As well as helping to understand local geology and tectonic processes, structural restoration can help validate interpretations. In 1969, Dahlstrom laid out the ground rules for cross section restoration in the marginal part of an orogenic belt, believing that a cross section built according to those rules, so that it is possible to restore it, is likely to be more accurate than a cross section that fails the restoration test.
Numerical modelling has improved over these first pen-and-paper efforts and cross sections, three-dimensional surfaces and full three-dimensional structural models can now be restored, with direct benefits on model consistency. Mechanical restoration requires grids that conform to geological structures, which can be difficult to build. Using an implicit representation for horizons relieves constraints on the mesh required by finite-element methods and enables mechanical restoration of complex structures.
Making full use of the implicit approach, the (u,v,t) space defined by the GeoChron framework provides a glimpse of geological structures as they were deposited but does not map the geological space to a true deposition space as the vertical dimension is a geological time, not deposition depth. In this lecture, we present a full adaptation of the mathematical GeoChron framework which enables three-dimensional restoration of complex structural models with no need for user input. Our new equations provide mathematically sound solutions illustrated by sequential restoration of an extensional sandbox model.
The benefits of working in a restored space are then shown by applying our restoration method to a complex structural framework. Using this transformation, any geological object can be converted from the present-day space to a restored state at a given time, where constraints set on the transformation ensure that the restored geological model is valid. Restoring models can help assess their validity and can make further interpretation easier by cancelling the effects of faulting and folding.