The nonuniqueness of gravity or magnetic data inversion is well known. In order to remove ambiguity, some authors have sought solutions minimizing a functional describing geometrical or physical properties. Last and Kubik (1983), in particular, developed a method explaining the observed anomaly by structures of minimum volume. In this method the domain where anomalous sources are searched is divided into elementary prisms of a constant density or susceptibility contrast. Each elementary contrast is allowed to vary individually. Thus a contrast distribution is computed. The search for this kind of solution leads in general to geologically more appropriate bodies, but exceptions do occur. In this paper, the technique is broadened to include the search for solutions minimizing the moment of inertia with respect to the center of gravity or with respect to a given dip line passing through it. The resulting structures are both deeper and more compact, precisely as is required in specific cases. Theoretical and actual examples illustrate this flexible inversion technique.

Gravity and magnetic anomalies may have the same source but it is always difficult to achieve correlated solutions if interpretations are carried out separately. Therefore it is useful to invert both anomalous gravity and magnetic profiles at the same time, so that the solution mav be more constrained. Existing inversion techniques do not lend themselves equally to this kind of extension, since the parameters—such as density and susceptibility contrasts—should not be related. The algorithms more easily adaptable to simultaneous inversion are those which look for the shape and the position of anomalous bodies with constant unknown density or susceptibility contrasts. In this study, we use the generalized inverse method in the 2 1/2 D case. Parameters are the coordinates of the vertices of the polygonal cross‐sections of the anomalous bodies and both density and susceptibility contrasts of each body. The two types of profile to be processed must be superposable but may have different lengths, spacings, and coordinate origins. Both synthetic examples and field data from geologically known areas have been processed, and it appears that the simultaneous inversion technique may provide an important additional degree of control in the interactive interpretation process.