PITFALLS AMONG THE PROMISE OF MECHANICS-BASED STRUCTURAL RESTORATION

Area and volume balancing restoration employs empirical, geometric descriptions and ad hoc kinematic mechanisms to describe rock deformation. These kinematic models are not based on causative physical principles and the deformation fields they describe are entirely dependent upon the selected kinematic mechanism. Area and volume balancing preclude volumetric deformation, and as such cannot represent volumetric strain, which is pervasive in nature, as evidenced by structures including joints, veins, pressure solution seams, and shear and compaction bands.

Mechanics-based restoration is based upon the same kinematic procedures of unfolding strata and back-slipping faults to some undeformed datum; however, the deformation is governed by fundamental principles of mechanics and a linear elastic-constitutive law. Mechanics-based restoration offers a variety of benefits over kinematic methods: conservation of mass, momentum and energy are honored instead of conservation of area or volume, a constitutive law is employed to relate stress and strain, and they accommodate non-uniform slip on three-dimensional fault surfaces and mechanical interaction between faults. Mechanics-based models admit material heterogeneity (elastic moduli) and are particularly well-suited to complex 3D systems where kinematic methods clearly fall short.

Given a mechanical foundation, such methods have been used to predict geologic strain; however, restoration boundary conditions applied to the earth's surface simulate a mechanically and kinematically different system than forward deformation driven by tectonic loads. Furthermore, large deformation of rock over geologic time is inelastic; however, restoration must be linear elastic due to load path-dependency of non-linear materials. We investigate the limitations of boundary conditions and elasticity in mechanics-based restoration, and suggest several improvements, but conclude that restoration results are not appropriate for all applications. Prediction of geologic stress and strain should be left to forward mechanical models driven by appropriate boundary conditions, which may accommodate non-linear material behavior, and whose initial configuration may benefit from insights of restoration.