3.1. Northern Cascadia
 Subduction along the Cascadia margin has been continuous for at least 200 Myr [e.g., Monger and Price, 2002]. In our study, we focus on the northern part of the Cascadia back arc (48–51°N), which has been tectonically quiescent since the early Cenozoic [e.g., Gabrielse, 1992]. The most recent significant tectonic activity was a short-lived (<10 Myr) period of extension in the Eocene in a small area of southeast British Columbia, but it has been concluded from thermochronologic studies of core complexes and thermal modeling that this area was hot well before extension [Liu and Furlong, 1993].
 We limit our study to the region north of 48°N. In the southern Cascadia back arc, there are large differences in geological structure and late Cenozoic tectonics, and the thermal regime is complicated by both the proximity of the Yellowstone hot spot and by current extension in the Basin and Range province. We note that heat flow, mantle seismic velocities, and other temperature indicators suggest that the mantle thermal structure here is similar to that of the northern Cascadia back arc [e.g., Roy et al., 1972; Blackwell et al., 1990a, 1990b; Lowry and Smith, 1994; Blackwell and Richards, 2004]. As argued by Blackwell [e.g., 1969, 1978], the entire Cordilleran mountain belt of the northwest United States appears to be uniformly hot and the high temperatures of the Basin and Range province are not simply due to extension. We further note that California and northern Mexico appear to be similarly hot [e.g., Goes and van der Lee, 2002; Dixon et al., 2004], although subduction terminated at 10–30 Ma. In section 6, we discuss the cooling of former back arcs.
 At the northern Cascadia subduction zone, surface heat flow is high in the volcanic arc region and for 500 km east into the back arc [Davis and Lewis, 1984; Lewis et al., 1988, 1992; Blackwell et al., 1990a, 1990b; Hyndman and Lewis, 1999; Flück, 2003] (Figure 4a). The back-arc heat flow increases eastward from ∼70 mW m−2 in the west to >100 mW m−2 in the east (Figure 4b). Numerous high-quality measurements of near-surface radiogenic heat production show that the eastward increase in surface heat flow is correlated with an eastward increase in radiogenic heat production, from 1 μW m−3 in the west to 3.6 μW m−3 in the east, such that the deep thermal structure is nearly uniform across the back arc, with a reduced heat flow of ∼60 mW m−2 [Lewis et al., 1992; Hyndman and Lewis, 1999]. To aid in the comparison with the heat flow of other back arcs, we have corrected the northern Cascadia heat flow to that for a common upper crustal heat production of 1.3 μW m−3, assuming uniform heat production in the upper 10 km of the crust. After correction, the surface heat flow across the Cascadia back arc is relatively uniform, 75 ± 15 mW m−2.
Figure 4. (a) Heat flow data for the northern Cascadia subduction zone. The white diamond indicates where mantle xenoliths have been recovered. Solid triangles are active arc volcanoes. The eastern limit of the back arc is the Rocky Mountain Trench (RMT). The solid line is the heat flow profile location; dotted lines show the profile data width. (b) Heat flow profile along line A-B. The measured heat flow values (open circles) have been corrected for variations in near-surface heat generation (solid circles) (see text). (c) Back-arc geotherm from surface heat flow (dotted lines are 20% uncertainty) and other thermal constraints.
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 We have calculated a geotherm for this surface heat flow and heat generation, following the procedure of Chapman . We use a three-layer model, consisting of a 10 km thick upper crust, 25 km thick lower crust, and an upper mantle. For the crust and mantle, we use the temperature-dependent thermal conductivity of Sass et al.  [see also Lewis et al., 2003]. The heat productions are 1.3, 0.6, and 0.02 μW m−3 for the upper crust, lower crust and mantle, respectively, consistent with estimates of crust and mantle heat production [e.g., Chapman, 1986; Rudnick and Fountain, 1995; Rudnick et al., 1998; Hyndman and Lewis, 1999].
 Figure 4c shows the calculated geotherm for the northern Cascadia back arc. This geotherm is similar to those from previous heat flow–heat generation studies for this area [e.g., Lewis et al., 1992; Hyndman and Lewis, 1999]. High temperatures in the uppermost mantle are predicted throughout the northern Cascadia back arc, with estimated temperatures at the Moho (∼35 km depth) greater than 900°C. As noted above, these temperatures may be somewhat too high because we neglect radiative thermal conduction at high temperatures, but it is difficult to obtain Moho temperatures less than 800°C with reasonable parameters. These temperatures are much higher than the solidus temperature for most crustal rocks that contain at least a small amount of water. As there is no obvious geological or geophysical evidence for significant melting of the lower crust in this region, this may indicate that the lower crust is mafic and dry.
 Additional constraints on uppermost mantle temperatures come from seismic velocity studies. Extensive seismic refraction data for the northern Cascadia back arc, especially from the Lithoprobe program, indicate consistently low Pn velocities of 7.8–7.9 km s−1 [Zelt and White, 1995; Clowes et al., 1995; Burianyk and Kanasewich, 1995], giving an estimated Moho temperature of 760–900°C (Figure 4c). This temperature is slightly lower that that determined from heat flow, but within the uncertainties of the methods. Seismic tomography studies have poor depth resolution but show that, relative to average mantle velocities at 50–150 km depth, the upper mantle throughout the northern Cascadia back arc has P wave velocities that are 1–3% slow [e.g., Bijwaard and Spakman, 2000] and S wave velocities that are 3% to more than 8% slow [e.g., Grand, 1994; van der Lee and Nolet, 1997; Frederiksen et al., 2001; van der Lee and Frederiksen, 2005] (Figure 5a), suggesting mantle temperatures greater than 1150°C at depths greater than 50 km. Small amounts of water and perhaps partial melt are expected to have only a small effect on P wave velocities. However, the extremely low observed S wave velocities likely reflect the combined effects of high temperatures and the presence of a small amount (<2%) of water, other volatiles and partial melt [e.g., van der Lee and Nolet, 1997; Frederiksen et al., 2001; Goes and van der Lee, 2002; Dixon et al., 2004].
 Upper mantle xenoliths have been recovered from several localities in the northern Cascadia back arc. Three suites of peridotite xenoliths from the central back arc yield temperatures of 1000°C at ∼40 km depth, increasing to 1300°C at 60–70 km depth [Ross, 1983] (Figure 4c). A recent study of xenoliths from the same region indicates temperatures of 900–1040°C at 1.2–1.6 GPa (35–50 km depth) [Saruwatari et al., 2001].
 Several observations indicate that the base of the lithosphere is at shallow depths throughout the northern Cascadia back arc. Clowes et al.  report an upper mantle reflector at ∼50 km depth in seismic data for the central back arc, which they interpret as the base of the lithosphere. An earlier surface wave study shows a low-velocity layer, interpreted to be the asthenosphere, with its upper boundary at 50–55 km depth [Wickens, 1977]. In addition, upper mantle xenoliths record a rapid downward increase in strain rate at depths of 50–60 km, which may indicate a transition from rigid lithosphere to convecting asthenospheric mantle [Ross, 1983]. A lithosphere thickness of 50–60 km is similar to the inferred intersection of the conductive geotherm discussed above with a standard 1300°C mantle adiabat (Figure 4c).
 High temperatures in the shallow back-arc mantle are also indicated by (1) widespread sporadic Cretaceous to Recent basaltic volcanic centers, including the Chilcotin Plateau basalts and Wells Gray–Clearwater volcanic field [e.g., Wheeler and McFeely, 1991]; (2) an effective elastic thickness of less than 20 km throughout the entire region [Flück et al., 2003] (Figure 5b); and (3) high electrical conductivity in both the lower crust and upper mantle, which is interpreted to reflect the presence of partial melt at shallow depth and a thin lithosphere [Soyer and Unsworth, 2006, and references therein].
 Taken together, the observations for the northern Cascadia back arc indicate a uniformly hot upper mantle for 500 km east of the volcanic arc, with no significant lateral variation. We estimate temperatures of 800–1000°C at the Moho (∼35 km depth) and a lithosphere thickness of 50–60 km, where temperatures are estimated to be ∼1200°C (Figure 4c). The high temperatures are especially surprising as the northern Cascadia back arc is bounded on the east by the edge of the unextended North America craton, which is much cooler. The eastern limit of the back arc is concluded to coincide with the Rocky Mountain Trench, based on rapid changes in lithosphere properties, thermal regime, and deformation styles across this boundary [Lowe and Ranalli, 1993; Hyndman and Lewis, 1999]. Earlier studies suggested that the Cascadia back arc, as well as regions to the north and south, overlie a large-scale upwelling of anomalously hot mantle [e.g., Gough, 1986]. Our current compilation supports an explanation of convective upwelling in the mantle, but suggests that it is not unique to this region. As shown below, high temperatures are found in most other back arcs, suggesting that a hot back arc may be a characteristic feature of subduction zones and may be a direct result of back-arc mantle dynamics associated with the subduction process [e.g., Davis and Lewis, 1984].
3.3. South America–Central Andes
 Along the central Andean segment of the South America subduction zone (15–28°S), the back-arc strain regime is dominated by shortening [e.g., Allmendinger et al., 1997; Klotz et al., 2001, and references therein]. Surface heat flow values are consistently high throughout the arc and back-arc regions, averaging 85 ± 16 mW m−2 [Hamza and Munoz, 1996; Springer and Forster, 1998] (Figure 6). The measured K, Th, and K contents in exposed basement sections in the central Andes (21–27°S) indicate a near-surface radiogenic heat production of 1.3 μW m−3 [Lucassen et al., 2001], similar to our Cascadia reference value. The eastern limit of high heat flow coincides with the Brazilian Shield craton, where surface heat flow averages 42 mW m−2 [Hamza and Munoz, 1996], comparable to the North America craton.
Figure 6. (a) Map of the central Andean part of the South America subduction zone. The white diamond shows the location of mantle xenoliths (erupted at 90 Ma). (b) Heat flow profile along line A-B. (c) Inferred thermal structure for the central Andes back arc. The well-constrained Cascadia and Archean craton geotherms are shown for comparison.
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 The back arc of the central Andes is made up of the Altiplano and Puna plateaus, which have elevations of 3.5–4 km and thick crust (60–75 km) [e.g., Allmendinger et al., 1997]. At depths greater than 20 km, the crust is characterized by low P wave velocities (VP), extremely low S wave velocities (VS), a high VP/VS ratio, low density, and high electrical conductivity [Schmitz et al., 1997; Baumont et al., 2002; Yuan et al., 2002; Oncken et al., 2003, and references therein]. The low S wave velocities, high VP/VS ratio and high conductivity are interpreted to indicate a small amount of melt [Yuan et al., 2002; Oncken et al., 2003]. Further constraints on crustal temperature are provided by widespread late Miocene–early Pliocene ignimbrites throughout the back arc, which appear to have resulted from voluminous melting in the lower part of the thickened felsic crust [Allmendinger et al., 1997]. Petrologic data indicates preeruptive midcrustal temperatures of 700–800°C [Babeyko et al., 2002, and references therein]. Taken together, the observations give a temperature of ∼800°C at 20–25 km depth (Figure 6c). Such midcrustal temperatures imply extremely high temperatures in the lowermost crust, unless the vertical gradient at depth is much reduced by radiative heat transfer or convection [Babeyko et al., 2002].
 High surface heat flow and high crustal temperatures in the central Andes back arc have often been attributed to increased radiogenic heat production associated with the thick felsic crust. However, geological evidence shows that the Altiplano and Puna plateaus formed by tectonic shortening and thickening over the last 25 Myr [Allmendinger et al., 1997]. For crustal thickening by pure shear, the surface heat flow first decreases and then increases as the crust is heated from below and by radiogenic heating. Babeyko et al.  showed that the cooling effects of thickening should still dominate, due to the short time since thickening.
 In addition, it is unlikely that the crust will deform and thicken under available plate tectonic forces unless it is already hot and weak. Indeed, numerical models indicate that to produce the observed plateau topography, there must have been thermal weakening of the mantle across the entire width of the Altiplano prior to shortening [Wdowinski and Bock, 1994]. This conclusion is supported by lower crustal xenoliths from the Altiplano back arc that suggest that this region was hot before crustal thickening occurred. Thermobarometry studies of mafic granulite xenoliths erupted at 90 Ma from the Salta Rift (∼24°S, 66°W) give temperatures of 850–900°C at 0.95–1.05 GPa (∼30 km depth) [Lucassen et al., 1999]. Upper mantle xenoliths from this location record temperatures of 1000–1200°C at 1.3–1.5 GPa (∼45 km depth) [Lucassen et al., 1999]. On the basis of these and other data, the Aliplano crust is inferred to have been ∼35 km thick at 90 Ma, with Moho temperatures of ∼900°C, i.e., similar to the current northern Cascadia back arc. High crustal temperatures before thickening and 10–20 Myr after thickening suggest a deep, long-lived heat source [e.g., Babeyko et al., 2002]. This is consistent with observations that indicate present-day high temperatures in the shallow mantle.
 A limited seismic refraction study shows moderately low Pn velocities (8.0–8.1 km s−1) below the Altiplano and an abrupt increase to 8.2 km s−1 at the Brazilian craton [Baumont et al., 2001]. As the crustal thickness in this region is ∼70 km, the somewhat higher Pn velocity relative to other back arcs may be partially due to higher pressure [e.g., Christensen, 1979], rather than lower temperatures. In addition, the refraction data are from an unreversed profile, which leads to large velocity uncertainties.
 Tomography data at ∼100 km depth indicates that the entire width of the central Andes is characterized by P wave velocities that are 2–3% slow [Bijwaard and Spakman, 2000] and S wave velocity that are 4% to >10% slow [van der Lee et al., 2001], relative to average mantle. Such low S wave velocities are likely the result of the combined effects of temperatures of at least 1200°C, as well as the presence of volatiles and partial melt [van der Lee et al., 2001]. Surface wave dispersion studies also indicate a low-velocity upper mantle [Baumont et al., 2002]. The back-arc upper mantle exhibits high seismic attenuation [Haberland and Rietbrock, 2001; Schurr et al., 2003]. In addition, this region is characterized by the presence of Oligocene to Recent basaltic volcanic centers and fissure flows [Allmendinger et al., 1997] and elevated 3He/4He ratios in groundwater [Hoke et al., 1994], suggesting near-solidus temperatures in the uppermost mantle throughout the central Andes back arc.
3.6. Aleutians and Alaska
 We summarize observations for the Aleutian and Alaska back arcs together, as there is some overlap in the observational data. The Aleutian back arc west of the Bering Sea shelf edge is composed of oceanic crust, overlain by up to 4 km of sediments [Langseth et al., 1980]. This part of the back arc was formed in the early Eocene (50–55 Ma), when subduction along the then-active Beringian margin (near the Bering Sea Shelf edge) jumped southwest to its present location, trapping a fragment of early Cretaceous (117–132 Ma) oceanic crust [Cooper et al., 1992]. Recent (<20 Ma) back-arc spreading is confined to Komandorsky Basin, in the westernmost part of the back arc [Cooper et al., 1992, and references therein]. The rest of the back arc is inactive, with no significant extension.
 High heat flow is found throughout the Aleutian back arc, averaging 63 ± 15 mW m−2 with no clear decrease with distance from the arc (Langseth et al.  and data from http://www.heatflow.und.edu) (Figure 9). Langseth et al.  note that due to rapid sedimentation rates in the Aleutian Basin, especially over the last 10 Myr, the observed heat flow should be increased by 16–22% to correct for sedimentation. With this correction, the average heat flow is ∼75 mW m−2. In addition, the Aleutian back arc is composed of oceanic crust, in which radiogenic heat production is significantly less than that in continental crust. Thus, for comparison to continental back arcs in our compilation, the Aleutian heat flow should be further corrected upward by at least 10 mW m−2 to allow for differences in crustal radiogenic heat production. As radiogenic heat production in the Aleutian back arc is not well constrained, we do not include this latter correction.
Figure 9. (a) Location map for the Aleutian and Alaska subduction zones. The diamonds indicate the volcanic fields of the Bering Sea basalt province; open diamonds are locations of mantle xenoliths [after Akinin et al., 1997]. (b) Heat flow profile for the Aleutian back arc. The observed heat flow (open circles) has been corrected for the effects of sedimentation (solid circles) [Langseth et al., 1980].
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 The Aleutian Basin heat flow is significantly higher than the expected ∼45 mW m−2 heat flow for ∼120 Ma oceanic crust [e.g., Stein and Stein, 1992]. There is some evidence for recent faulting in parts of the basin which might perturb the heat flow [Cooper et al., 1992], but the spatial extent and apparent uniformity of the high heat flow seem to require a more widespread explanation. This conclusion is supported by seismic studies that indicate low Pn velocities of 7.8–8.0 km s−1 throughout the Aleutian Basin [Levshin et al., 2001] and tomography data that indicates P wave velocities that are 1–2% slower than average mantle at 50–150 km depth [Jin and Herrin, 1980; Bijwaard et al., 1998; Bijwaard and Spakman, 2000].
 The eastern Aleutian back arc and Alaska back arcs are composed of the Bering Shelf and Alaska mainland, respectively, which are both continental [Fliedner and Klemperer, 2000]. There are no surface heat flow data. However, seismic studies indicate that mantle velocities are anomalously low with Pn velocities of ∼7.8 km s−1 beneath the Bering Sea shelf [Fliedner and Klemperer, 2000; Levshin et al., 2001] and 7.8–8.0 km s−1 below continental Alaska [Stone et al., 1987; McNamara and Pasyanos, 2002; Levshin et al., 2001], suggesting shallow mantle temperatures of 650–900°C. Seismic tomography studies of this region indicate upper mantle (50–150 km depth) P wave velocities 1–3% slower than average mantle [Estabrook et al., 1988; Zhao et al., 1995; Bijwaard et al., 1998; Bijwaard and Spakman, 2000], consistent with temperatures greater than 1150°C. In addition, throughout the Aleutian and Alaska subduction zone back arcs, there are at least 15 distinct basaltic volcanic fields younger than 10 Ma that form the Bering Sea basalt province [Akinin et al., 1997] (Figure 9a). Upper mantle xenoliths from three fields indicate equilibrium temperatures of 850–1030°C at an estimated pressure of 1.5 GPa (∼45 km) [Akinin et al., 1997].
 The Kamchatka subduction zone was established by at least 50 Ma [Konstantinovskaia, 2001]. Only diffuse small magnitude seismicity and GPS observations of little or no deformation suggest negligible present extension in the Kamchatka back arc [Seno et al., 1996; Takahashi et al., 1999]. The adjacent Kuril back arc (southernmost Sea of Okhotsk) was formed by spreading between 32 and 15 Ma [Baranov et al., 2002], but this region of extension is more than 500 km southeast of our study area. In the Kamchatka back arc, the Sea of Okhotsk is characterized by high heat flow, 70 ± 18 mW m−2 (Figure 10) (Sugrobov and Yanovsky , Yamano , and data from http://www.heatflow.und.edu). Neither the effects of sedimentation on heat flow nor the amount of crustal radiogenic heat production are well constrained. Given that the crust is at least partially composed of oceanic material [Konstantinovskaia, 2001] with heat generation less than our reference value and that sediment thickness in the Sea of Okhotsk is >2 km [e.g., Mooney et al., 1998], it is likely that the heat flow should be corrected upward for comparison to continental back arcs.
Figure 10. (a) Location map for the Kamchatka subduction zone. The hatched area is the region of Kuril back-arc extension. (b) Heat flow profile along line A-B.
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 Pn velocities are 7.8–7.9 km s−1 [Levshin et al., 2001], suggesting uppermost mantle temperatures of 760–900°C. Tomography data at 50–120 km depth shows that, relative to average mantle velocities, P waves are generally 2% slow [Bijwaard et al., 1998; Gorbatov et al., 1999; Bijwaard and Spakman, 2000] and S waves are 4% to >7% slow [Shapiro et al., 2000], consistent with upper mantle temperatures in excess of 1200°C. Slow mantle velocities are also observed in surface wave studies [e.g., Kaila and Krishna, 1984; Ritzwoller and Levshin, 1998]. In addition, the Kamchatka back-arc region is characterized by relatively low gravity, which has been modeled using a hot, low-density mantle [Kogan, 1975].
 The thermal structure of the northernmost Kamchatka back arc may be affected by the proximity of the edge of the subducting Pacific Plate, which could represent a region of complex mantle flow and unusual thermal conditions. However, mantle temperatures appear to be high well away from this boundary, and far from the region of Oligocene-Miocene extension in the Kuril back arc.
 The tectonics of the Sunda subduction zone and surrounding areas are relatively complex [Hall and Morley, 2004], but tectonic reconstructions, seismicity, and GPS observations indicate that neither the Sumatra nor Java segments of the Sunda margin have experienced significant recent back-arc extension [Hamilton, 1979; Lee and Lawver, 1995]. We focus our analysis on the Borneo region of the Sunda back arc (eastern Java). High heat flow is found at the volcanic arc and for over 800 km behind the arc, with an average value of 76 ± 18 mW m−1 (Figure 12) (data from http://www.heatflow.und.edu and Hall and Morley ). The heat flow data primarily come from sedimentary basins where there has been rapid Neogene sedimentation [Hall and Nichols, 2002], which may decrease the surface heat flow. As neither the effects of sedimentation nor the crustal radiogenic heat production are well constrained, we have not introduced any corrections. Further evidence for high mantle temperatures comes from tomography studies that indicate P wave velocities that are ∼2% slow [Puspito and Shimazaki, 1995; Widiyantoro and van der Hilst, 1997; Bijwaard et al., 1998] and S wave velocities are ∼4% slow [Lebedev and Nolet, 2003], relative to average mantle at ∼100 km depth. These velocities are consistent with temperatures >1200°C in the shallow upper mantle.
 The high temperatures appear to extend well west of Borneo. Below the Sunda Shelf and Sumatra regions, upper mantle P wave velocities are ∼2% slower than average upper mantle [Puspito and Shimazaki, 1995; Widiyantoro and van der Hilst, 1997; Bijwaard et al., 1998] and S wave velocities are ∼4% slower [Lebedev and Nolet, 2003]. This region is also characterized by high heat flow, >100 mW m−2 (data available at http://www.heatflow.und.edu), but factors that complicate the heat flow include recent folding and faulting in the sedimentary basins of Sumatra [Tharmin, 1985], enriched radiogenic heat production (up to 5 μW m−3) in the granitoid basement rocks of the basins [Gasparon and Varne, 1995], and minor extension of the Sunda shelf between 30 and 40 Ma [Lee and Lawver, 1995; Hall and Morley, 2004]. Additional evidence for high temperatures are provided by sporadic Miocene-Quaternary basaltic volcanism throughout the Sunda back arc (including northern Borneo), and studies of gravity and basin subsidence history on the western Sunda shelf that indicate a thin elastic thickness [Hall and Morley, 2004 and references therein].