Local and Regional Comparisons of Gravity and Magnetic Fields

Abstract

A long recognized connection between the gravitational gradients of the Earth’s crust and its magnetic anomalies, known as Poisson’s relationship, is the object of investigation in this paper. We develop the mathematical and theoretical basis of this relationship in both the space and frequency domains. Anomalies of the magnetic field thus implied by the gravitational gradients (or other derivatives of the gravitational potential) are called pseudo-magnetic anomalies; and, they assume a linear relationship between the mass density of the source material and its magnetization induced by the Earth’s main magnetic field. Tests in several regions of the U.S. that compare gravitational gradients derived from the high-resolution model, EGM08, and a continental magnetic anomaly data base reveal that the correlation implied by Poisson’s relationship is not consistent. Some areas exhibit high positive correlation at various frequencies, while others have even strong negative correlation. Therefore, useful applications of Poisson’s relationship depend on the validity of the underlying assumptions that, conversely, may also be investigated and studied using a combination of gradiometric and magnetic data.