An original method has been developed to model geology using the location of the geological interfaces and orientation data from structural field. Both types of data are cokriged to interpolate a continuous 3D potential-field scalar function describing the geometry of the geology. Geology contact locations set the position of reference isovalues while orientation data are the gradients of the scalar function. Geometry of geological bodies is achieved by discretising reference isovalues. Faults are modelled using the same method by inserting discontinuities in the potential field. Potential fields can be combined to model realistic, complex geometry: scalar functions representing separate geological series are merged automatically using geological rules to enable fast computation and easy update of interpretation. The methodology has been applied to a wide range of geological contexts including orogenic domains, basins, intrusive and extrusive environments.

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.

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The analysis of multiple data sets is required to select a realistic 3D geological model among an infinite number of possibilities. An inverse method that aims at describing the 3D geometry of geological objects is presented. The method takes into account the geology and the physical properties of rocks, while respecting the topological properties of an a priori model. The a priori model is built from the geological data-set and its geometry is largely dependent upon assumptions about inaccessible geology at depth. This method, referred to as "total litho-inversion" is a generalized 3D inversion that results in quantifying the lithology and the distribution of rock property in a probabilistic way. Its application is demonstrated through (i) a simple synthetic case and (ii) the relative distribution characterization of granites and diorites in an orogenic domain.

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