Understanding kinematic displacement rate effects on transient thermal processes: A comparison of analytical (Ti-diffusion) and numerical (finite-element) solutions to footwall heating in thrust belts J. Ryan Thigpen – University of Kentucky Kyle Ashley – University of Texas, Austin Richard D. Law – Virginia Tech *Supported by NSF and Rockfield Software

Modified from Ashley et al. (2015) from Willett et al. (1993) Thermal evolution of mountain belts Modified from Ashley et al. (2015) from Willett et al. (1993) Most whole wedge models involve a strain continuum (i.e. no discrete kinematic boundaries) At the orogen-scale, bulk thermal architecture controlled by kinematic asymmetry (pro- v. retro-wedge zones) In natural systems, kinematic asymmetry (and thermal architecture?) governed by motion on major thrust and normal faults (i.e. Himalayan MCT and STD coupled system)

From Beaumont et al. (2001), Nature Thermal evolution of mountain belts (channel flow model) Key components of orogen include: Central high-grade hinterland zone Sillimanite-migmatite, anatectic granites, generally deepest exhumed rocks Separated from lower-grade flanking hinterlands by major structures (kinematic discontinuities) Structurally-higher flanking hinterland zone Greenschist-amphibolite, minor intrusions Vertically-compressed mid- to upper crustal isotherm sequence Structurally-lower accretionary hinterland zone Greenschist-amphibolite, displacement dominated by slip on major structures Vertically-extended isotherm sequence From Beaumont et al. (2001), Nature

From Thigpen et al. (2013), JMG Scandian orogenic wedge From Thigpen et al. (2013), JMG

Thermal evolution of mountain belts (thrust-wedge)

From Thigpen et al. (2013), JMG If advection related to thrust stacking and crustal thickening drives metamorphic heating, at what rates should this occur? Ashley et al. (2015), Lithos Sample MT-09-09 collected from immediate footwall of major crustal thrust (Ben Hope) Models of Ti diffusion profiles of quartz inclusions in garnet indicate heating rates of ~50° C in ~200,000 yrs (250° C Myr-1) Ague and Baxter (2007), EPSL Scottish Dalradian, classic Barrovian sequence Peak thermal conditions lasted <300,000 yrs and were attributed to advective magmatism and fluid flow? From Thigpen et al. (2013), JMG Spear et al. (2012), Contr. Min & Pet Staurolite zone, New England Appalachians Heating from 450° C to peak-T (550-600° C) and back to 450 °C occurred in 0.2-2.0 Myr Dachs and Proyer (2002); others? From Ashley et al. (2015), Lithos

What heating rates are predicted by numerical models of thrust stacking? Peacock “sawtooth” style models of isotherm relaxation following thrusting Scandian wedge example Initial crustal thickness = 30 km Initial geothermal gradient = 25° C km-1 Exponential depth distribution of heat producing elements Thrusts of 30, 30, and 20 km structural thickness emplaced instantaneously at 2 Myr intervals Only considers vertical heat flow ~200° C Myr-1 Early post-emplacement heating rates

Finite-element model set-up (and selection of rates) Initial crustal thickness = 30 km Basal heat flow = 0.025 W m-2 Upper crust radiogenic component U - 2.5 ppm, Th - 10 ppm, K = 3.2 wt % Lower crust radiogenic component U – 1.2 ppm, Th - 5 ppm, K = 1.6 wt % Thermal conductivity (k) = 3.00 W m-1 K-1 From Mirakian et al. (2012), Lithosphere Taiwan (~80 mm yr-1), Nazca plate (~50 mm yr-1) Himalayas (Indian plate, ~50 mm yr-1), convergence ~10-30 mm yr-1 From Avouac et al. (2001), Tectonics

Finite-element model set-up

Single overthrust model results Thrust rate = 20 mm yr-1 Thrust rate = 50 mm yr-1 Thrust rate = 100 mm yr-1

Single overthrust model results Thrust rate = 5 mm yr-1 Thrust rate = 20 mm yr-1 ~32° C Myr-1 ~15° C Myr-1 Thrust rate = 50 mm yr-1 Thrust rate = 100 mm yr-1 ~150° C Myr-1 ~75° C Myr-1

Surface slope = 2º Basal detachment dip = 6º Thermal architecture of broadly foreland-propagating thrust systems Hangingwall – Compressed isotherm sequence (relative to footwall) due to surface-directed heat advection Wedge geometry leads to thrust-driven exhumation of deeper, hotter rocks than those in simple model Surface slope = 2º Basal detachment dip = 6º HW initial geothermal gradient = ~30º km-1 , FW initial geothermal gradient = ~23º km-1

Results of modified wedge model with elevated HW geothermal gradient ~88° C Myr-1 ~190° C Myr-1

Conclusions 2-D conduction/advection numerical models involving “average” thrust displacement rates (5-20 km Myr-1) yield footwall heating rates of 15-32° C Myr-1. Footwall heating rates equivalent to those derived from mineral diffusion studies (e.g. 150-250° C) are only observed in models with very high, albeit possible thrust rates (100 km Myr-1). More kinematically complex models involving thrust wedge geometries and transient elevated HW geothermal gradients (wrt to footwall) yield even higher peak heating rates for thrust rates of 50 km Myr-1(75 v. 88° C Myr-1) and 100 km (150 v. 190° C Myr-1). Future work will include investigations of multiple thrust sequencing, erosion, and igneous intrusions.

Acknowledgements John Cain and Adam Bere, Rockfield Software Elfen finite-element software and support Portions of this work funded by NSF EAR grant 1220345 (to R.D. Law)