The inversion of three-dimensional gravity source moments is analyzed in two situations. In the first one only the anomalous field is assumed to be known. In the second situation a priori information about the anomalous body is assumed to be known besides the field data. Without using a priori information, we show that it is possible to determine uniquely any moment, or linear combination of moments, whose polynomial kernel: (a) is not a function of the Cartesian coordinate which is orthogonal to the measuring plane and (b) has null Laplacian. Besides, we show that it is impossible to determine any moment whose polynomial kernel has non-null Laplacian. On the other hand, we show that a priori information is implicitly introduced if the source moment inversion method is based on the approximation of the anomalous field by the truncated series obtained from its multipole expansion. Given any center of expansion, the series truncation impores a regularization condition on the equipotential surfaces of the anomalous body that allows the moments and linear combination of moments (which are the coefficients of the multipole expansion basis function) to be uniquely estimated. So, a mass distribution equivalent to the real mass distribution is postulated, being the equivalence criterion specified by the fitting conditions between the observed anomaly and the anomaly calculated with the truncated multipole expansion series. The highest order for the retained terms in the truncated series is specified by the previously defined maximum order for the moments. The moments of the equivalent mass distribution were identified as the stationary solution of a system of first order linear differential equations, for which uniqueness and assymptotic stability are assured. For the series having moments up to 2nd order, it is implicitly assumed that the anomalous body: (1) has finite volume, (2) that it is sufficiently far from the measuring plane and (3) that its spatial naass distribution is convex and presents three orthogonal ...