Pressure‐temperature‐time paths from two‐dimensional thermal models: Prograde, retrograde, and inverted metamorphism

Two‐dimensional thermal models of time‐transitive crustal thickening and subsequent unroofing in large‐scale overthrust terrains generate pressure‐temperature‐time (PTt) paths that generally resemble those produced by earlier one‐dimensional instantaneous models, but that differ in detail. These differences in PTt path morphology are most pronounced proximal to major fault zones, where postthrusting geotherms are characterized by large temperature inversions in one‐dimensional models but generally lack inversions in two‐dimensional models. Tests using the two‐dimensional fault model developed here indicate that (1) burial rate (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 the maximum temperature that rocks attain during the later, unroofing stage in their thermal histories; (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 thrusting are a function of the rate of unroofing (−dP/dt) during this period; (4) fast unroofing rates lead to the attainment of lower maximum temperatures after greater amounts of unroofing; (5) the initial thermal state of the lithosphere prior to thrusting has a profound effect on PT path morphologies and on the peak metamorphic conditions attained by samples; (6) for excess heat distributed across the entire lithosphere (e.g., due to increased background thermal gradients), a plot of peak temperatures experienced by metamorphic rocks versus structural depth (TMAX plot) closely represents the initial geotherm; (7) excess heat in the crust only (e.g., increased radioactive heating in a layer) yields a different result, with the TMAX plot corresponding to the initial geotherm only near the top of the hanging wall (TMAX plots for both (6) and (7) show no temperature inversion which exceeds the nominal uncertainties (±50 K) for geothermometric data); (8) shear heating can lead to significant temperature inversions at the fault zone if the frictional coefficient μ is 0.6 or greater; and (9) simultaneous thrusting and erosion produce PT loops significantly narrower than those resulting from sequential thrusting and erosion, suggesting that any formulation which fails to account for some degree of simultaneity between thrusting and erosion represents a far endmember model. Forward models like those presented here provide important guidelines for understanding the sensitivity of metamorphic PTt paths to various thermal, mechanical, and geometric factors related to tectonism, but they are generally inappropriate for reconstructing metamorphic thermal histories from actual petrologic and geochronologic data. Analytical inversion techniques that use a postthrusting thermal regime, consistent with two‐dimensional forward models, and that integrate values of dP/dt, dT/dt, and radioactive heating rates extracted from suites of metamorphic rocks provide the best hope for furthering our understanding of the thermal evolution of metamorphic terrains.