Crustal shortening, root spreading, isostasy, and the growth of orogenic belts: A dimensional analysis

Scaling laws that describe the growth of mountain belts and the change in their regional topographic profiles with time ( t ) are obtained by physical arguments that account for crustal shortening, isostasy, and creeping flow at the mountain roots. An average power law rheology characterized by an exponent n is assumed, and different values of n are considered. The model predicts the formation of a localized range characterized by a height ( h ) and a width ( a ). As crust on the sides of a range is compressed, the root broadens due to buoyancy‐driven creep. This process in conjunction with isostasy causes h to increase with time as t 1/4 – t 1/3 , and a as t 3/4 – t 2/3 , as n is varied from 1 (Newtonian rheology) to ∞ (plastic rheology). Accordingly, the aspect ratio a / h increases as t 1/2 – t 1/3 . The scaling laws depend on the rheology, but rather weakly; the aspect ratio increases with age but is nearly independent of the rate of shortening. The deformation extends gradually inland with increasing time, so that the age of tectonic deformation decreases with distance from the continental border. Uplift takes place inland from the crest while subsidence occurs at the opposite side. The ratio a / h of the Andes and Tibet is consistent with this model.