The method of moment inversion, based on the approximation of the gravity anomaly by thetruncated series obtained from its multipole expansion, uses, implicitly,a priori information about the anomalous body. The series truncation imposes a regularizing condition on the equipotential surfaces (produced by the anomalous body), allowing the unique determination of some moments and linear combinations of moments that are the coefficients of the basis functions in the multipole expansion series. These moments define a class of equivalent distributions of mass. The equivalence criterion is based on the misfit between the observations and the field produced by the series truncated at a prefixed maximum order for the moments.
The estimates of the moments of the equivalent distribution are shown to compose the stationary solution of a system of first-order linear differential equations for which uniqueness and asymptotic stability are guaranteed.
Specifically for the series retaining moments up to second order, the implicita priori information introduced requires that the source have finite volume, be sufficiently distant from the measurement plane and that its spatial distribution of mass present three orthogonal planes of symmetry intersecting at the center of mass. Subject to these hypotheses, it is possible to estimate uniquely and simultaneously the total excess of mass, the position of the center of mass and the directions of the three principal axes of the anomalous body.
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Medeiros, W.E., Silva, J.B.C. Analysis of gravity source moment inversion. Part II: Usinga priori information about the source. PAGEOPH 144, 95–116 (1995). https://doi.org/10.1007/BF00876476
- Moment inversion
- gravity inversion
- multipole expansion