Estimating rock-vector magnetization from coincident measurements of magnetic field and gravity gradient tensor

Abstract

Poisson’s theorem relating components of the magnetic field to components of the gradient of the gravity vector assuming a common source has been cast into a general form. A given magnetization distribution in the terrain or in the underlying crust is propagated into the corresponding magnetic field through the gravity gradient tensor. Conversely, measured magnetic field anomalies and measured gravity gradient tensor anomalies can be used to estimate the unknown magnetization vectors without knowledge of the geometry of the sources. We have tested the method on recently acquired data over a greenstone belt in Northern Sweden. The topographic relief was sufficiently variable to dominate the measured gravity gradient tensor. In practice, we have concentrated on areas where the norm of the gravity gradient tensor reached a maximum so that there was a better chance of identifying isolated sources with well-defined density and magnetization. We have surrounded the selected points by a small window and used all the data lying within that window to estimate the magnetization vectors. We have compared the estimated amplitudes and directions of magnetization with those measured from selected rock samples in the area and found a relatively modest agreement. We have interpreted this as a result of two effects: (1) Measured magnetizations are generally lower than those estimated by this method, and we believe that this is related to the fact that the collection of samples in the field is biased because of a small number of outcrops in most parts of the area. (2) This analysis is biased toward high-amplitude magnetic anomalies; i.e., the estimation procedure works best for high-amplitude magnetic anomalies, in which case, the influence of neighboring anomalies is reduced. The estimated magnetization directions show a strong dominance of remanent magnetization over induced magnetization in agreement with laboratory measurements on rock samples from the area.