Fractal strain distribution and its implications for cross-section balancing

Abstract Rock units having different physical properties show contrasts in structural styles. Massive competent rocks have relatively simple geometry and control the structural framework, whereas thin-bedded, less competent units are characterized by complex deformation at smaller scales. These contrasting structural styles can be quantified by a fractal dimension D . A fold profile with a D close to 1 has a simple geometry. A value of 2 > D > 1 indicates a fractal profile. A fractal profile has a fractal strain distribution such that the measured shortening increases with resolution. For rock units having different values of D , the shortening strains measured with the same resolution cannot be compared because a significant amount of deformation takes place at smaller scales for these units with a larger D . Proper balancing requires high-resolution analysis for these units to resolve strain at smaller scales. In the central Appalachians, West Virginia, the Cacapon Mountain anticlinorium has a large ramp anticline in Cambrian-Ordovician rocks, which has a net shortening of 10.510 km as measured by section restoration. In contrast, restoration of the overlying complexly folded and faulted Upper Ordovician through Devonian units indicated a 3.660-km shortening. Thin section analysis revealed a 15–20% strain, equivalent to another 3-km shortening, and the remaining difference in shortening between the cover and the underlying blind thrust sheet has been previously attributed to forethrusting. Fractal analysis indicates that the Cambrian-Ordovician thrust sheet has a D = 1.001 and the cover fold profile has a D = 1.072, which indicates a fractal geometry. If thin section scale through outcrop scale to map scale strains are included in the cross-section balancing, the cover sequence has a comparable shortening to that in the underlying thrust sheet.