Sequential restoration and unstraining of structural cross sections: Applications to extensional terranes

We restore cross sections using a strain-minimization strategy that concent rates displacement on known faults and on slip systems within fault blocks. Growth strata are used to sequentially restore cross sections, and the mis fit of rigidly restored fault blocks is used to determine the internal stra in a within each fault block. Texture mapping allows data (e.g., seismic pr ofile, photograph of an analog model or outcrop) to be imaged onto the rest ored state, and the image is translated, rotated, and unstrained during the restoration. Growth strata are stripped layer by laver to sequentially res tore 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 uns trained by dividing them into smaller triangular elements that accommodate the internal deformation within each fault block. Translations and rotation s of the smaller rigid elements within each fault block produce a least-squ ares minimized best fit. After attaining a best fit of rigid elements, cont inuity is regained by moving initially coincident triangle vertices to a co mmon centroid. The change in shape of the triangular elements in regaining continuity is a measure of strain at that location, assuming homogeneous st rain within each triangular element. Sequential restoration and unstraining determines the spatial variation and temporal evolution of strain orientat ions and magnitudes, calculated at: each vertex during each increment of re storation. The method is tested on an analog sandbox model of deformation i n 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 develope d over salt from the North Sea, The sequential restoration accurately deter mines the sequence of faulting in the analog model and provides insights in to the development of the natural examples. The restoration method determin es the orientations and magnitudes of strain, which can be used to predict the orientation intensity, and timing of small-scale deformation features.