Restoration of structural cross-sections

Cross-section restoration transforms deformed stratigraphic boundaries (the cross-section) into a less deformed state at an earlier time in the structural history. It is best described by transformation equations which incorporate rigid translation and rotation plus deformation. These equations can be linear (affine) or non-linear. Strain is a function of the transformation constants, and linear transformation equations produce homogeneous strain. Most existing restorations use linear transformations, and many assume simple shear strain, a special case of linear transformation. transformations (such as simple shear) cannot, in general, preserve both area and continuity in cross-section restoration: i.e. if area is constrained, there will be gaps and overlaps between different regions of the restored cross-section. If gaps and overlaps are eliminated, area cannot be constrained. section restoration can be achieved by solving a geometric boundary value problem using quadrilateral domains with non-linear transformations. The geometric boundary conditions are specified by knowlege of the position of an undeformed layer boundary and the pin line. Strain measured in the field can be incorporated as an initial condition. tinuities (faults) can be incorporated into the solution by treating them as an internal boundary without gaps or overlaps.