Temperatures, heat flux, and frictional stress near major thrust faults

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Abstract
We examine the two‐dimensional advective and conductive transport of heat in a region of thrust faulting. Both simple theoretical considerations and numerical experiments show that the steady state temperatures near the fault are reduced by a divisor, below what they would be with the same heat sources but in the absence of advection. In this expression zƒ is the depth to the fault, V is the slip rate, δ is the component of the dip of the fault in the direction of underthrusting, κ is thermal diffusivity, and b is a dimensionless factor that is essentially equal to one for most forms of heating. Initial changes in temperatures near the fault are given by . These simple formulae are successful because of the neglible influence of lateral conduction of heat, at least for slip rates of a few mm/yr or more. Two time constants govern the transition from the initial change in temperature to steady state: t1 = uƒ/V, where uƒ is the distance along the fault in the direction of underthrusting from the surface to the depth in question, and , where zƒ is the depth to the fault. When elapsed times exceed the sum of these two time constants, temperatures differ from their steady state values by only about 10 percent. The numerical experiments indicate that the simple formulae are sufficiently accurate that sophisticiated numerical modeling of temperatures in specific regions is unwarranted. Putain. An application of these simple formulae to measurements of conductive heat flow at island arcs implies that shear stresses at island arcs approach 100 MPa and are greater than 30 MPa. Calculations of temperatures appropriate for the Himalaya suggest that shear stresses of 100 MPa on the Main Central Thrust probably are required to account for the Tertiary granites of the region, if melting took place after slip began on the thrust. Similarly, the cut‐off in seismicity at a depth of about 15 km in the Himalaya, if due to temperatures exceeding 350° to 450°C, implies a deviatoric stress close to 100 MPa.