Inverse and forward numerical modeling of trishear fault‐propagation folds

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Abstract
Fault‐propagation folds commonly display footwall synclines as well as changes in stratigraphic thickness and dip on their forelimbs, features that cannot easily be explained by simple parallel kink fold kinematics. An alternative kinematic model, trishear, can explain these observations, as well as a variety of other features which have long intrigued structural geologists. Trishear has received little attention until recently, in part because it must be applied numerically rather than graphically. A new computer program has been developed to analyze trishear and hybrid trishear‐fault‐bend fold deformation. Trishear fold shape can vary considerably by changing the apical angle of the trishear zone and/or the propagation to slip ratio (P/S) during the evolution of the structure. Breakouts, anticlinal and synclinal ramps, and inversion structures can also be modeled, tracking the kinematics with growth strata. Strain within trishear zones can be used to predict fracture orientations throughout the structures as demonstrated by comparison with analog clay models. Also presented is a method for inverting data on real structures for a best fit trishear model by performing a grid search over a six‐parameter space (ramp angle, trishear apical angle, displacement, P/S, and X and Y positions of the fault tip line). The inversion is performed by restoring a key bed to a planar orientation by least squares regression. Because trishear provides a bulk kinematic description of a deforming zone, it is complementary to, rather than competing with, other kinematic models.