Multiscale estimation of excess mass from gravity data

We describe a new multiscale method to estimate the excess mass of gravity anomalies sources, based on the theory of source moments. Starting from a multipole expansion of the potential field and considering only data along the vertical direction, a linear system of equation is obtained. The expansion is truncated to an arbitrary order and a criterion is defined allowing the selection of the optimal highest altitude. The inversion provides an estimate of the total anomalous mass and of the depth z of the center of mass of the source. The method has several advantages in estimating the excess mass with respect to known methods, such as the Gauss’ method. One reason is that we need just a 1D inversion to obtain our estimates, being the inverted data sampled along a single vertical profile. We also show that the method is stable with respect to the interference from close anomalies and for low signal-to-ratio cases. This because the inversion is performed along a vertical profile, which may be chosen in such a way to minimize the effects from interfering anomalies. The results obtained with this method show that a multiscale analysis of potential fields can successfully bring important information about the source parameters.