Brittle frictional mountain building: 2. Thermal structure and heat budget
Authors: Barr Terence D. , Dahlen F. A. 
Published: February 2008

This paper describes a simple thermal model of an actively deforming critically tapered fold‐and‐thrust belt. The model determines the steady state temperature distribution and heat flow, as well as the pressure‐temperature‐time histories of rocks that outcrop at the surface. The main parameters controlling the thermal structure are the accretion and erosion rates, the undisturbed geothermal gradient at the toe, and the amount of frictional heating. Both shear heating on the decollement fault and internal strain heating within the deforming brittle wedge are incorporated in a mechanically consistent manner, and they dominate the effect of radiogenic heating, except in fold‐and‐thrust belts with significantly overpressured pore fluids. The mean stresses, temperatures, and surface heat flow all increase with an increase in the basal and internal coefficients of friction, and this dependence is used to constrain the level of friction on the decollement fault beneath the steady state fold‐and‐thrust belt in Taiwan. Rocks outcropping in the core of the Central Mountain Range of Taiwan experience maximum theoretical temperatures in excess of 400° C and maximum mean pressures in excess of 500 MPa if the coefficient of basal friction is μb = 0.5. Qualitatively, these conditions are in good agreement with the observed high greenschist facies metamorphism. The theoretical surface heat flow, which increases from 95 mW/m2 at the front of the fold‐and‐thrust belt to 240 mW/m2 at the rear, is in excellent agreement with the results of a recent geothermal survey of Taiwan, and theoretical cooling histories are in good agreement with fission track and other geochronologic studies. Taken together, these results provide strong evidence that sliding on the basal decollement fault beneath Taiwan is governed by a coefficient of friction in the range of typical laboratory measurements, μb = 0.5 ± 0.2. Approximately 35% of the total surface heat flux of 3 GW is heat conducted into the base of the wedge from the top of the basal decollement fault, and somewhat more than 30% is heat advected into the toe by accretion. The remaining heat is generated internally, about 25% by internal strain heating and about 10% by radiogenic heating. Either an increase in the coefficient of basal friction μb or a reduction in the pore fluid pressure ratio λ = λb leads to an increase in the surface heat flow, because of the increased frictional heating within the wedge and on the basal decollement fault. The overall balance of energy in a steady state fold‐and‐thrust belt is described by the equation
, where Ė is the rate at which both mechanical and heat energy are added from external sources,
is the rate at which work is performed against gravitational body forces in a reference frame attached to the overriding plate, and Q is the rate at which waste heat flows out of both the upper and lower boundaries. The total power input into the Taiwan fold‐and‐thrust belt is approximately 4.2 GW. The mechanical work being done on the base and front of the fold‐and‐thrust belt accounts for 3 of these 4.2 GW. In addition, 0.9 GW of heat are being advected from the subducting plate into the toe by accretion; the remaining 0.3 GW are being supplied by in situ radiogenic heating. The outgoing energy is dominated by the 3 GW of heat conducted out the top in the surface heat flow; however, another 0.8 GW are conducted down beneath the rear portion of the basal decollement fault, to heat the underlying subducting slab. Only 0.4 of the incoming 4.2 GW do useful mechanical work against gravity within the wedge; the efficiency of brittle frictional mountain building in Taiwan is therefore 10%.