Localization of maximum-depth gravity anomaly sources by a distribution of equivalent point masses

A method is proposed for localizing the maximum depth sources of a gravity anomaly data set collected on a generally uneven, free surface topography. First, the Newtonian-type integral defining the Bouguer anomaly function is solved as a sum of elementary contributions from pointlike mass contrast (Delta-mass) elements. Using this solution, the power associated with the Bouguer effect is derived as a sum of crosscorrelation integrals between the Bouguer anomaly data function and a scanner function expressing the gravity effect from a pointlike Delta-mass element. Finally, applying Schwarz's inequality to a single crosscorrelation power term, a Delta-mass occurrence function is introduced as a suitable tool for localizing the maximum-depth sources (MDS) of a given gravity anomaly field. The MDS localization procedure consists of scanning the half-space below the survey area by a unit strength Delta-mass element and calculating the Delta-mass occurrence function at the nodes of a 3-D regular grid. The grid values exceeding in modulus a prefixed threshold can be contoured to single out the zones underground where the Delta-mass occurrence function shows the highest values. These zones are interpreted as the equivalent MDS pattern for the observed gravity field. Synthetic examples demonstrate that the MDS localization approach is a powerful tool especially suited for analyzing unconstrained gravity data. In the case of an isometric source body, we show that the maximum depth of the equivalent point mass virtually coincides with the position of the actual source center. In the case where the source is not isometric, besides giving the maximum depth of the equivalent point mass, the method also allows obtaining useful information on the upper limit for the source depth. An application to a real case in the field of volcanology (Mt. Etna volcano, Sicily, Italy) is finally presented and discussed.