Trishear in 3D. Algorithms, implementation, and limitations

The algorithms and implementation of pseudo-3D and true-3D trishear models are explained, including a strategy to model lateral fault propagation. I show that the pseudo-3D algorithm is adequate and sufficient to model trishear in three-dimensions. Although ad-hoc, the pseudo-3D algorithm preserves volume in simulations without and with lateral fault propagation. A disadvantage of the pseudo-3D algorithm is that it produces very simple, and perhaps not realistic hanging wall geometries, specially in simulations in which the fault slip varies along strike. The true-3D algorithm has a more elaborate and richer kinematics that produces more realistic hanging wall geometries. However, the true-3D algorithm contains mathematical inconsistencies that result in considerable volume changes when the slip gradients along the tip line are high and the tip line is highly oblique to the slip vector and/or the fault strike. The volume changes occur to a large extent in the hanging wall, and to a minor extent in the forelimb and footwall areas.