There are three obvious sources of heat that affect the temperature in a region of thrust faulting: heat supplied from below the lower thrust plate, radiogenic heating within the crusts of both the upper and, especially, the lower plates, and frictional heating along the fault. We assume that heat is conducted primarily in the vertical direction and that solutions to the one-dimensional, time-dependent heat conduction equation can be used to describe the temperature field in overthrust zones. The effects of these three sources of heating can be isolated from one another, treated separately, and then combined in ratios proportional to various assumed rates of heating provided by each. We then use calculations for a range of possible combinations of heat sources that may have caused two-mica granites of late Tertiary age in the Greater Himalaya. Because of the uncertainties in the age of the granites, in the depth at which they formed, in the amounts of heat flux supplied to the base of the lithosphere and of radiogenic heat production in the crust, in the value of the coefficient of thermal conductivity and in other parameters, a broad range of possible combinations of parameters is possible. Temperatures can reach the solidus for granite melts with various plausible combinations of parameters both that include no shear heating and that require frictional stresses of 100'S of MPa on the Main Central Thrust. For instance, if the initial steady state geotherm in the crust now comprising the Himalaya were that of a typical shield, then frictional heating with a stress in excess of 100 MPa (1 kbar) would be necessary to raise the temperature of material near a thrust fault at 20 or 30 km depth to 650°C. Alternatively, if the heat production in the crust and the flux from the base of the lithosphere were similar to those inferred from scattered measurements on the Indian shield (high for a shield), then temperatures at depths 10 to 20 km below the thrust could reach 650°C (near the wet solidus) 20 to 30 m.y. after thrusting began without frictional heating. If the granites formed by melting near the fault, or if they formed shortly after thrusting began (∼10 m.y.), then frictional heating would be needed. The amount of stress required would depend upon the rate of slip and the amounts of the other heat sources, but would probably not be less than 50 MPa (500 bars) and probably would exceed 100 MPa. All of these statements, however, are based on an assumed average coefficient of thermal conductivity of 2.09 W/m K for the crust. If the value were 2.5 W/m K, then the lower bounds on the frictional stresses given above would be increased by 50–100%. Temperatures at miderusual depths would barely reach 650°C in 30 m.y. and then only for some combinations of plausible values of the other parameters. If frictional stresses of 100 MPa cannot be sustained for 10 m.y. or more, and the initial geotherm is that of a typical shield, then some other heat source, such as that caused by crustal delamination, would be required.
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