AAPG Bulletin, V. 84, No. 2 (February 2000), P. 234-249.

We restore cross sections using a strain-minimization strategy that concentrates displacement on known faults and on slip systems within fault blocks. Growth strata are used to sequentially restore cross sections, and the misfit of rigidly restored fault blocks is used to determine the internal strain within each fault block. Texture mapping allows data (e.g., seismic profile, photograph of an analog model or outcrop) to be imaged onto the restored state, and the image is translated, rotated, and unstrained during the restoration. Growth strata are stripped layer by layer to sequentially restore a cross section. This approach determines the history of deformation, including the activity of faults and the internal strain accumulated during each growth increment. During each increment of growth, a cross section is initially restored to a horizontal datum, assuming that deformation is by rigid-body translations and rotations of fault blocks. Fault blocks are unstrained by dividing them into smaller triangular elements that accommodate the internal deformation within each fault block. Translations and rotations of the smaller rigid elements within each fault block produce a least-squares minimized best fit. After attaining a best fit of rigid elements, continuity is regained by moving initially coincident triangle vertices to a common centroid. The change in shape of the triangular elements in regaining continuity is a measure of strain at that location, assuming homogeneous strain within each triangular element. Sequential restoration and unstraining determines the spatial variation and temporal evolution of strain orientations and magnitudes, calculated at each vertex during each increment of restoration. The method is tested on an analog sandbox model of deformation in the hanging wall of a listric normal fault and on two seismic profiles, a listric normal fault system from the Gulf of Mexico, and a graben developed over salt from the North Sea. The sequential restoration accurately determines the sequence of faulting in the analog model and provides insights into the development of the natural examples. The restoration method determines the orientations and magnitudes of strain, which can be used to predict the orientation, intensity, and timing of small-scale deformation features.