First-order analysis of deformation of a thrust sheet moving over a ramp

John L. Rich introduced the revolutionary concept that many folds in the Appalachian Mountains can be explained as superficial structures formed by passive translation of thrust blocks over ramps in detachment surfaces. The amount of layer-parallel shortening can be negligible in the formation of these folds. Rich primarily was concerned with an explanation for the Powell Valley anticline, in the southern Appalachians, but the essential kinematic features of his model of folding have been verified in other folds in the Appalachians, in the Canadian Rockies, in the Idaho-Wyoming thrust belt, and in the Pyrenees. In this paper we solve the boundary-value problem for an idealized thrust block moving over a detachment surface and ramp with zero drag, and produce theoretical fold forms in the thrust block that closely resemble those in Rich's idealized model. The anticline is narrow and rounded if the translation is small, and broad and flat-topped if the translation is large. The limbs of the anticline are symmetric. We also incorporate drag along the ramp part of the detachment surface in order to derive a possible explanation for the asymmetry of dips of the two limbs of the Powell Valley anticline. We show that drag can explain the asymmetry, particularly if drag between relatively competent rocks in opposition at the ramp caused an initial anticline to form as the thrust block began to move, and then drag reduced markedly as relatively soft shales at the base of the block were thrust over competent rocks in the ramp. The existence of the initial anticline should be reflected in asymmetry of the two limbs and in a bulge at the distal edge of the broad anticline. ?? 1980.