The Sierra Madre del Sur mountain range is an uplifted forearc associated with the subduction of the Cocos plate along the Acapulco trench beneath mainland southern Mexico. The shallow subduction angle, the truncation of geologic features along the modern Acapulco trench, and direct seismic and drill hole observations in the trench through deep sea drilling data suggest that subduction erosion is an important process during the evolution of this margin. Turbidites derived from the uplifted forearc are the predominant sedimentary input into this trench, while pelagic sediments are subordinate. Apatite (U-Th)/He ages were obtained on 23 samples from two transects across the Sierra Madre del Sur (Acapulco and Puerto Escondido) and reveal slow cooling during the Miocene. (U-Th)/He ages range between ∼25 and 8 Ma and correlate inversely with elevation. Long-term erosional exhumation rates inferred from these ages range from 0.11 to 0.33 km/m.y., with higher rates in the range core, and suggest that the Sierra Madre del Sur has been a slowly decaying mountain range, since at least the early Miocene. Apparent Miocene-Pliocene sedimentation (“preservation”) rates in the Acapulco trench derived from Deep Sea Drilling Project data are about an order of magnitude smaller than the Miocene forearc erosion rates estimated from (U-Th)/He ages, suggesting that the terrigenous input to the trench was almost entirely recycled via subduction erosion, at least during the Miocene. The Miocene subducted flux per unit length of the margin is about 30 km3/(km m.y.), or a subducted volume per unit time of 44 × 103 km3/m.y., when integrated over the length of the trench.
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 One of the most important large-scale geochemical and geodynamic problems in the Earth Sciences is quantifying the mass exchange between the crust and the mantle during plate tectonic processes [Albarede, 1998]. Unfortunately, fluxes associated with some processes are hard to quantify in complex tectonic settings such as subduction zones [Stern, 2002], especially for geologic timescales. For example, sediment subduction and/or subduction erosion [von Huene and Scholl, 1991; Clift and Vannucchi, 2004] are processes of returning trench deposits into the mantle or transferring them to the overriding plate (Figure 1). The rate of sediment recycling for any given time period is the difference between the rate of sediment accumulation in the trench and the rate of sediment preservation.
 Subduction erosion [von Huene and Scholl, 1991] is a term for the process of sediment and forearc basement recycling into the mantle at subduction zones. Subduction accretion is the process of sediment and/or forearc basement underthrusting followed by transfer to the lower crust of the overriding plate (“underplating”) (Figure 1). In recent years, it has become clear that subduction erosion and accretion are major processes at convergent margins, and are capable of recycling significant amount of continental crust [Reymer and Schubert, 1984; Plank and Langmuir, 1998; Albarede, 1998; Clift and Vannucchi, 2004]. Consequently, it is important to quantify the rates of subduction erosion at trenches worldwide. Advances in offshore geophysical and drilling techniques during the past couple of decades have allowed successful exploration of subsurface structures at convergent margins [e.g., Vanneste and Larter, 2002; Vannucchi et al., 2003; von Huene and Ranero, 2003]. Geophysical and drill hole data from trenches (e.g., the vast array of available deep sea drilling project (DSDP) and ocean drilling project (ODP) data) and our general knowledge of present-day plate kinematics, have led to estimates of instantaneous sediment accretion and recycling rates [von Huene and Scholl, 1991]. The rate of accretion and recycling of pelagic sediments at a trench is relatively easy to quantify if one has a first-order estimate of plate convergence rate and thickness of the downgoing plate sedimentary cover. However, long-term (106–107 yr) accretion and recycling rates at margins dominated by continental erosion from the overriding plate have been difficult to obtain [e.g., Hartley et al., 2000; Thomson et al., 2001]. Overall, the terrigenous input from the overriding plate is difficult to quantify over time, especially when the forearcs are uplifted continental domains.
 Low-temperature thermochronology (e.g., apatite fission track and (U-Th)/He chronology) can be used to monitor timing of processes in subduction zones, e.g., subduction initiation [House et al., 2002]. Here, we present a simple technique to determine subduction erosion rates averaged over ∼17 m.y. for the Acapulco trench in southern Mexico (Figure 2). The trench was active for the past 25 Ma [Watkins et al., 1982], and marks the plate boundary where the Cocos plate subducts beneath mainland Mexico, currently a part of the North American continent. In this case, the sediment preservation rates are well known for the past 23 Ma from DSDP drilling and seismic images offshore Acapulco and Puerto Escondido. In addition, the Acapulco trench is predominantly filled by turbidites derived from the upper plate, with very little pelagic sediment from the oceanic plate [Leggett, 1982]. We determined cooling and exhumation rates for the basement rocks of the Sierra Madre del Sur mountain range in the Acapulco-Puerto Escondido area using (U-Th)/He thermochronology [Farley, 2000]. Interpretation of these ages as reflections of long-term erosion rates then provides a proxy for sedimentation rates in the trench. Mismatch between sedimentation rates and preservation rates for the Miocene then represent the rate of sediment subduction erosion beneath southern Mexico. Our data show that the almost all (>90%) material eroded off the top of the uplifted forearc during the Miocene has been recycled by subduction erosion.
 The rates of thicknesses of sedimentary packages over time interval in the accretionary wedge will be used here to determine “sediment preservation” rates. Sediment preservation rates would represent “sediment accumulation” rates if the entire package of accreted sediment would altogether escape subduction erosion, which is not the case here or at any other subduction margin [Plank and Langmuir, 1998]. The rate of sediment preservation in the Acapulco trench varies between 20–45 m/m.y. for the past 23 Ma (Figure 3), as inferred from DSDP Leg 66 drill holes (Figure 2b for location), after a compaction correction was applied to the drill hole data [Shepard and McMillen, 1982]. Figure 3 is an average of all DSDP available data for slope and accreted sediments of early Miocene to Quaternary ages. These rates incorporate the sediment that lies on top of forearc basement. The sediments are predominantly turbidites [Enkeboll, 1982; Lopez, 1982] rich in quartz, feldspar, and metamorphic rocks clasts that closely resemble rocks found in the forearc region. Pelagic sediments are subordinate in all drilled sections [Leggett, 1982]. The dominance of terrigenous sedimentary material is consistent with the nature of the subducting Cocos plate—plates entering fast converging trenches are typically sediment starved. Chemically, the average composition of the sediments recovered from DSDP Leg 66 is one of an andesite [Bachman and Leggett, 1982; Plank and Langmuir, 1998], indicating that the most important source rocks were earlier Cenozoic arc rocks present throughout the continental margin of southern Mexico [Enkeboll, 1982]. High-resolution seismic data collected offshore Acapulco also shows that structurally the accretionary wedge is deformed by an in sequence thrust fault system - progressively younger faults toward the modern trench [Lundberg and Moore, 1982]. The seismic data indicate that subduction erosion takes place in the Acapulco trench [Moore and Watkins, 1982] and elsewhere along the Middle America trench [Ranero and von Huene, 2000]. The magnitude of trench retreat rate was estimated for the Acapulco region to be around 1 km/m.y. [Clift and Vannucchi, 2004], on the basis of subsidence data from DSDP Site 493.
 The Sierra Madre del Sur is a broad physiographic province that includes a coastal mountain range comprising crystalline rocks and a mountainous inland area of Mesozoic and Tertiary sedimentary and volcanic units. Although Sierra Madre del Sur is geologically the forearc of the Trans Mexican Volcanic Belt, it is a high mountain range that reaches over 3.5 km in elevation (Figure 2b). The average elevation of the Sierra Madre del Sur is 1.6 km. The southern flank of the coastal range comprises primarily the Xolapa Complex [DeCserna, 1965], which is the basement of the Xolapa terrane [Campa and Coney, 1983], also called Chatino terrane [Sedlock et al., 1993]. The Xolapa terrane includes a crystalline assemblage of deformed gneisses and migmatites and undeformed granitoids and gabbros, together representing arc-related rocks ranging in age from Jurassic to Oligocene [e.g., Ortega-Gutierrez, 1981; Herrmann et al., 1994; Morán-Zenteno et al., 1999; Ducea et al., 2004]. Calc-alkaline, arc related plutons were emplaced in the Xolapa Complex between Puerto Escondido and Acapulco as recently as 25–35 Ma [Moran-Zenteno et al., 1999; Ducea et al., 2004] and are found along coastal exposures and as backstop to the modern accretionary wedge [Bellon et al., 1982]. Arc magmatism that produced the youngest, undeformed plutons has been interpreted by some to represent the southern continuation of the major 35–25 Ma flare-up event that formed the Sierra Madre Occidental magmatic belt [Ferrari et al., 1999]. Undeformed, Eocene-Oligocene plutons comprise about 30–40% of the Xolapa Complex between Puerto Escondido and Acapulco [Morán-Zenteno, 1993; Werre-Keeman and Rodarte, 1999; Castillo-Nieto and Rodríguez-Luna, 1996]. Al-in-hornblende igneous barometry data suggest that the several Oligocene plutons now at the surface were emplaced at midcrustal depths (13–20 km) [Morán-Zenteno et al., 1996], thus requiring significant unroofing of the Xolapa Complex during the Neogene.
 The modern plate margin is clearly truncated, as the Acapulco trench developed immediately south of the Eocene-Oligocene arc, and magmatism migrated inland [Ferrari et al., 1999]. Some have speculated that truncation took place via a left lateral transform fault that transferred the Chortis block from southern Mexico to its present location in the Caribbean [e.g., Pindell et al., 1988], although a positive geologic tie between Chortis and Xolapa Complex geology has yet to be established. In addition, geologic data constrain that a lateral truncation from Acapulco to Tehuantepec could have taken place mainly in the Paleogene [Herrmann et al., 1994; Schaaf et al., 1995]. The truncation of the Eocene-Oligocene arc and thus of the Xolapa Complex progressed by subduction erosion, as arc magmatism continued migrated inboard toward its present location, the Trans Mexican Volcanic Belt [Ferrari et al., 1999; Morán-Zenteno et al., 1996, 1999]. Several Late Cenozoic normal faults have been mapped throughout the Sierra Madre del Sur region; however there is no evidence for large-scale extension in the area after the Oligocene [Morán-Zenteno, 1993].
 Subduction of the Cocos plate beneath southern Mexico continues today; the convergence rates are high, 5.2 cm/yr and the subduction decollement dips shallowly (∼25°) to the north [Pardo and Suárez, 1995]. The subduction plane passes at depths of 15–25 km beneath the coastal range between Acapulco and Puerto Escondido [Nava et al., 1998; GEOLIMEX Working Group, 1993; Pardo and Suárez, 1995], suggesting that a significant fraction of sediment eroded from the trench might be transferred to the lower crust of the overriding plate. An ancient analogue to the sediment-rich shallow subduction beneath the Sierra Madre del Sur might be the underthrusting of the Pelona-Orocopia-Rand type schists beneath southwestern North America during the Laramide orogeny [Saleeby, 2003]. However, there are some differences between these two cases, as will be discussed below.
3. Samples and (U-Th)/He Results
 Twenty-three Xolapa Complex samples were collected and analyzed for He thermochronometry from two North-South transects, Acapulco and Puerto Escondido (Figure 2b). Some of the rocks analyzed here for (U-Th)/He thermochronometry (Table 1) were also used in two companion studies, one focusing on U-Pb zircon crystallization ages of the Xolapa Complex [Ducea et al., 2004], and the other on apatite fission track ages [Shoemaker et al., 2002]. Other ages obtained on hand samples from this study are also reported in Table 1, when available.
Table 1. Location, Petrography, and Previously Reported Ages on Analyzed Samples
 Samples were collected from the south-facing slopes of the range and are all basement rocks of the Xolapa Complex - they are migmatitic ortho-gneisses or undeformed tonalites, granodiorites and granites (Table 1). The topography of the Sierra Madre del Sur does not allow collection of a “vertical transect”, i.e., a region with significant relief over a short horizontal distance. At each sample locality 1–2 kg of fresh whole rock were collected. Samples were prepared for analysis using standard crushing and apatite-separation techniques, including heavy liquids and magnetic separation, at the University of Arizona. Apatite yields ranged from tens to thousands of grains per sample.
 (U-Th)/He analysis preparation was performed at Yale University, and included picking inclusion-free and euhedral grains. The apatite crystals were then enclosed in small (∼1 mm) Pt, Mo, or Pd foil envelopes and degassed by CO2 laser heating. Degassed He is measured by 3He isotope dilution on a quadrupole mass spectrometer [Reiners et al., 2003], following cryogenic purification and concentration, with a two-sigma analytical uncertainty of about 2%. The heated foil packets are then retrieved and crystals are dissolved in 229Th- and 233U-spiked acids. The U and Th contents of the same crystal aliquots used for He measurement are measured by isotope dilution on a Finnigan Element 2 high-resolution ICP-MS (analytical uncertainties on U and Th contents are 1–2%). Standard alpha ejection corrections are applied using the modified Farley  methods, similar to those of the Farley et al.  method. Durango apatite age determinations at WSU and Yale average 32.0 Ma, with two standard deviations of 2.0 Ma (n = 65). On the basis of reproducibility of these and other standard samples in the WSU and Yale He dating labs, 2σ uncertainties are estimated for typical nonstandard samples of about 6%. Results are given in Table 2.
Table 2. (U-Th)/He Analytical Data for the Acapulco and Puerto Escondido Transects
Corrected using Ft parameter after method of Farley . Estimated age uncertainties are 6% at 2σ. Samples M006 through M0015 were measured by resistance furnace heating at Washington State University; all others were measured by laser heating [House et al., 2002] at Yale. Analytical methods for both are described by Reiners et al. .
3.1. Acapulco Transect
 The Acapulco transect samples are undeformed tonalites, diorites, and granodiorites as well as gneissic tonalites and a ductily deformed granite, ranging from 0 to 670 m in elevation and 0 to 60 km inland from the Pacific coast. Twelve analyzed samples span ∼17 m.y. (26 to 8.4 Ma) and show a weak inverse correlation with elevation (Figure 4). Apatite fission track ages determined on the same samples [Shoemaker et al., 2002] are in all cases older than the apatite (U-Th)/He ages; the difference between ages recorded by the two thermochronometers ranges between 3 and 24 Ma. The fission track ages do not correlate with elevation or distance from the coast; most of the fission track ages were locked in during the time of arc magmatism in the area and reflect transient effects due to igneous cooling and not cooling related to exhumation [Shoemaker et al., 2002].
3.2. Puerto Escondido Transect
 The Puerto Escondido transect samples are undeformed calc-alkaline plutons, as well as gneissic tonalites and granodiorites containing biotite, hornblende, and in one instance pyroxene, ranging from 10 to 1954 m in elevation and 0–48 km inland from the Pacific coast. Eleven samples analyzed for (U-Th)/He data display a ∼7 m.y. age span (17.7 Ma to 10.4 Ma) and again show a weak inverse correlation with elevation (Figure 4). Apatite fission track ages determined on the same samples [Shoemaker et al., 2002] are either indistinguishable with error from (U-Th)/He ages (samples M01-27 and M01-28) or older than (U-Th)/He by as much as 25 m.y.
 Overall, ages from both transects range from 8.4 to 25 Ma, indicating a relatively slow time-averaged rate of cooling and, we infer, exhumation (0.1–0.3 km/m.y.) for the Sierra Madre del Sur since the early Miocene.
4. Exhumation Rates From (U-Th)/He Ages
 Low-temperature thermochronology is commonly used to help determine exhumation rates for crustal blocks, either by collecting samples along a “vertical” transect [e.g., House et al., 1998; Ducea et al., 2003], or by using (U-Th)/He data in conjunction with a higher temperature chronometer, e.g., apatite fission track [e.g., Stockli et al., 2000; House et al., 2002; Reiners et al., 2003]. Because the regional topography in the Sierra Madre del Sur does not permit simple vertical transects of sufficient relief and fission track ages overlap with intrusion ages in Sierra Madre del Sur [Shoemaker et al., 2002], we used a modified version of the Brandon et al.  algorithm to calculate exhumation rates from horizontal transects. In these calculations, we assume that cooling of the analyzed rocks below their closure temperature for apatite (U-Th)/He is entirely related to unroofing. This assumption is justified given the lack of Miocene or younger plutons in the region. Below, we briefly summarize the Brandon algorithm and its assumptions for the case of (U-Th)/He thermochronology. We assume a linear temperature profile through the shallow crust prior to the onset of exhumation:
We use a surface temperature Ts of 10°C and a thermal gradient g0 = 25°C/km, which is a reasonable gradient for this tectonic environment. Since the shallow isotherms will tend to follow the longest wavelength topography, the parameter z′ is the effective closure depth [Brandon et al., 1998], which is measured relative to the mean local elevation h′ of the landscape. We determined h′ for every sample location by filtering digital elevation data to remove wavelengths less than 30 km. The difference (Δ) between actual and filtered (averaged) elevations in our data set is −200 to 350 m.
 Onset of exhumation perturbs the initial thermal profile. The steady state exhumation profile for a one-dimensional layer of thickness L is a function of exhumation rate ɛ [Stuwe et al., 1994]:
where κ is thermal diffusivity. We use κ = 20 km2/m.y. and a layer thickness equal to crustal thickness beneath the Sierra Madre del Sur (L = 20 km). The solution to equation (2) is not particularly sensitive to κ or L [Brandon et al., 1998].
 The closure temperature (Tc) for the apatite (U-Th)/He thermochronometer is a function of the rate of cooling (), as expressed in the classic equation of Dodson :
where E is the activation energy, and D0 the pre-exponential factor for He diffusion [Farley, 2000] (see also footnote of Table 3), R is the gas constant, A is a geometric parameter, and a is the characteristic diffusion domain size, assumed here to be the radius or mass-weighted radius of analyzed apatites [e.g., Farley, 2000]. The actual cooling rate at closure is a function of exhumation rate and the vertical temperature gradient:
The closure depth zc relative to the true elevation can be calculated using equation (2):
Finally, zc is related to the He age (t) by a constant exhumation rate:
Table 3. Parameters Used in Model Calculations and Exhumation Rates Based on (U-Th)/He Chronometry
Δ, a, and Tc are calculated using the method described in text.
Tc is closure temperature. The relevant diffusion parameters used here are E0 = 33 kcal/mol and D0 = 50 cm2/s [Farley, 2000].
 We solved these equations for two unknowns, ɛ and Tc. Numerical solutions for exhumation rates and closure temperatures were obtained using Mathcad® and are given in Table 3. The closure temperatures for the analyzed apatite grains are between 64 and 71°C, very close to the average “nominal” closure temperature of the system [Farley, 2000]. The calculate exhumation rates are between 0.1 and 0.33 km/m.y., with an average of 0.22 km/my for the Puerto Escondido transect and 0.18 km/m.y. for the Acapulco transect.
 Significantly, the calculated exhumation rates inversely correlate with elevation and with distance from the range axis (Figure 5). Higher exhumation rates in the range core than on the flanks has also been observed in both topographically steady state and decaying mountain ranges [e.g., Brandon et al., 1998; Reiners et al., 2003]. Alternatively, such correlations could be due to a recent decrease in the relief of a mountain range [Braun, 2002], but that can be ruled out for the Sierra Madre del Sur on the basis of geomorphologic evidence [Werre-Keeman and Rodarte, 1999]. These results also suggest that large-scale topographic form of the range was broadly similar to the modern one at the time of (U-Th)/He closure. The relatively slow exhumation rates are also consistent with erosional and not tectonic processes being the cause of unroofing. Typical exhumation rates for regions undergoing major extensional faulting are about 1 order of magnitude higher than reported here [e.g., Stockli et al., 2000, 2001; Reiners et al., 2000]. On the basis of the rates calculated here and the lack of geologic evidence for large-scale normal faults, we interpret that Miocene exhumation rates locked in by the (U-Th)/He chronometer are due to erosion (i.e., exhumation rates are ∼equal to erosion rates). Since all analyzed sample are from the south-facing slope of the Sierra Madre del Sur, the erosion rates calculated here have to equal the terrigenous sedimentation rate in the Acapulco trench during the Miocene. There is no geologic evidence for coast parallel transport during the Miocene [Morán-Zenteno et al., 1996]. The average Miocene exhumation rate constrained by our data is about 0.2 km/m.y., with a range of 0.1 to 0.3 km/m.y.
5. Regional Tectonic Implications
 These ages and calculated exhumation rates have several implications for the regional geology of southern Pacific Mexico. First, the slow exhumation rates for the Neogene is in contrast with calculated emplacement depths of 13–20 km for late Eocene (27–35 Ma) plutons within the Sierra Madre del Sur along the Acapulco and Puerto Escondido transects [Morán-Zenteno et al., 1996]. These emplacement depths are calculated with the Al-in-hornblende igneous barometer. Our data constrain that most of the exhumation of these plutonic rocks of the coastal Xolapa complex must have taken place before the Miocene when (U-Th)/He thermochronometry records slow cooling and exhumation rates (some 3 km since 20 Ma). Hence there is a limited temporal window for high exhumation rates. For instance, in the Acapulco section this window can be placed between the late Eocene (34 Ma) emplacement age of the youngest plutons [Morán-Zenteno et al., 1999; Ducea et al., 2004] and the early Miocene (as early as 25 Ma) time since apparently slow time-averaged exhumation inferred from the (U-Th)/He ages. In the Puerto Escondido section the documented window would be between 27 and 18 Ma. Could some 9–16 km of the Xolapa Complex have been eroded within a very short period of time (∼9 m.y.)? If so, such a high unroofing event had to take place in the very early stage of margin truncation, inland migration of arc magmatism, and subduction erosion. There is no evidence anywhere along the Pacific margin of southern Mexico for high rate of accumulation (∼1–2 km/m.y.) of trench sediments derived from the new forearc at the end of Oligocene – if such deposits existed, they were recycled by subduction erosion. There is some evidence for major truncation via subduction erosion during the early Miocene, on the basis of the rapid subsidence of the shelf between 24–17 Ma [Watkins, 1989]. It is noteworthy that these predicted forearc fast exhumation rates for the latest Oligocene just predate the inferred start of a major subduction erosion episode derived from subsidence studies of the submarine forearc [Clift and Vannucchi, 2004]. It is possible that the two processes are linked in that the crust removed from the outer forearc may have been underplated under the continental forearc, driving exhumation.
 A second implication of our results is that the Sierra Madre del Sur range has been a mountainous landscape since at least the late Oligocene, when it was in an arc position. In fact, the distribution of ages and exhumation rates across the flank of the mountain range suggest that this is a steadily decaying range (see Reiners et al.  for an analogous example), a former arc section that is slowly being eroded away in a forearc position. This is an example in which (U-Th)/He chronometry can put constraints on the antiquity of a mountain range.
 The third implication is that the modest exhumation rates determined from (U-Th)/He data are consistent with the lack of major extensional structures in this forearc. As magmatism migrated inland, the new forearc has been dynamically stable, experiencing constant exhumation rates throughout much of the Miocene and possibly continuing into the Pliocene and Quaternary. Similar cases have been described from the modern and ancient forearcs of western North America [e.g., Ring and Brandon, 1994; Brandon et al., 1998]. With a sudden decrease in angle of subduction, inland migration of magmatism and the onset of subduction erosion, some forearcs collapse extensionally. One classic example is the southwestern North American margin at the onset of Laramide orogeny [Coney and Reynolds, 1977]. In that case, the upper plate underwent a major extensional episode at the onset of shallow subduction, leading to exposing North American midcrustal to deep crustal rocks and even windows into the metamorphosed equivalent of the subducted trench greywacke, the Rand, Pelona, Orocopia and Sierra de Salinas schists [Jacobson et al., 1996]. It has been postulated that the extension in that case was triggered by subduction of seamounts and/or a ridge [Saleeby, 2003]. A similar case of a collapsing forearc during shallow subduction is exposed in the Osa Peninsula of Costa Rica [Meschede et al., 1999; Vannucchi et al., 2003]; in that case the tectonic uplift of the upper plate which comprises a Miocene arc in the Cordillera Talamanca was caused by the indentation of the Cocos Ridge in the subduction channel during the Pliocene. In contrast, the lack of major extensional features in the Sierra Madre del Sur is consistent with the relatively smooth topography of the subducting Cocos plate [Pardo and Suárez, 1995]. The youth and buoyancy of the Cocos plate is probably the cause of shallow subduction beneath southern Mexico.
6. Quantifying Sediment Recycling
 The relatively slow Sierra Madre del Sur exhumation rates measured for the time interval 25–8 Ma by (U-Th)/He chronology, are about an order of magnitude faster than preservation rates in the trench for the same time period (Figures 3 and 5). This indicates that at least 90% of the sedimentary wedge in the Acapulco trench has been recycled either by sediment subduction directly into the mantle or transferred to the North American lower crust by underplating. The steady denudation rates in the Sierra Madre del Sur and sediment preservation rates in the adjacent trench indicate that the trench-forearc system was in steady state for most of the Miocene and perhaps continuing to present day. One mechanism that could explain the steady state of this system is that much of the terrigenous sediment that is being eroded from the trench does not return to the mantle by subduction but gets underplated to the lower crust beneath the Sierra Madre del Sur forearc. Testing this hypothesis and overall attempting to resolve the proportion of sediment that was subducted versus sediment that was underplated, will require high-resolution seismic imaging of the deeper crust and upper mantle beneath the Sierra Madre del Sur.
 The history of growth of this accretionary wedge can also be quantitatively modeled using the methods of DeCelles and DeCelles , in which the key input parameters are as follows: velocity of subduction = 5.2 cm/yr [Pardo and Suárez, 1995]; taper of the accretionary wedge = 8° to 10° [Moore and Watkins, 1982]; average thickness of sediment in the trench = 190 m [Watkins et al., 1982]; zero erosional loss of material from the subaqueous portion of the wedge; and zero change in taper through time (i.e., self-similar growth). If the wedge has been growing since 25 Ma, its expected width would be ∼53–61 km if all of the material entering the trench were accreted into the wedge (Figure 6). The actual width of the wedge in the Acapulco region is only ∼30 km, and may be less on average along the southern Mexico subduction zone [Watkins, 1989], which suggests that only ∼15% or less of the sediment entering the trench is actually being preserved within the wedge (Figure 6); conversely, >85% of the material must be subducted. This analysis ignores possible temporal changes in wedge taper, subduction rate, and sediment flux rates, which are difficult to document. Nevertheless, the closeness of this independent estimate to the estimate on the basis of thermochronology is striking, and supports the general contention that the volume of subducted material exceeds the preserved material by approximately 1 order of magnitude.
7. Global Implications for Sediment Recycling
 The approach presented here, determining the long-term erosion rates of subaerial forearcs and comparing them against the apparent sedimentation rates in adjacent trenches can provide new insights into quantifying long-term subduction erosion, specifically the terrigenous input to subduction erosion.
 In the case of the Acapulco trench, we can estimate that the one-dimensional rate of subduction erosion of terrigenous material was at least about 0.18 km/m.y. for much of the Miocene. The ratio of terrigenous/pelagic sedimentary input to the trench is about 10/1, so if a ∼0.02 km/m.y. is added as a pelagic contribution, the rate would be 0.2 km/m.y. The width of the accretionary wedge is about 30–35 km or less, which would imply that the Miocene subducted flux per unit length of the margin is at least about 30 km3/(km m.y.), which is similar to the 40 km3/(km m.y.) global average rate of subduction erosion [von Huene and Scholl, 1991], and about a third of the short-term erosion rates (107–125 km3/(km m.y.)) measured off the Pacific margin of Costa Rica [Vannucchi et al., 2003]. Integrated over the length of the Acapulco trench (1450 km), this yields a subducted solid fraction of 44 × 103 km3/m.y., which comparable to the 35 × 103 km3/m.y. estimation by von Huene and Scholl  for the same trench.
 The bulk of the recycled sediment is derived directly from continental denudation of the Xolapa Complex, a midcrustal exposure of a continental arc. The calculated average chemical composition of the Acapulco trench resembles that of an andesite [Plank and Langmuir, 1998], which is the average of the Xolapa Complex [Martiny et al., 2000]. If the bulk of this material is underplated to the overriding plate, it will be chemically indistinguishable from the rest of the Xolapa crust.
 This research was partly supported by a faculty research grant from the University of Arizona to Mihai Ducea. The University of Arizona Geo-Structure Program, and a student grant from Chevron to Sarah Shoemaker supported fieldwork. Stefan Nicolescu is acknowledged for running the (U-Th)/He analyses at Yale and Washington State University. We are also indebted to Rebekah Wright for assistance in sample preparation. Journal reviews by Ronald Von Huene, an anonymous reviewer and associate editor Victoria Bennett have significantly improved the quality of the manuscript.