TECTONICS, VOL. 13, NO. 1, PAGES 17-44, FEBRUARY 1994 Pressure-temperature-time paths from two-dimensional thermal models: Prograde, retrograde, and inverted metamorphism C. Ruppel • and K. V. Hodges Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge Abstract. Two-dimensional thermal models of time- transitive crustal thickening andsubsequent unroofing in large- scale overthrust terrains generate pressure-temperature-time (PTt) paths that generally resemble those produced by earlier one-dimensionalinstantaneous models, but that differ in detail. These differences in PTt path morphology are most pronounced proximalto major fault zones, where postthrusting geotherms are characterized by largetemperature inversions in one-dimensional models but generally lack inversions in two- dimensional models. Tests using the two-dimensional fault modeldeveloped hereindicate that (1) burialrate (proportional to dP/dt), not thrust fault geometry(dip angle), controls the topology of synthrusting PT paths, but plays only a minor role in determining themaximum temperature that rocks attain duringthe later, unroofingstage in their thermalhistories; (2) normal ranges of thrusting and erosion rates and fault parameters result in PT paths with the usual sense (clockwise on conventional PT diagrams; counterclockwise in our diagrams); (3) the amount of heating and duration of heating following the end of thrustingare a function of the rate of unroofing (-dP/dt) duringthis period; (4) fast unroofing rates lead to the attainment of lower maximum temperatures after greateramounts of unroofing; (5) the initial thermalstateof the lithosphere prior to thrusting hasa profound effect on PT path morphologies and on the peak metamorphic conditions attained by samples;(6) for excess heatdistributed across the entirelithosphere (e.g., due to increased background thermal gradients), a plot of peak temperaturesexperienced by metamorphicrocks versus structural depth (TMAX plot) closely represents the initial geotherm; (7) excess heatin the crust only (e.g., increased radioactive heating in a layer) yields a differentresult, with the TMAX plot corresponding to the initial geotherm only near the top of the hanging wall (TMAX plotsfor both(6) and(7) show no temperature inversion which exceeds the nominaluncertainties (+50 K) for geothermometric data); (8) shearheating can lead to significanttemperature inversions at the fault zone if the frictional coefficient •t is 0.6 or greater; and (9) simultaneous thrusting anderosion produce PT loops significantly narrower than those resulting from sequential thrusting and erosion, suggestingthat any formulation which fails to account for some degree of simultaneity betweenthrusting and erosion represents a far endmember model. Forwardmodels like those presented here provide important guidelines for understanding the sensitivity 1Now at Dept. ofGeology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts. Copyright 1994 by the AmericanGeophysical Union. Papernumber 93TC01824. 0278-7407/94/93TC01824510.00 of metamorphic PTt paths to various thermal, mechanical, and geometric factors relatedto tectonism, but they are generally inappropriate for reconstructing metamorphic thermal histories from actual petrologic and geochronologic data. Analytical inversiontechniques that use a postthrusting thermalregime, consistent with two-dimensional forward models, and that integratevalues of dP/dt, dT/dt, and radioactiveheatingrates extracted from suites of metamorphic rocksprovidethe best hopefor furthering our understanding of the thermal evolution of metamorphic terrains. INTRODUCTION Metamorphic and geochronologic data from ancient mountain belts provide theprincipal constraints on the thermal evolution of the lower crust during orogenesis. Numerical techniques basedon idealized analytical models have been developed for the inversion of such datain orderto establish thermalparameters [Royden and Hodges,1984; McNutt and Royden,1987]. Generally,however, significant uncertainties in geothermometric, geobarometric, and geochronologic data hamper the application of such analytical inversion techniques in most compressional settings. In the absence of better metamorphic data, developing a more generalized picture of the thermal evolution of compressional terrains requires the useof forward-modeling techniques. This goal was first recognized by Oxburgh and Turcotte [1974], who developed one-dimensional models for thethermal effects of thrust emplacement to explain deformation in the Alps. Later work by England and Thompson [1984] greatly increased the sophistication of the one-dimensional models to include the effects of variations in manyparameters, including radioactive heatingrate, heat flow, and thermalconductivity. Both of thesestudies relied on assumptions of instantaneous thrust emplacement and one-dimensional(vertical) heat conduction.The instantaneous juxtaposition of a "hot" thrust nappe on a "cold" footwall produced the now-familiar, postthrusting sawtooth geotherm, which is characterized by a large temperature inversion along the thrust fault. In recent years, thermobarometric data from large-scale overthrust terrains like the Himalaya [LeFortet al., 1987; Hubbardet al., 1991] have lent support to models predicting thermal inversions in the vicinity of major thrustzones. At the same time, two-dimensional analysesof the thermal effects of transient thrust emplacement [Shiand Wang,1987;Ruppel et al., 1988a] have failed to reproduce the postthrusting thermal inversion of earlier one-dimensional models. The study described in this paper was motivatedby the apparent contradiction between metamorphic dataconsistent with long-lived thermal inversions and two-dimensional models which yield such inversions only for thrust emplacement at unrealistically high rates [Shi and Wang,