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Existing geometric models allow master fault shapes to be constructed, given the shape and heave or displacement of a deformed marker horizon in the hanging wall. These models assist in projecting normal faults to depth where the fault geometry is poorly constrained by available seismic data. Currently, it is unclear which model best predicts the actual relation between rollover and fault geometries. To address this deficiency, the relative accuracies of the constant-heave, constant-displacement, constant-bed-length, slip-line, and inclined-shear constructions are evaluated using clay model analogs and seismic examples. Each of the geometric models predicts a different fault shape and depth to detachment for the same rollover shape, because different hanging-wall deformat on mechanisms are assumed. A construction is developed for determining the hanging-wall geometry from a known fault geometry. This construction is based on the inclined-shear model and geometric constraints imposed by material displacement paths viewed from different reference frames fixed to the hanging-wall and footwall blocks. In clay models, the inclined-shear (antithetic shear, (Greek) alpha = 20 degrees) and slip-line constructions produce the best agreement between actual and modeled fault and marker bed shapes in rollovers. For subsurface examples, the inclined-shear model (antithetic shear, (Greek) alpha = 20-40 degrees) and the constant-displacement model predict fault trajectories that are the most similar to the positions and shapes of the master-fault segments interpreted fr m offshore Norway and Gulf of Mexico seismic lines. The shear angle required in the inclined-shear model can often be estimated from the orientation of minor faults in the hanging wall. The shear angle may also be determined through iterative modeling in which the shear angle is systematically varied, and the resultant model fault shape is compared to the shape of the shallow segment of the master fault interpreted from the seismic record.
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