular components of the gravity and magnetic fields, thus requiring either a known magnetization direction or the implementation of iterative procedures to determine it. To allow one‐pass estimates for both MDR and magnetization direction (more precisely, its inclination projected on the plane normal to the source strike), this paper presents simple analytical solutions for these parameters by relating suitable gravity and magnetic vector fields that are derived from the gravity and magnetic data sets. Because current geophysical surveys usually provide only a single‐field component, a data processing scheme is developed to determine the required components in evaluating the desired vector fields. This is done by applying suitable linear transformations on the measured components according to well‐established filtering techniques in processing gravity and magnetic data. Except for distortions from noise, the proposed method automatically determines the MDR and the projected magnetization inclination for the underlying rocks everywhere the Poisson conditions are satisfied. Two‐dimensional sources are assumed, but no constraint upon their depth and cross‐section shape is required. Distorted estimates only appear close to the sources where at least one of the Poisson conditions is violated. In this case, the proposed technique furnishes apparent values for the rock properties. The abrupt changes of apparent values over contacts detect edges, thus facilitating the mapping of geological boundaries. The proposed technique is used to interpret two profiles across the Appalachian fold belt from the eastern portion of the State of Georgia, and the results are compared with some of the geological information available for the area.
Martin Harold Phillips Bott. 12 July 1926—20 October 2018
