Brittle frictional mountain building: 1. Deformation and mechanical energy budget

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Abstract
An active fold‐and‐thrust belt is analogous to a wedge of soil or snow that forms in front of a moving bulldozer; such wedges exhibit a critical taper and a regional state of stress that is everywhere on the verge of Coulomb failure. The width of such a critically tapered fold‐and‐thrust belt does not depend on its brittle strength or frictional properties but rather on the accretionary influx rate of fresh material at its toe and on the rate of erosion; a steady state fold‐and‐thrust belt is one in which the accretionary influx is balanced by the erosive efflux. Rocks are accreted at the toe and then horizontally shortened as they are transported toward the rear; those that enter lower in the accreted section are more deeply buried before being uplifted by erosion. Mass balance and isotropy constrain the kinematics of this large‐scale deformation, enabling us to infer the trajectories, residence times, and stress‐strain histories of rocks incorporated into eroding fold‐and‐thrust belts. A typical rock resides in the steady state Taiwan wedge for 2–3 m.y. before it is uplifted and eroded; during its motion through the wedge, it experiences strain rates in the range 10−13 to 10−14 s−1. The mechanical energy budget of brittle frictional mountain building is described by the equation , where is the rate of work performed on the base and front of the fold‐and‐thrust belt by the subducting plate, is the rate at which energy is dissipated against friction on the decollement fault, is the rate at which energy is dissipated by internal frictional processes within the deforming brittle wedge, and is the rate of work performed against gravitational body forces in a reference frame attached to the overriding plate. The total mechanical power being supplied by the subducting Eurasian plate to the active fold‐and‐thrust belt in Taiwan is slightly over 3 GW. Approximately 60% of this work of steady state mountain building is being dissipated against friction on the decollement fault, and about another 25% is being dissipated against internal friction; this leaves only 15% or roughly half a gigawatt available to do useful work against gravity. In general, fold‐and‐thrust belts with moderate pore fluid pressures are dominated by work done against friction on the decollement fault; however, those with nearly lithostatic pore fluid pressures may be dominated by work done against gravity. Internal frictional dissipation is always less than basal frictional dissipation, as it is in Taiwan. An alternative and equivalent description of the mechanical energy balance of a steady state fold‐and‐thrust belt is provided by the equation . In this version the quantity on the left, , is the rate at which work is performed on the back of the wedge by the overriding plate and is the rate of work performed against gravity in a reference frame attached to the subducting plate. The latter quantity is always positive for any critically tapered fold‐and‐thrust belt whose decollement fault dips toward its rear, in contradiction to the central premise of the gravity spreading theory of fold‐and‐thrust tectonics.