The Effects of Accretion, Erosion and Radiogenic Heat on the Metamorphic Evolution of Collisional Orogens

J. metamorphic Geol., 1999, 17, 349–366

The effects of accretion, erosion and radiogenic heat on the metamorphic evolution of collisional orogens

A. D. HUERTA,* L. H. ROYDEN AND K. V. HODGES Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (email: [email protected])

ABSTRACT Petrological and thermochronological data provide our best record of the thermal structure of deeply eroded orogens, and, in principle, might be used to relate the metamorphic structure of an orogen to its deformational history. In this paper, we present a two-dimensional thermal model of collisional orogens that includes the processes of accretion and erosion to examine the P–T evolution of rocks advected through the orogen. Calculated metamorphic patterns are similar to those observed in the field; metamorphic temperatures, depths and ages generally increase with distance from the toe of the orogen; P–T paths are anti-clockwise, with rocks heating during burial and early stages of unroofing, followed by cooling during late-stage unroofing. The results indicate that peak metamorphic temperatures within the core of a collisional orogen and the distance from the toe of an orogen to the metamorphic core can be related to the relative rates of accretion, erosion and plate convergence. Model orogens displaying high metamorphic temperatures (>600 °C) are associated with low ratios of accretion rate to plate convergence velocity and with high heat flow through the foreland. Model orogens with metamorphic cores far from the toe of the orogen are associated with high ratios of accretion rate to erosion rate. Calculated metamorphic gradients mimic steady-state geotherms, and inverted thermal gradients can be preserved in the metamorphic record, suggesting reconsideration of the concept that the metamorphic record does not closely reflect geothermal gradients within an orogen. Key words: accretion; erosion; orogeny; metamorphism; radiogenic heat.

observed metamorphism and in determining at what INTRODUCTION rates these processes occur. An important goal in geological research is to relate the metamorphic record of orogens to the basic CONSTRAINTS ON THE METAMORPHIC processes of mountain building. Most thermomechan- EVOLUTION OF OROGENS ical models of the orogenic process have been unable to reproduce the high-temperature, low-pressure meta- Numerous geochemical methods may be used to help morphic conditions observed in real orogens without reconstruct the temperature and pressure evolution of relying on the introduction of speculative orogenic rocks as they are cycled through an orogenic system processes (e.g. mantle delamination, very high rates of (Ghent et al., 1989; Hodges, 1991; Spear, 1993). For shear heating along the subduction contact). However, example, temperatures and pressures at final equilib- recent numerical experiments indicate that accretion rium can be determined with reasonable precision of heat-producing crust from the down-going plate (±20–50 °C and ±100–150 MPa) by applying various to the over-riding plate and surface erosion during major element thermobarometers (Hodges & collisional orogeny can greatly increase temperatures McKenna, 1987; Essene, 1989; Hodges, 1991; Kohn & in model orogens and produce thermal conditions Spear, 1991a,b); analysis of compositionally zoned consistent with the observed metamorphic grades porphyroblasts and their inclusions yields information (Huerta et al., 1996, 1998). on the earlier P–T history (Spear & Selverstone, 1983; In light of these promising results, we further explore Spear, 1993), and the temperature–time (T –t) history the effects of erosion and accretion on the P–T hist- of a sample can be constrained using isotopic therm- ories of metamorphic rocks and the distribution of ochronometers with closure temperatures ranging from metamorphic isograds in orogenic systems. Ultimately, >700 °C (U–Pb zircon) to c. 100 °C (fission track our goal is to determine whether, and to what extent, annealing in apatite) (McDougal & Harrison, 1988; pressure, temperature and cooling data can be useful Heaman & Parrish, 1991). in reconstructing the processes responsible for the Unfortunately, most thermobarometric techniques recover the high-temperature portion of a rock’s P–T *Presently at: Department of Geology, Idaho State University, path, while the closure temperatures of most isotopic Pocatello, ID 83209, USA. thermochronometers record the low-temperature

© Blackwell Science Inc., 0263-4929/97/$14.00 349 Journal of Metamorphic Geology, Volume 17, Number 1, 1999 350 A. D. HUERTA ET AL . portion of the rock’s T –t history. As a consequence, it metamorphism, in millions of years before the rock is very difficult to reconstruct most of the pressure–time reaches the surface). Metamorphic field gradients are (P–t) path of a metamorphic terrane directly from displayed as a function of the horizontal distance from petrological and geochemical data. Inasmuch as the the toe of the orogen (xsur) including temperature P–t path is a valuable proxy for the burial and arrays (Tmax vs. xsur), depth arrays (zm vs. xsur) and unroofing history of orogenic belts, many attempts metamorphic age arrays (tm vs. xsur). The term have been made to use forward and inverse models to metamorphic core is used to describe the region at the compensate for the limited temperature overlap surface where metamorphic temperatures are at a local between recovered P–T and T –t paths (e.g. England & maximum (peak Tmax). Richardson, 1977; England & Thompson, 1984; The relationship between the thermal structure of Royden & Hodges, 1984; Dahlen & Barr, 1989; Molnar model orogens and their metamorphic records is & England, 1990; Royden, 1993; Ruppel & Hodges, investigated by comparing geotherms to piezotherms, 1994). In this paper, these efforts are extended to and structural thicknesses to metamorphic depths. include a new, relatively simple numerical model of Geotherms (profiles of T as a function of depth), either collisional orogenesis that emphasizes the importance transient or steady-state, display the thermal structure of accretion and erosion in the thermal evolution of of a vertical column within the orogen at any one mountain ranges (Huerta et al., 1996, 1998). We begin time, while piezotherms (profiles of Tmax as a function with the hypothesis that these processes play such a of depth at Tmax) refer to the array of metamorphic dominant role in orogenic heat transfer that the conditions observed along a surface transect (e.g. metamorphic structure of any given mountain range Richardson & England, 1979). The structural height reflects the absolute and relative rates of erosion and of a column of rocks within the orogen (Dzcol) is the accretion during mountain building. We then explore distance, measured perpendicular to the subduction how variations in these two processes should be boundary, from the top to bottom of the column manifest in the distribution of metamorphic isograds (Fig. 1, upper panel). The structural thickness of a and in the topology of P–T and T –t paths across transect along the surface of the orogen (Dzstruct) is the the orogen. distance, measured perpendicular to the subduction To avoid possible ambiguities the following termi- boundary, along the transect (Fig. 1, upper panel). nology is used to describe model results presented in Pressure–depth profiles (arrays of Dzm as a function of this paper (see Table 1 for symbols, variables, and Dzstruct) display the relationship between the preserved values used). Tmax is the maximum temperature metamorphic depths and the structural thickness of experienced by a rock as it is cycled through the model rocks along a surface transect, and are used to orogen; zm is the depth of the rock at Tmax, and tm is determine whether the metamorphic depths are consist- the time at which the rock reaches Tmax (i.e. the age of ent with a lithostatic gradient.

Table 1. Deﬁnitions of variables and values used.

Variable Physical meaning Value or units Comments

x horizontal distance from upper-plate toe (km) z vertical distance from surface (km) t time since initiation of collision (Myr) A radioactive heat production rate (mW/m) e erosion rate (km/Myr) nc convergence velocity (km/Myr) velocity of rocks in the down-going plate relative to rocks in the upper plate a accretion rate (km/Myr) vertical component relative to subduction boundary nu velocity vector of particles in the upper plate (km/Myr) n1 velocity vector of particles in the down-going plate (km/Myr) sw maximum surface width of heat-producing wedge (km) dw maximum thickness of heat-producing wedge (km) tw time to steady state shape of heat-producing wedge (Myr) h vertical thickness of accreted slab (km) ta period of accretion cycle (Myr) T (x,y) temperature at a location within the orogen (°C) xsur location where rock surfaces measured from upper-plate toe (km) ° Tmax maximum temperature experienced by a rock ( C) zm depth at Tmax (km) tm time at Tmax (Ma) age of metamorphism, in millions of years prior to rock reaching the surface zstruct structural thickness of a surface transect (km) measured perpendicular to the subduction boundary zcol structural height of a column of rocks (km) measured perpendicular to the subduction boundary H dip of subduction zone 11.3° dr initial thickness of heat-producing layer 18 km l thickness of foreland lithosphere 126 km ° Ta temperature at base of lithosphere 1260 C K thermal conductivity 2.5 W/mK a thermal diﬀusivity 10−6 m2/s EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 351

ward migration of the subduction boundary at a rate of e/tan H. In this work we use a frame of reference fixed with respect to the toe of the upper plate (Fig. 1, lower panel). In this case the subduction boundary remains stationary, while the velocity of upper-plate rocks (vu) has a horizontal component (a–e)/tan H and a vertical component −e, and the velocity of rocks in the down-going plate (vl) is the sum of the upper-plate velocity and the convergence velocity. This approach ignores internal deformation within the down-going or upper plate, and thus within each plate all particle paths are parallel. At the time of collision (t=0), continental lithosphere (with heat-producing crust) in the down-going plate enters the orogenic system, and accretion and erosion are initiated (Fig. 2). The subduction of heat-producing crust and the subsequent accretion of this crust from the down-going plate to the upper plate results in the development of a wedge of heat-producing crust in the upper plate. The wedge grows with time, and for cases Fig. 1. Upper panel: model geometry used to simulate the where e≠0, a steady-state geometry is eventually thermal evolution of collisional orogens. Material is accreted attained. At this time (t=t ), the surface width of the from the down-going plate to the upper plate at rate a (vertical w component relative to the subduction boundary) and removed wedge is such that the amount of heat-producing crust at the surface at rate e. Lower panel: particle paths in frame of removed from the surface by erosion equals the amount reference fixed with respect to the toe of the upper plate so of heat-producing crust accreted to the upper plate. that the position of the subduction boundary remains fixed The steady-state size of the wedge is a function of through time. vu, velocity of material in the upper plate with the initial thickness of the heat-producing layer in the respect to frame of reference; v , velocity of material in the l down-going plate, convergence velocity, erosion rate, down-going plate with respect to frame of reference; vc, convergence velocity of the down-going plate. accretion rate, and subduction angle. The wedge reaches a steady-state shape by time (for cases where e≠0): d v THERMAL MODEL t = r 1+ c sin h (1) w C e DC a D The first-order effects of accretion and erosion on the metamorphic evolution of collisional zones are investi- with steady-state maximum thickness (dw) and surface gated using the approach described by Huerta et al. width (sw): (1996, 1998). In this model, ‘continental’ lithosphere d d = r [a−e+v tan h](2) (with heat-producing crust distributed uniformly above w C aD c a depth of dr) is subducted beneath an upper plate of continental lithosphere along a planar subduction a s =d (3) contact with constant and uniform dip H (Fig. 1, upper w wCe tan hD panel). Convergence velocity (vc) is defined as the velocity of rocks in the down-going plate with respect Huerta et al. (1996, 1998) have shown that the to rocks in the upper plate. Erosion removes material thickness of the wedge and the magnitude of the heat from the surface of the upper plate (at a constant rate production rate (A) within the wedge exert primary e), while accretion transfers material from the down- control on the magnitude of temperatures within going plate to the upper plate across the subduction model orogens, while the width of the wedge determines boundary (at a constant rate a, measured vertically the lateral extent of high temperatures within the with respect to the subduction boundary). Although upper plate. Thus this redistribution of heat-producing accretion serves to transfer material horizontally across crust is a crucial factor in determining the thermal the subduction zone, the accretion rate is measured in history of an orogen, and heat produced within the the vertical direction. We choose this measurement wedge can be a significant part of the overall since it is the thickness of accreted material that is a heat budget. primary factor in the thermal evolution (independent For example, Fig. 3(a) shows the thermal evolution of the subduction angle). As seen by an observer on of a convergent zone as it evolves from the cool the upper plate, the accretion of material from the oceanic subduction regime to the steady-state thermal down-going plate to the upper plate would result in structure of a collisional orogen. The initial thermal the left-ward migration of the subduction boundary at structure (t=0) of the model orogen is obtained by a rate a/tan H, and erosion would result in the right- calculating the steady-state temperatures of a non- 352 A. D. HUERTA ET AL .

magmatic subduction regime in which an ‘oceanic’ plate (no heat-producing crust) is subducted beneath the upper plate with no erosion or accretion. Early in the evolution of the orogen (t<10 Myr), temperatures increase rapidly as warm continental lithosphere of the down-going plate is introduced to the orogen and accreted to the upper plate. As collision ensues, temperatures throughout the orogen continue to increase as the heat-producing wedge grows and erosion brings hot crust towards the surface. By t= 40 Myr, a signiﬁcant amount of heat-producing crust has accumulated in the upper plate, and upper-plate temperatures are in excess of 545 °Catz=40 km. At t=70 Myr, the heat-producing wedge is fully developed = (tw 69 Myr), and maximum upper-plate temperatures are 637 °C, or 98% of the maximum steady-state temperature. By t=80 Myr, temperatures across the model orogen have reached steady state, with a maximum upper-plate temperature of 647 °C. In contrast, Fig. 3(b) shows the thermal evolution of a model orogen based on the same initial thermal structure, convergence velocity, erosion rate and accretion rate as Fig. 3(a), but the down-going plate does not have an upper layer of heat-producing crust. In this case, no wedge of heat-producing crust develops within the upper plate, and temperatures remain cool throughout the evolution of the collisional zone. By t=70 Myr, temperatures across the orogen have reached steady state, and temperatures within the orogen are cooler than temperatures within the foreland. Since there is no accumulation of heat- producing crust in the upper plate, the thermal regime is primarily controlled by the subduction of cool crust into the orogen. The slight increase in temperatures in the upper plate (as compared to temperatures at t=0) is the result of the accretion of down-going lithosphere to the upper plate and the upward advection of warm material via erosion. In model orogens that develop heat-producing wedges, the elapsed time to thermal steady state for a particular location is directly related to the time it takes for a rock to travel from x=0 to that location, which is a function of both the location and the advective rates. In general, temperatures in the region of the heat-producing wedge are within 98% of steady- = state temperatures by t tw, and orogens with quickly developing wedges can come to thermal steady state within tens of millions of years.

Fig. 2. Generalized cross-sections showing the modelled distribution of heat-producing crust through the evolution of a collisional orogen as material is subducted, accreted from the down-going plate to the upper plate, and eroded from the surface. During the evolution of the orogen, a wedge of heat- = producing crust forms within the upper plate, and at t tw the wedge achieves a steady-state geometry with a maximum thickness dw and a surface width sw. EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 353

STEADY-STATE METAMORPHISM The metamorphic record of an orogen reflects not only the thermal structure of the orogen, but also the interaction between the thermal structure and the particle paths of rocks moving through the system. To illustrate this point, we examine the metamorphic signature of three examples with similar thermal structures but different particle paths. For each case, the orogen has reached thermal steady state, and additional time has passed such that the metamorphic record of rocks exposed at the surface is time-invariant. We focus on combinations of parameters that produce thermal structures compatible with the high- temperature, low-pressure conditions (>500 °Catc. 20 km) common to many collisional orogens. Case A has a deep and narrow heat-producing wedge with moderate heat production (Fig. 4a, Table 2), case B has a moderately deep and wide wedge with relatively high heat production (Fig. 4b), and case C has a shallow and wide wedge with very high heat production (Fig. 4c). For each modelled orogen, convergence rate, subduction angle and the thickness of the layer of heat- producing upper crust are the same. Thermal structures for the three orogens are similar; temperatures exhibit a local maximum in the upper plate of c. 650 °Cata depth of c.25kmlocatedc. 300 km from the toe of the orogen, closed 600 °C isotherms, and inverted geotherms within the upper plate (Fig. 4, Table 3). Particle paths show the impact of changing the relative rates of accretion and erosion. Model orogens with higher ratios of vc/a have steeper particle trajectories in the down-going plate and deeper heat-producing wedges, while model orogens with higher ratios of a/e have shallower particle trajectories in the hanging wall and wider heat-producing wedges. Although the thermal structures of the three example model orogens are generally similar, differences in particle paths result in different temperature–depth histories for individual rocks and distinct metamorphic temperature arrays observed at the surface. For each of the example model orogens, the metamorphic temperatures, pressures and ages observed at the surface increase with distance from the toe of the orogen until metamorphic temperatures reach a local maximum in the metamorphic core of the orogen, and Tmax decreases with distance immediately beyond the core (Fig. 4, Table 3). Peak metamor-

Fig. 3. Cross-sections showing the thermal evolution and the distribution of heat-producing crust for an evolving orogen from t=0 (initiation of collision) to thermal steady state (accretion rate a=1.2 km Myr−1, erosion rate e= 1.12 km Myr−1; see Table 2 for other parameters). Contours are isotherms with contour interval of 200 °C, the stippled pattern is the area of heat-producing crust, and the heavy line shows the position of the subduction boundary. (a) Orogen with layer of heat-producing crust in down-going plate (A= 1.75 mWm−3). (b) Orogen with no layer of heat-producing crust in down-going plate. 354 A. D. HUERTA ET AL .

phic temperatures are similar for the three modelled orogens (reflecting the similar maximum temperatures within the upper plate); however, the distance from the toe of the orogen to the metamorphic core varies from 300 km (case A, Fig. 4a) to 440 km (case C, Fig. 4c), while metamorphic depths and ages at peak Tmax vary = = somewhat (zm 30–38 km and tm 32–38 Ma). In addition, P–T and T –t paths are different for each model orogen (Fig. 5, Table 3). Rocks in the core of case A were buried to a maximum depth of 57 km and experienced an average cooling rate of 31 °C Myr−1 (Fig. 5a, Table 3), while rocks in the core of case C were buried to a maximum depth of 42 km and cooled at the rate of 19 °C Myr−1 (Fig. 5c). In each case, portions of the piezothermic arrays closely approximate portions of crustal geotherms within the orogen (Fig. 5). Shallow portions of piezo- < < therms (0 km zm 15 km) mimic geotherms from near the foreland, while deeper portions of the piezotherms > (zm 25–35 km) are steep-to-inverted and mimic geotherms from the high-temperature region of the upper plate. Pressure–depth profiles of the inverted portion of the piezotherms display metamorphic depths consistent with lithostatic gradients (Dzm#Dzstruct). These metamorphic records are similar to commonly observed metamorphic patterns in real orogens: metamorphic temperatures, depths and ages increase with distance from the toe of the orogen; P–T paths are anti-clockwise; rocks are heated during burial and reach their maximum temperature either at the end of burial or during early stages of unroofing; and inverted piezotherms develop, similar to those observed in places like the Himalaya (Le Fort, 1975; Hubbard, 1989). To understand better the relationship between metamorphism and the processes acting within an orogen, we investigate how varying specific tectonic processes affects regional metamorphic patterns and the P–T and T –t paths of rocks within the metamorphic core. Since accretion and erosion rates not only control the paths of rocks advected through a model orogen but also exert primary control on the thermal structure

Fig. 4. Steady-state thermal structures (top) and metamorphic ﬁeld gradients (bottom) for three example model orogens that produce maximum upper-plate temperatures of about 600 °C at depths of c. 30 km. (a) Case A: deep and narrow heat- producing wedge. (b) Case B: moderately deep and wide heat- producing wedge. (c) Case C: shallow and wide heat-producing wedge (see Table 2 for parameters).Top panels: solid white line shows position of the subduction boundary; heavy black arrows show particle trajectories and outline region of heat- producing crust; dashed white line shows positions where rocks achieve their maximum temperatures, Tmax. Bottom panels: maximum metamorphic temperatures (Tmax), depths at Tmax (zm) and ages of Tmax (tm, measured in millions of years prior to reaching the surface) of rocks that reach the surface at distance xsur from the toe of the orogen. Shaded region of ﬁeld gradients indicates general location of the ‘metamorphic core’ where metamorphic temperatures observed at the surface reach a local maximum. EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 355

Table 2. Values of parameters used in computing temperatures in Figs 3–11, 13 and 14.

Figure Comments Accretion rate Heat Maximum Surface Time to full number (a) continuous accretion Erosion production thickness of width of development of (ah/ta) discrete accretion rate (e), rate, (A) wedge (dw) wedge (sw) wedge (tw) km/Myr km/Myr mW/m3 km km Myr

3a case A 1.2 1.12 1.75 60 320 69 b 1.2 1.12 0 DNA DNA DNA 4,5a case A 1.2 1.12 1.75 60 320 69 b case B 1.46 1.0 2.0 54 440 66 c case C 2.0 0.93 3.0 45 480 57 = 6,7a sw 320 km (case A) 1.2 1.12 1.75 60 320 69 = b sw 480 km 1.33 0.83 1.75 60 480 86 = c sw 640 km 1.39 0.67 1.75 60 640 103 = 8,9a dw 60 km (case A) 1.2 1.12 1.75 60 320 69 = b dw 50 km 1.54 1.2 1.75 50 320 53 = c dw 40 km 2.12 1.33 1.75 40 320 39 10a case C 2.0 0.93 3.0 45 480 57 b case A 1.2 1.12 1.75 60 320 69 11 case A 1.2 1.12 1.75 60 320 69 13a Continuous (case A) 1.2; continuous 1.12 1.75 60 320 69 = b Thin slab; nc 21 km/Myr 1.2; 6 km/5 Myr 1.12 1.75 60 (avg) 320 (avg) 69 = c Thick slab; nc 1.2; 18 km/15.2 Myr 1.12 1.75 60 (avg) 320 (avg) 69 23 km/Myr 14 Thick slab 1.2; 18 km/15.2 Myr 1.12 1.75 60 (avg) 320 (avg) 69

= = ff = −6 2 Unless otherwise specified, the following values are used in all figures: convergence velocity, nc 20 km/Myr; subduction angle, tanH 0.2; thermal di usivity, a 10 m /s; thermal = = = = ° conductivity, K 2.5 W/mK; lithospheric thickness, l 126 km; initial thickness of heat-producing crust, dr 18 km; basal lithospheric temperature, Ta 1260 C. DNA=does not apply.

Table 3. Details of thermal structure and metamorphic record for 3 example orogens, Figs 4 & 5.

Figure Comments Parameters Thermal structure Field gradients PT-Tt paths

Surface Depth Heat Maximum Maximum upper location of at peak Age of production Accretion Erosion upper plate plate geothermal peak Tmax Peak Tmax peak Tmax rate (A) rate (a) rate (e) temperature inversion (xsur) Tmax (zm)(tm) Cooling rate# mW/m3 km/Myr km/Myr °C °C/km km °CkmMa °C/Myr

4,5a Case A 1.75 1.2 1.12 646 −74/18=−4.1 296 646 38 34 31.3 b Case B 2.0 1.46 1.0 637 −90/22=−4.1 367 637 38 38 25.8 c Case C 3.0 2.0 0.93 662 −102/24=−4.3 443 662 30 32 19.4

# For rock from metamorphic core (from 500 °Cto0°C).

(by controlling the geometry of the heat-producing but the metamorphic age of rocks in the core increases wedge), it is impossible to generalize the impact of with increasing wedge width, and rocks from the varying either the accretion or erosion rate alone. metamorphic core cool much more slowly in orogens Instead, we examine the impact of varying the geometry with wide wedges (Fig. 7, Table 4). Deep portions of of the heat-producing wedge by changing a and e each of the piezothermic arrays mimic the steep- together. First the surface width of the heat-producing inverted portions of crustal geotherms, and pressure– wedge is modified while holding the maximum thick- depth profiles of the inverted portion of the piezotherms ness constant. Then the maximum thickness of the heat- approximate lithostatic gradients. producing wedge is modified while holding the surface Because the thermal structure of a model orogen is width constant. In the following analysis, case A is used strongly dependent on the thickness of the heat- as a basis of comparison and only a and e are varied, producing wedge, decreasing the maximum wedge keeping all other input parameters constant (Table 2). thickness from 60 to 40 km decreases maximum Broadening the surface width of the heat-producing temperatures within the wedge from c. 650 to c. 450 °C wedge does not change the magnitude of maximum and decreases the magnitude of the geothermal inver- temperatures within the model orogen (Fig. 6, Table 4), sion (Fig. 8, Table 5). These changes in the thermal but increases the distance from the toe of the orogen structure are reflected in the metamorphic record. to the locus of maximum temperatures and broadens Shallow wedges are associated with cooler metamor- the region enclosed by the 600 °C isotherm. The phic temperatures within the metamorphic core, and distance from the toe of the orogen to the metamorphic less of a decrease in temperature on the ‘back’ side of core also depends on the width of the heat-producing the core, opposite the subduction boundary. Varying wedge, such that doubling the width of the heat- the thickness of the wedge does not change the distance producing wedge almost doubles the distance to the from the toe of the orogen to the location of peak metamorphic core. Peak metamorphic temperatures metamorphic temperatures. P–T and T –t paths from within the core do not change as the width is varied, the metamorphic cores show that rocks from model 356 A. D. HUERTA ET AL .

Fig. 5. Steady-state temperature–time (T –t) and pressure– temperature (P–T ) paths (top), steady-state thermal structures (middle), and steady-state piezothermic arrays and pressure– depth proﬁles (bottom) for three model orogens that produce maximum upper-plate temperatures of about 600 °C at depths of 30–50 km. (a) Case A: deep and narrow heat-producing wedge. (b) Case B: moderately deep and wide heat-producing wedge. (c) Case C: shallow and wide heat-producing wedge (see Table 2 for parameters). Top panels: T –t and P–T paths for ~ ~ rocks that reach the surface at xsur 240 km, xsur 540 km, and for the rock that passes through the locus of maximum upper- plate temperatures. Aluminium silicate phase diagram after Holdaway (1971). A, andalusite; S, sillimanite; K, kyanite. Middle panels: solid white line shows position of subduction boundary; heavy black lines show particle paths for rocks that = = reach the surface at xsur 240 km, xsur 540 km, and for the rock that passes through the locus of maximum upper-plate temperatures. Bottom left panels: bold line shows array of metamorphic temperatures versus metamorphic depths observed at the surface (Tmax vs. zm), thin lines display geotherms within orogen (T vs. z). Bottom right panels: bold line shows array of metamorphic depths versus structural thickness (Dz vs. Dz ), dashed line indicates lithostatic m= struct gradient (Dzm Dzstruct). EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 357

Table 4. Details of thermal structure and metamorphic record as a function of surface width of the heat-producing wedge, Figs 6 & 7.

Figure Comments Parameters Thermal structure Field gradients PT-Tt paths

Surface Depth Maximum Maximum upper location of at peak Age of Accretion Erosion upper plate plate geothermal peak Tmax Peak Tmax peak Tmax rate (a) rate (e) temperature inversion (xsur) Tmax (zm)(tm) Cooling rate# km/Myr km/Myr °C °C/km km °CkmMa °C/Myr

= − =− 6,7a sw 320 km (case A) 1.2 1.12 646 74/18 4.1 296 646 38 34 31.3 = − =− b sw 480 km 1.33 0.83 661 106/26 4.1 448 661 38.5 46 20.4 = − =− c sw 640 km 1.39 0.67 664 112/32 3.5 582 664 41 61 17.1

# For rock from metamorphic core (from 500 °Cto0°C).

Table 5. Details of thermal structure and metamorphic record as a function of maximum thickness of the heat-producing wedge, Figs 8 & 9.

Figure Comments Parameters Thermal structure Field gradients PT-Tt paths

= − =− 6,7a dw 60 km (case A) 1.2 1.12 646 74/18 4.1 295 646 38 34 31.3 = − =− b dw 50 km 1.54 1.2 548 36/12 3.0 300 548 34.4 29 25.0 = − =− c dw 40 km 2.12 1.33 447 10/12 0.8 307 447 31.3 24 18.7

# For rock from metamorphic core (from 500 °Cto0°C). orogens with shallow wedges are not buried as deeply steep, such that no single column of rocks passes and cool more slowly than rocks from model orogens through the high-temperature region. Rocks passing with deep wedges (Fig. 9, Table 5). Deep portions of through the hottest region of the upper plate record the piezothermic arrays mimic the steep-inverted high temperatures at shallow levels, while rocks that portions of crustal geotherms, and pressure–depth pass to the right of the hottest region record lower profiles of the inverted portion of the piezotherms temperatures at deeper levels. Again, the metamorphic approximate lithostatic gradients. record observed at the surface displays an inverted Variations in the foreland geotherm can also affect thermal gradient which closely mimics geotherms the metamorphic record of an orogen. Increasing A or in the region, although arrays of Tmax vs. zm are dr in the down-going plate (while holding sw and dw not direct records of any one geotherm within the constant) increases temperatures within the model orogen. orogen, and metamorphic temperatures increase Rocks passing through the region of inverted accordingly. The location of the metamorphic core as geotherms of model orogens not only preserve meta- well as metamorphic pressures and ages within the morphic conditions similar to geotherms of this region, core remain relatively unaffected. but also preserve metamorphic depths that record a To understand the relationship between piezotherms nearly lithostatic gradient (Dzm#Dzstruct; Figs 5, 7 & and geotherms, we examine in detail the relationship 9). In all cases where model orogens exhibit inverted between the particle paths and thermal structures of thermal gradients and closed isotherms, rocks passing model orogens. First, consider a column of rocks through the region of inverted geotherms will record oriented perpendicular to the subduction boundary as metamorphic depths closely approximating lithostatic it passes through the high-temperature region of case gradients. However, only in model orogens with upper- C, where isotherms are closed and thermal gradients plate particle paths that are relatively horizontal are inverted (Fig. 10a). As the column passes through (a/(tan H×e)>~8), will a single column of rocks this region, rocks higher in the column pass through retain metamorphic depths consistent with a lithostatic the hottest region of the upper plate, while deeper gradient (Dzm#Dzcol). rocks in the column pass below the hottest region. These results may provide a resolution to the Thus, metamorphic temperatures and depths preserved apparent contradiction between theory and obser- by the column record an inverted thermal gradient vation. While previous numerical experiments indicate similar to geotherms in this region, and this metamor- that piezotherms should bear little resemblance to any phic gradient will be observed at the surface. However, actual geotherm (England & Richardson, 1977), piezo- ff rocks within the column achieved Tmax at di erent therms from the Himalaya record pressure gradients times, and arrays of Tmax vs. zm are not direct records that are consistent with lithostatic gradients and retain of any one geotherm within the orogen. Next, we steep-to-inverted temperature gradients (Hodges et al., examine case A (Fig. 10b) where particle paths are 1988; Hubbard, 1989; Macfarlane, 1995). 358 A. D. HUERTA ET AL .

TRANSIENT METAMORPHIC EVOLUTION The above analysis is based on model orogens with steady-state metamorphic records. These general obser- vations are also valid for orogens with evolving metamorphic records. For example, we track the metamorphic history of case A as it evolves from the subduction regime to a fully developed collisional orogen (Fig. 11, Table 2). Following initial collision, as rocks from the down-going plate are moved through the orogen, the surface width of accreted material increases at a rate of c.5kmMyr−1.Byt=40 Myr, nearly 200 km of the upper-plate surface is accreted material. At this time, metamorphic temperatures for x<140 km are within 95% of the steady-state metamorphic temperatures, and for x=140–185 km, temperatures are within 78% of the steady-state metamorphic temperatures. By t=80 Myr, the thermal structure of the orogen has achieved steady state; the surface width of accreted crust is nearly 400 km, and metamorphic temperatures observed at the surface are as high as c.575°C, or c. 90% of the maximum invariant metamorphic temperatures. By t=120 Myr, metamorphic temperatures of rocks exposed within the core no longer change, and by t=160 Myr metamorphic temperatures across the orogen are invariant. The transient metamorphic record of model orogens approximates the steady-state metamorphic record. Once crust has been cycled through the orogen and brought to the surface, metamorphic temperatures preserved at the surface are within c. 70% of invariant metamorphic temperatures. In general, metamorphic temperatures of rocks exposed near the foreland become invariant within a few tens of millions of years after initial collision, and temperatures of rocks exposed in the region of the core become invariant after an elapsed time of roughly 1.5tw.

DISCRETE ACCRETION In real orogenic belts, accretion rarely acts continuously and may occur episodically, transferring discrete slabs of the down-going plate to the upper plate. To investigate how this may aﬀect the metamorphic record, we modify our model such that convergence

Fig. 6. Steady-state thermal structures (top) and metamorphic ﬁeld gradients (bottom) as a function of surface width of the heat-producing wedge. (a) s =320 km (case A). (b) s =480 km. = w w (c) sw 640 km (see Table 2 for other parameters). Top panels: solid white line shows position of the subduction boundary; heavy black arrows show particle trajectories and outline region of heat-producing crust; dashed white line shows positions where rocks achieve their maximum temperatures, Tmax. Bottom panels: maximum metamorphic temperatures (Tmax), depths at Tmax (zm), and ages of Tmax (tm, measured in millions of years prior to reaching the surface) of rocks that reach the surface at distance xsur from the toe of the orogen. The shaded region of ﬁeld gradients indicates the general location of the ‘metamorphic core’ where metamorphic temperatures observed at the surface reach a local maximum. EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 359

Fig. 7. Steady-state temperature–time (T –t) and pressure– temperature (P–T ) paths (top), steady-state thermal structures (middle), and steady-state piezothermic arrays and pressure– depth proﬁles (bottom) as a function of surface width of the heat-producing wedge. (a) s =320 km (case A). (b) s =480 km. = w w (c) sw 640 km (see Table 2 for other parameters). Top panels: T –t and P–T paths for the rock that passes through the locus of maximum upper-plate temperatures. Aluminium silicate phase diagram after Holdaway (1971). A, andalusite; S, sillimanite; K, kyanite. Middle panels: solid white line shows position of subduction boundary, heavy black lines show particle paths for the rock that passes through the locus of maximum upper-plate temperatures. Bottom left panels: bold line shows array of metamorphic temperatures versus metamorphic depths observed at the surface (Tmax vs. zm), thin lines display geotherms within orogen (T vs. z). Bottom right panels: bold line shows array of metamorphic depths versus structural thickness (Dz vs. Dz ), dashed line indicates m= struct lithostatic gradient (Dzm Dzstruct). and erosion act continuously while accretion occurs wedge is such that during an accretion cycle the amount episodically, at regular intervals (Fig. 12). During each of heat-producing crust removed from the surface by accretion cycle of duration ta, the down-going plate is erosion equals the amount of heat-producing crust subducted and erosion removes material from the upper accreted to the upper plate. plate. At the end of the cycle, accretion instantaneously The thermal structures of model orogens undergoing transfers a slab of the down-going plate of vertical episodic accretion do not achieve steady state. thickness h to the upper plate, and a new cycle begins However, after an elapsed time, roughly 1.5 tw, with subduction continuing along a new surface at the temperatures throughout the orogen will vary system- base of the accreted slab. In the case of discrete atically over a time period equal to the accretion cycle. accretion, the heat-producing wedge does not attain a We calculate the thermal structures and metamorphic = steady-state shape, but by t tw the surface width of the evolution for cases of thin-slab accretion (6 km) and 360 A. D. HUERTA ET AL .

thick-slab accretion (18 km) that have achieved cyclic steady state and compare them to the results for case A from above (Fig. 13, Table 2). (To construct orogens with equivalent time-averaged sw and dw, the convergence velocity for cases of slab accretion has to be increased slightly, while the time-averaged accretion rate and the erosion rate are kept the same.) In both cases of discrete slab accretion, maximum upper-plate temperatures do not change significantly during the accretion cycle, but the location of maximum upper-plate temperatures migrates towards the toe of the orogen between accretion events. Maximum upper- plate temperatures for slab accretion are somewhat cooler than for the continuous accretion case (c. 600 °C vs. c. 650 °C), perhaps reflecting the additional cooling due to the higher convergence rate. We calculate field gradients of model orogens that have matured to the point that temperatures within the orogen vary systematically during each accretion cycle. Thus, each slab experiences the same thermal history as it is subducted, accreted and unroofed by erosion, and it is only the level of exposure that varies from slab to slab. For ease of comparison, we determine field gradients immediately following accretion. At that time, the slab adjacent to the foreland has not been eroded, and Tmax,zm and tm observed at the surface are all zero. Slabs further from the foreland have been attached to the upper plate for a longer time and are more deeply eroded, and therefore generally exhibit hotter, deeper and older metamorphic conditions. The field gradients of model orogens undergoing slab accretion are similar to continuous accretion field gradients; Tmax,zm and tm all increase with distance from the toe of the orogen, and metamorphic tempera- > ° tures reach a peak Tmax c. 600 C for rocks exposed in the metamorphic core located at x#300–400 km. However, in the cases of slab accretion, there are distinct steps in the field gradients, commonly at the contacts between slabs. Rocks exposed near the foreland achieve Tmax at the time of accretion. Thus, for these slabs, tm and zm are constant across the slab, and steps in the field gradients at slab contacts reflect the different erosion levels of the slabs. However, far from the toe of the orogen, the steps may occur within a slab.

Fig. 8. Steady-state thermal structures (top) and metamorphic ﬁeld gradients (bottom) as a function of maximum thickness of the heat-producing wedge. (a) d =60 km (case A). (b) d = = w w 50 km. (c) dw 40 km (see Table 2 for other parameters). Top panels: solid white line shows position of the subduction boundary; heavy black arrows show particle trajectories and outline region of heat-producing crust, and dashed white line shows positions where rocks achieve their maximum temperatures, Tmax. Bottom panels: maximum metamorphic temperatures (Tmax), depths at Tmax (zm), and ages of Tmax (tm, measured in millions of years prior to reaching the surface) of rocks that reach the surface at distance xsur from the toe of the orogen. The shaded region of ﬁeld gradients indicates the general location of the ‘metamorphic core’ where metamorphic temperatures observed at the surface reach a local maximum. EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 361

Fig. 9. Steady-state temperature–time (T –t) and pressure– temperature (P–T ) paths (top), steady-state thermal structures (middle), and steady-state piezothermic arrays and pressure– depth profiles (bottom) as a function of maximum thickness of the heat-producing wedge. (a) d =60 km (case A). (b) d = = w w 50 km. (c) dw 40 km (see Table 2 for other parameters). Top panels: T –t and P–T paths for the rock that passes through the locus of maximum upper-plate temperatures. Aluminium silicate phase diagram after Holdaway (1971). A, andalusite; S, sillimanite; K, kyanite. Middle panels: solid white line shows position of subduction boundary, heavy black lines show particle paths for the rock that passes through the locus of maximum upper-plate temperatures. Bottom left panels: bold line shows array of metamorphic temperatures versus metamorphic depths observed at the surface (Tmax vs. zm), thin lines display geotherms within orogen (T vs. z). Bottom right panels: bold line shows array of metamorphic depths versus structural thickness (Dz vs. Dz ), dashed line indicates m= struct lithostatic gradient (Dzm Dzstruct). To understand the morphology of the calculated at the left-hand edge of the core-slab (x=270 km) field gradients far from the toe of the orogen, we show a complex P–T history: temperatures increase examine P–T and T –t paths of rocks exposed in and for a short period during unroofing, decrease as cold near the slab of the metamorphic core for the thick- crust is subducted below, increase again after the slab case (Fig. 14). Maximum temperatures for rocks underlying slab is accreted, and then decrease again exposed in this region were achieved in the upper until they reach the surface. For these rocks, maximum plate, some time after accretion. And, although meta- temperatures are achieved at shallow levels, after morphic temperatures vary smoothly across the core accretion of the underlying slab. Meanwhile, P–T paths = slab, zm and tm do not vary smoothly. Rocks exposed for rocks on the right-hand edge of the core slab (x 362 A. D. HUERTA ET AL .

Fig. 10. Details of modelled steady-state thermal structures and particle paths showing the passage of rocks through the region of inverted geotherms within the upper plate. Symbols represent rocks, ﬁlled symbols indicate locations where rocks achieve Tmax. Note preservation of inverted gradient in the metamorphic record with metamorphic depths approximating a lithostatic gradient (Dzm#Dzstruct). (a) Case C. (b) Case A (see Table 2 for parameters).

350 km) are not as strongly affected by the subduction of the underlying slab, and maximum temperatures are achieved during early stages of unroofing, prior to accretion of the underlying slab. Thus, maximum temperatures for rocks within the slab are achieved at disparate times and depths, and tm and zm step within the slab. The P–T history of rocks exposed immediately to the left of the core slab (x=260 km) reach maximum temperatures at the same time as rocks immediately to the right (in the overlying core slab), and Tmsd, tm and zm are continuous across the contacts. Thus, model results imply that episodic accretion can result in continuous field gradients across structural discontinuities and metamorphic discontinuities where there is no structural break. Is there field evidence to corrobor- ate these conclusions? Relict fault contacts without Fig. 11. Evolution of metamorphic field gradient for case A discrete metamorphic breaks are not uncommon in (see Table 2 for parameters). Thick lines show metamorphic real orogens. However, step-like increases of metamor- conditions of rocks which have been cycled through the orogen and have reached the surface, thin line shows steady-state phic pressure equivalent to c. 15 km within structurally metamorphic temperatures for comparison. coherent transects have not been reported. Since only metamorphic pressures change dramatically at the predicted metamorphic break, it is conceivable that DISCUSSION there would be no change in mineral assemblages (as most mineral reactions are relatively insensitive to The processes of accretion and erosion and the pressure changes at these conditions; Spear & Cheney, resulting accumulation of a wedge of heat-producing 1989), and such a metamorphic break would not be crust in the upper plate exert primary control on the recognized in the field. metamorphic evolution of model orogens. Two key EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 363

features of the calculated metamorphic pattern are strongly dependent on the wedge geometry: peak metamorphic temperatures, and the distance from the toe of the orogen to the metamorphic core. High peak metamorphic temperatures are associated with deep wedges, while orogens with metamorphic cores located at a large distance from the toe of the orogen are associated with wide wedges. In turn, the dimensions of the wedge are directly controlled by the relative rates of accretion (a), erosion (e) and plate convergence (vc) such that high values of vc/a result in deep wedges, and high values of a/e result in wide wedges (Eqs (2) and (3)). Thus, we may be able apply these simple relationships and use petrological data to constrain the rates of orogenic processes. As an example, we use petrological data from the Himalaya to constrain the thickness and width of the heat-producing wedge and to estimate rates of accretion and erosion. These results can then be compared to independently constrained estimates of accretion and erosion rates. Within the Himalaya, peak metamorphic temperatures are on the order of 600–700 °C at depths of c. 20–30 km (Hubbard, 1989; Macfarlane, 1995), while measured heat production rates range from c. 1.5 to >6 mWm−3, with an average reported value of 2.6 mWm−3 (Vidal et al., 1982; Cuney et al., 1984; Scharer, 1984; Scharer et al., 1986; France Lanord & Le Fort, 1988; Macfarlane, 1992). Average surface heat ﬂow of the northern Indian continent is c.70mWm−2 (Rao et al., 1976), corre- = = −3 sponding to dr 18 km for A 2.6 mWm . From this, we estimate a wedge thickness for the Himalaya of = ± dw 52 12 km (Fig. 15). The distance from the metamorphic core to the toe of the Himalayan orogen provides a minimum value of sw of c. 150 km. Applying these estimates of dw and sw and current Himalayan convergence rates (15–20 mm yr−1; Lyon-Caen & Molnar, 1985; Bilham et al., 1997) and slab dip (7–15°; Makovsky et al., 1996; Lyon-Caen & Molnar, 1985) to Eqs (2) and (3), we estimate rates of accretion and erosion of a=1.4±1.0 km Myr−1 and e= 1.8±0.7 km Myr−1. How do these rates compare to estimates of Himalayan accretion and erosion rates based on other evidence? During the past c. 50 Myr, slabs of the Indian plate have been accreted to the Eurasian plate (Gansser, 1964). The total width of material accreted over the 50 Myr extends 300 km from the suture zone to the active Himalayan front, giving an estimated accretion rate of 1.2±0.5 km Myr−1 for H of c.11±4°. Erosion within the Higher Himalaya has carved some of the deepest gorges in the world, and has been responsible for supplying sediment to the largest delta, the Bengal fan. Estimates for long-term erosion

Fig. 12. Generalized cross-sections showing the modelled distribution of heat-producing crust through the evolution of a collisional orogen in which accretion acts episodically with period of ta, while subduction and erosion act continuously. 364 A. D. HUERTA ET AL .

Fig. 13. Thermal structures (top) and metamorphic field gradients (bottom) during steady state or cyclic steady state for orogens with the same average accretion rate (h/ta) and erosion rate (e) as a function of thickness of the accreted slab (h). (a) continuous accretion (case A). (b) Thin-slab accretion, (c) Thick-slab accretion (see Table 2 for parameters). Top panels: solid white line shows position of the subduction boundary. Bottom panels: shaded region of field gradients indicates general location of the ‘metamorphic core’ where metamorphic temperatures observed at the surface reach a local maximum; dashed lines indicate surface location of relict subduction boundaries. rates in the central Himalaya range from 0.5 to We have not incorporated intraplate deformation >5 km Myr−1 (Corrigan & Crowley, 1989; Copeland (either contractional or extensional) in our analysis, & Harrison, 1990; Hubbard et al., 1991). although it occurs in real orogens. Thus, major features The rates of erosion and accretion estimated from such as detachment systems or internal thickening are the distribution of metamorphism within the Himalaya not simulated, and the effects on the metamorphic (e=1.8±0.7 km Myr−1, a=1.4±1.0 km Myr−1) are patterns are not addressed. Intraplate deformation thus consistent with independent estimates of erosion could modify metamorphic patterns observed at the and accretion rates (e#0.5 to >5 km Myr−1, a= surface as a result of changes to both the thermal 1.2±0.5 km Myr−1). These results suggest that meta- structure and particle paths within an orogen. In morphism may be strongly linked to the deformational addition, in this model erosion acts constantly and history of orogenic belts via erosion and accretion, uniformly across the surface of the orogen. Thus, the and that it may be feasible to invert metamorphic data model predicts wide exposures of rocks metamor- to obtain information about the rates of these processes phosed at very deep levels on the back side of the during orogenesis. core, a phenomenon not recognized in real orogens. The results described here are based on a highly Incorporation of more realistic refinements to the simplified model of collisional zones in which rocks model will not change the basic conclusions of this are moved solely by subduction, accretion and erosion. study, although they are worthy of study. EFFECTS OF ACCRETION AND EROSION ON METAMORPHISM 365

Fig. 14. Metamorphic ﬁeld gradient (bottom), temperature–time (T –t) and pressure–temperature (P–T ) paths (top) for exposed rocks near and within the metamorphic core for the case of thick-slab accretion (h=18 km) during cyclic steady state (see Table 2 for parameters). Top panels: dash–dot lines indicate accretion events, bold dots indicate conditions at Tmax. Aluminium silicate phase diagram after Holdaway (1971). A, andalusite; S, sillimanite; K, kyanite. Bottom panel: shaded region of ﬁeld gradients indicates the general location of the ‘metamorphic core’ where metamorphic temperatures observed at the surface reach a local maximum; dashed lines indicate surface location of relict subduction boundaries.

Fig. 15. Maximum upper-plate temperatures as a function of heat production rate (A) and maximum thickness of the heat = = producing wedge (dw). (a) Maximum upper-plate temperatures at z 20 km, and (b) maximum upper-plate temperatures at z 30 km (after Huerta et al., 1998).

mountain belts as a response to erosion, accretion and ACKNOWLEDGEMENTS radiogenic heating’, PhD thesis, Massachusetts Thanks to R. Jamieson and S. Peacock who provided Institute of Technology, by A.D.H. Early stages of this helpful and thoughtful reviews. This work comprises study were supported by National Science Foundation part of ‘The thermal and metamorphic evolution of grant EAR 9418062 to K.V.H. 366 A. D. HUERTA ET AL .

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