Trishear modeling: methods and results
Trishear is distributed shear in a triangular shear zone one of whose apex is located at the tip of the propagating
fault. In the triangular shear zone slip is assumed to vary linearly from a finite value (in the hangingwall) to 0 (in the
footwall), thus respectively from the top to the bottom of the shear zone (Fig. 1). Six basic parameters describe the
trishear fault kinematics: a) slip; b) ramp angle; c) apical angle; d) and e) X and Y tipline position; f) P/S –
propagation / slip. The mathematics of trishear kinematics, as modeled in the used program, are fully described in
Hardy and Ford [1997] and Zehnder and Allmendinger [2000].
Fig. 1: Basic trishear geometry as described by
Erslev [1991] and Hardy and Ford [1997].
(modified from Allmendinger, [1998]).
Allmendinger [1998] developed a code to perform forward Trishear modeling and inverse retrodeformation basing
on the geometry of a deformed reference bed. Here we used the FORCED FOLDS program (MAC version 5.4),
developed by Rick Allmendinger, and available at http://www.geo.cornell.edu/geology/faculty/RWA/FF_DL.html .
Inverse procedure for bed restoration
The inverse method for bed restoration takes advantage of the fact that the trishear kinematics is reversible and
thus is it possible to run models backward to unfold the beds to their original, un-deformed geometry.
Once a reference bed is defined and an initial planar geometry is postulated, all the 6 parameters mentioned
above are inverted by performing a grid search across a pre-specified parameter space (for each parameter min,
max values and step size has to be specified). The program finds the best fitting model for one reference bed and
then evaluates how that model applies to the other beds. Results are evaluated using a simple least squares linear
regression, carried out minimizing .
In this study, we run 3 successive grid searches over the parameter space. At each successive step we upscaled
the model resolution running successive searches over parameters ranges indicated by the previous ones, thus
allowing to considerably save computing-time.
References:
Allmendinger, R. W., 1998, Inverse and Forward numerical modeling of trishear fault-propagation folds: Tectonics,
v. 17, no. 4, p. 640-656.
Erslev, E. A., 1991, Trishear fault-propagation folding: Geology, v. 19, no. 6, p. 617-620.
Hardy, S., and Ford, M., 1997, Numerical modelling of trishear fault-propagation folding and associated growth
strata: Tectonics, v. 16, no. 5, p. 841-854.
Zehnder, A. T., & Allmendinger, R. W., 2000, Velocity field for the trishear model. Journal of Structural
Geology, 22(8), 1009-1014.