Evaluating 3D Finite Element–Based Structural Restoration Methods through Applications to Discrete Element Forward Models and Natural Examples

We evaluate a new 3D structural restoration method, which employs simple elastic constitutive relations, by applying it to a series of mechanical forward models and natural examples. The restoration method uses standard finite element approaches to minimizing total strain energy imposed on a model by restoration of a geological datum horizon. In the initial restoration step, the internal and external forces of the model generated by the boundary conditions are calculated using the prescribed elastic constitutive laws and a Lagrangian finite element algorithm. When balanced by the inertial and dampening forces, the total force balance provokes movements of the model nodes. This leads to deformations of each element, where the internal and external forces are again updated using the constitutive relationship. The algorithm iterates this process until it achieves steady state (i.e. a minimum global strain energy), yielding a fully 3D restoration vector field.

The elastic constitutive laws employed in the restorations are simple approximations of the naturally complex deformation processes that govern the growth of geological structures. To evaluate the effectiveness of these restorations, we apply the method to restore a series of forward models and natural examples. We restore forward models developed using the discrete element method, which are governed by complex macroscopic deformation styles, and natural examples where 3D deformation paths are constrained by growth strata. We find that by partitioning restoration models into fault-bounded regions, by incorporating flexural slip surfaces, and by summing small increments of deformation that the method effectively restores both the forward models and natural examples. This suggests that the 3D structural restoration method may prove useful in defining the deformation history of geological structures, including predictions of strain patterns that may be used to constrain properties such as the distribution of natural fractures.