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Mildly deformed structural surfaces with high-angle faults of moderate displacement can be approximated only poorly with standard polynomial regression models. Discontinuities can, however, be introduced into the regression equations and the least-squares criterion used to estimate parameters simultaneously describing the position of a fault, amount and direction of displacement along the fault plane, and coefficients of the polynomial regression model. This paper treats two simple models for such a fault: (1) where the fault plane is vertical and only vertical translation has occurred and (2) where the fault plane is vertical and both vertical and lateral translations have occurred.
The models are applied to published structural data from the Ramsey pool, Payne County. Oklahoma, where stratigraphic and other evidence indicates the presence of a high-angle fault in the subsurface. The results show close agreement with the inferred position and amount of vertical displacement associated with this fault, but seem to indicate that the previously inferred amount of lateral translation is overestimated.
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