INVERSION OF 3-D STRUCTURAL GEOMETRY USING GEOLOGICAL LEAST-SQUARES CRITERIA

Oil exploration requires quantitative determination of structural geom etry in sedimentary basins. This leads to back-and-forth use of geolog ical methods, e.g. cross-section balancing and geophysical techniques, such as tomography, and the synthesis becomes tedious, especially in three dimensions. This suggests that they should be as much as possibl e quantitatively integrated into a single consistent framework. For th is integration, we propose using inversion techniques, i.e. multicrite ria optimization. We locally model a geological structure as a (geomet ric) foliation, the leaves of which represent deposition isochrons. We consider a geological structure as a set of foliations joined along f aults and unconformities. We propose five kinds of geological data to constrain structural geometry quantitatively: dip measurements that ma y be available along wells, developability and smoothness of depositio n isochrons, the directions of fold axes, and layer parallelism. Using concepts of differential geometry, we formulate these data in terms o f least-squares criteria. To solve the canonical non-uniqueness proble m raised by the inversion of parametric representations of geometrical objects such as foliations (many parametrizations describe the same o bject), we introduce the additional criterion method which consists of adding an unphysical objective function to the physical objective fun ction, so as to make the solution unique. Assuming well trajectories a nd borehole correlations to be known, we optimize, with respect to the se criteria, several simple structures comprising one foliation, inclu ding a field example.