Effects of subduction parameters on geothermal gradients in forearcs, with an application to Franciscan Subduction in California

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Abstract
Geothermal gradients in forearcs are often suppressed below normal values because of the cooling effect of the relatively cold downgoing plate. In this paper, finite difference thermal modeling is used to evaluate the influence on forearc gradients of variations in six potentially important subduction zone parameters. Variations in forearc radiogenic heat production over the general range likely in forearc rocks (0 to 1.5 × 10−6 W m−3) cause only minor changes in temperatures at the base of the forearc (about 2 to 35%, depending on other parameters) and thus have relatively little effect on pressure‐temperature (PT) conditions of metamorphism. However, their effect on gradients at shallow levels and thus on surface heat flows may be greater (up to about 100%). Likely variations in forearc thermal conductivity (1.5 to 3.5 W m−1 °C−1) similarly change temperatures at the base of the forearc only modestly (10–25%) but change surface heat flows more substantially (1.45–1.75 times). Decreasing the subduction angle from 27° to 3.6° increases gradients by about a factor of 2 at both deep and shallow levels. Decreasing the subduction rate by a factor of 8 (160 to 20 km/m.y.) increases gradients by about a factor of 2 when frictional heating at the plate contact is excluded, and less when modest amounts of frictional heating are included. Forearc gradients increase virtually linearly with the presubduction geothermal gradient in the subducting slab and thus are higher above a younger slab. When frictional heating is excluded, forearc gradients are 2.0–2.8 times higher above a 10 m.y. old slab than above a 150 m.y. old slab. Again, the relative effect is lessened when frictional heating is incorporated. The amount of frictional heating at the plate contact potentially has the greatest influence on forearc gradients. The frictional heat production, h, is given by h = τ Vs, where τ is the shear stress along the plate contact and VS is the subduction rate. The modeling shows that forearc gradients increase linearly with τ. Unless plate contact shear stresses are only a small fraction of those expected with frictional sliding of dry rocks, outer parts of forearcs would be the sites of pervasive low‐P/T metamorphism (greenschist facies) rather than high‐P/T metamorphism (blueschist facies). Very high fluid pressures along the plate contact are probably the way shear stresses are reduced. Pressure‐temperature conditions of blueschist‐facies metamorphism in the Franciscan subduction complex of California are easily explained with typical subduction rates and slab ages with plate contact shear stresses of the order of 10 MPa (equivalent to around 3% of lithostatic pressure), but stresses within the range zero to a few tens of megapascals are probably permitted by the thermal constraints. Speculative application of the modeling results assuming a shear stress of 4% of lithostatic pressure to plate motion reconstructions for the Franciscan forearc suggests that forearc gradients were about 8°C/km around 85 Ma when the subducting slab was perhaps 145 m.y. old and the subduction rate was perhaps 95 km/m.y. Gradients increased moderately through the latest Cretaceous to middle Tertiary as subduction became slower and the subducting slab became younger, reaching about 16°C/km at 28 Ma when the slab age was about 11 m.y. and the subduction rate was about 48 km/m.y. The slab age, subduction rate, and forearc gradient then remained fairly constant until 5 Ma, when subduction slowed to about 32 km/m.y. and the slab age decreased to about 8 m.y., causing gradients to rise to about 20°C/km.