3-D restoration of complexly folded and faulted surfaces using multiple unfolding mechanisms

The ability to extract the history of motions associated with geologic stru ctures is a key element in understanding fundamental deformation processes, for example, the growth of folds or faults in three dimensions, the intera ctions between faults, and the spatial relationships between deformation an d sedimentation. Here, we show how to extract these motions for complexly f aulted and folded structures using a new method of three-dimensional (3-D) restoration. We perform the restoration on sets of stratigraphic horizons defined in thr ee dimensions as irregular triangular networks (triangulated surfaces), wit h the unfaulting and unfolding as separate steps. The unfolding is achieved by a best-fit packing of the triangular surface elements, implementing sev eral restoration mechanisms, including (1) flexural slip, (2) homogeneous i nclined shear, and (3) 3-D inclined shear oriented in the azimuth of the lo cal surface dip. After unfolding, we restore the displacement on the faults in map view by a best-fit rigid-body packing of fault blocks in a way that allows for complex systems of faults. By performing the combined unfolding and unfaulting with multiple orientations of the unfolding vectors, we det ermine the optimum combination of unfolding plus unfaulting, which yields a best estimate of the surface-strain fields, the particle-displacement fiel d, and the fault-slip vectors in three dimensions. We illustrate the restoration method with synthetic examples and a complexl y faulted structure from the western Niger Delta that is imaged in 3-D seis mic data. We include the results of tests to quantify some potential source s of error in the restorations.