An independent test of thermal subsidence and asthenosphere flow beneath the Argentine Basin

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Earth and Planetary Science Letters 161 (1998) 73–83

An independent test of thermal subsidence and asthenosphere flow beneath the Argentine Basin Warren L. Hohertz Ł , Richard L. Carlson Department of Geology & Geophysics, Texas A&M University, College Station, TX 77843-3115, USA Received 27 October 1997; revised version received 20 April 1998; accepted 6 May 1998

Abstract We have used primary precision depth recorder and single channel seismic data from three cruises of the R=V Conrad to test thermal subsidence and asthenosphere flow models for seafloor depth versus age in the Argentine Basin in the western South Atlantic. We found a region in the west central part of the basin where anomalously shallow depths, that can not be explained by any simple thermal or dynamic model, are associated with a local free-air gravity anomaly. Elsewhere, over ages ranging from 1 to 104 Ma, there is no evidence of the “flattening” of the depth=age trend that is characteristic of the plate cooling model for the thermal subsidence of the oceanic lithosphere. The halfspace thermal subsidence model accounts for nearly 98% of the variance of seafloor depth, but the slope, b D 425 š 10 m Ma 1=2 , implies improbably high mantle temperatures and=or low mantle densities. Moreover, there is some systematic misfit between the data and the halfspace model. A thermal subsidence model in which initial conditions vary with age accounts for the misfit, but also requires an implausible variation of mantle temperature and=or density. Alternatively, a model that includes the effect of induced flow in the asthenosphere eliminates the misfit and yields a reasonable rate of thermal subsidence b D 330 š 20 m Ma 1=2 . That the mantle temperature .Tm ¾ 1150 š 70/ºC implied by the subsidence rate is slightly lower than normal is consistent with the hypothesis that this region has not been affected by hot spots or mantle plumes. The viscosity of the asthenosphere derived from the model (3–4 ð 1019 Pa s) is high, but consistent with viscosities estimated from plate dynamics models when the low mantle temperature is taken into account. Finally, the PMS flow model is consistent with measured heat flow in the region. These results lend weight to the hypothesis that the bathymetry of the Argentine Basin is influenced by induced flow in the asthenosphere, as well as by halfspace cooling of the upper mantle.  1998 Elsevier Science B.V. All rights reserved. Keywords: Argentine Basin; bathymetry; subsidence; mantle heat flow; geodynamics

1. Introduction The long-wavelength bathymetry of ocean basins reflects fundamental thermal and dynamic processes Ł Corresponding

author. Present address: ARCO International Oil and Gas Company, 2300 West Plano Parkway PAl H2204, Plano, TX 75075, USA.

affecting the upper mantle of the Earth. In many regions, subsidence of the seafloor in proportion to the square root of the age of the lithosphere is explained by a cooling halfspace thermal contraction model [1,2]. In the western North Atlantic, North Pacific and Indian Oceans, however, the observed depth=age trends “flatten” relative to the root-t line after about 80 Ma [3–6]. The “plate” cooling model,

0012-821X/98/$19.00  1998 Elsevier Science B.V. All rights reserved. PII S 0 0 1 2 - 8 2 1 X ( 9 8 ) 0 0 1 3 8 - 1

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which requires the addition of heat to the base of the plate, was proposed to explain this departure from the halfspace model [4], but has been challenged for a number of reasons [2,8,9]. Moreover, geoid anomalies and depth=age trends suggest that some ocean basins are affected by flow in the asthenosphere, as well as by the thermal=isostatic effects of cooling [10]. The causes of large-scale bathymetric patterns and their significance are not yet fully understood. A long-standing hypothesis to explain the observed flattening of depth=age relations is thermal rejuvenation of the lithosphere by hot spots or mantle plumes [11]. Heestand and Crough [12] found that in the North Atlantic flattening of the depth-versus-age trend is not observed when proximity to hot spots or hot spot tracks is taken into account. Based on this result, they predicted that flattening would not be observed in regions far from the nearest hot spot track, and they went on to suggest that the Argentine Basin in the western South Atlantic is a suitable place to test this hypothesis. Subsequently, Phipps-Morgan and Smith [10] proposed that the anomalous depth of the Argentine Basin, even relative to the halfspace model, can be explained by flow in the asthenosphere induced by the rapid westward movement of the South American plate. The relationship between depth and age in corridors across the Argentine Basin has been studied by a number of investigators [2,10,13,14]. A feature common to these studies is that none of the depth=age data sets shows evidence of the flattening relative to the halfspace cooling model that is characteristic of plate cooling, even where the age of the crust is significantly older than 100 Ma; the best fitting halfspace model parameters are summarized in Table 1. There are also important differences between Table 1 Summary of halfspace model parameters from previous studies Location Age (Ma)

dr (m)

b S R2 (m Ma-1=2 ) (m)

Source

38–47ºS 35–45ºS 40-48ºS 40-48ºS

2544 š 96 2300 2602 š 10 2285 š 56

368 š 11 380 271 š 5 367 š 8

[2] [13] [14] [10] a

a Fit

0–111 0–145 0-65 0-92

– – – 72

made for this study using data from [10].

0.90 0.83 0.81 0.99

these studies. Marty and Cazenave [2] and Hayes [13] used data from as far north as 35ºS, where the thermal history of the seafloor is likely to have been affected by the Tristan de Cun˜a–Rio Grande Rise hot spot track. Moreover, both of these studies are based on the ETOPO5 (DBDB5) gridded bathymetry data base. In reality, ETOPO5 is not a dataset, but a digital bathymetry model or representation that has been shown to contain artifacts that may render it ill-suited for depth=age studies [15]. Phipps-Morgan and Smith [10] and Kane and Hayes [14] studied the corridor between the Gough and Agulhas Fracture Zones, and both used bathymetry data from ship tracks as opposed to ETOPO5, but there is a significant inconsistency between their results. Our fit to the Phipps-Morgan and Smith data (Table 1) yields parameters that are in good agreement with the results reported by Marty and Cazenave [2] and Hayes [13] for slightly different regions, but the parameters reported by Kane and Hayes [14] for the same region are markedly different. Phipps-Morgan and Smith [10] made a qualitative fit of their flow model to depth=age data from the Argentine Basin, but did not test the model by formal inverse methods. Stein and Stein [16] have tested both the PMS and GDH1 plate models using depth and heat flow data from several regions including the western South Atlantic (for which they used the corrected seafloor depths from Hayes [13]). They concluded that thermal models explain the data better than the flow models, but their analysis does not constitute a valid test of either the Heestand and Crough hypothesis or the PMS flow model for several reasons. One is that they assume that the plate cooling and flow models are mutually exclusive alternative hypotheses to explain the observed flattening of age=depth trends relative to the halfspace model. They therefore included regions such as the North Pacific and western North Atlantic that have clearly been affected by hot spots or other thermal effects in their analysis. Within this framework, their conclusions are justified by the data, but this treatment of the problem neglects the possibility that the influence of flow is masked in those regions by the larger effects of thermal processes. Similarly, their data for the western South Atlantic include all of the ocean floor west of the Mid-Atlantic Ridge and south of the equator and thus includes lithosphere in

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the northern part of the region that has clearly been affected by hot spots. The inclusion of lithosphere that has been affected by hot spots may mask the effects of flow in the asthenosphere, and specifically precludes a useful test of the Heestand and Crough hypothesis. In this study, we seek to determine what factors affect the seafloor in a region that has not been affected by mantle plumes. For that purpose, we have made an independent evaluation of the relationship between depth and age in the Argentine Basin using primary depth and sediment thickness data from several cruises. We find no evidence of plate-like flattening in the depth=age data, but we do find that the data are better explained by models that include either age-dependent initial conditions or the effects of both halfspace cooling and asthenosphere flow.

2. Data To test the thermal subsidence and flow models we used precision depth recorder (PDR) and single channel seismic (SCS) data from three cruises of the R=V Conrad: C1213, C1214 and C1504 (Fig. 1). Because the northern parts of C1213 pass over seafloor that may have been affected by the Tristan de Cun˜a–

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Rio Grande Rise hot spot track, we included only the southernmost part of the ship track, from 27-Ma isochron to the margin of the continent, in the data set. The portion of the Argentine Basin covered by this study thus lies between about 42 and 48ºS, within region 15 of the Marty and Cazenave study [2] and the Gough–Agulhas corridor [10,14]. Depths to the seafloor were picked from the PDR records and corrected for the velocity of sound in the water column using echo sounding correction tables [17]. The seismic records were used to estimate the two-way traveltime from the seafloor to the basement surface. Where it can be recognized in the seismic records, basement was identified by its characteristically rough or hyperbolic appearance. Areas affected by obvious buried seamounts were not included, and data were taken only from those portions of the tracklines where both seafloor depth and sediment thickness were available. A 100-km along-track running-average filter was applied to the PDR and SCS data to remove the effects of short-wavelength, uncompensated topography [18]. The number of data points in each 100-km interval is variable, ranging from 55 š 10 for line C1214, to 60 š 10 for line C1213 and 80 š 18 for line C1504; the sample interval within each window is 1–2 km.

Fig. 1. Location map showing the track lines of R=V Conrad cruises C1213, C1214 and C1504 in the western South Atlantic. Free-air gravity from Sandwell and Smith [24] is shown in gray-scale; lighter shades represent higher free-air gravity values. Also shown are 10-Ma isochrons from Mu¨ller et al. [19].

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Seafloor age was taken from the global model of Mu¨ller et al. [19]. For the South Atlantic, this model is based on a detailed reconstruction of the opening of the South Atlantic beginning at about 130 Ma [20], and on the geomagnetic reversal time scales of Gradstein et al. [21] and Cande and Kent [22] for the Mesozoic and Cenozoic reversal sequences, respectively. Mu¨ller et al. estimate the errors in age to be <1%, except for crust in the Cretaceous Quiet Zone (¾84 to 120 Ma), where the error is about 5%. Ages were assigned prior to filtering, and averaged along with the depths and sediment thicknesses, so that the data set consists of depths and ages averaged over 100-km segments of the three ship tracks. Two-way traveltimes through the sediment cover were used to correct the seafloor depths for the sediment load, 603 š 12 m s 1 two-way traveltime [23]. Because of the large sediment drift that occupies the center of the Argentine Basin, the correction for the sediment load increases dramatically for seafloor older than about 65 Ma (Fig. 2), and reaches nearly 1200 m before it decreases over the western flank of the sediment pile. Though some of the corrections are large, the errors in the load correction are comparatively small, generally less than 40 m (Fig. 2 inset). The 82 average depth=age pairs are shown in Fig. 2. Depths increase systematically with age to about 90 Ma. There, the depths shoal abruptly by about 500 m, then increase again beyond about 110 Ma. Of 24 depths with ages greater than about 90 Ma, only three, from the southwestern corner of the basin on line C1214, lie on the trend defined by the data from younger seafloor. Significantly, this pattern of anomalous depths does not correspond to the sediment pile beneath the Zapiola Ridge. The thickness of the sediment pile begins to increase at about 65 Ma, while the corrected depths begin to shoal at the crest of the drift, near 90 Ma (Fig. 2). Shoaling of the basement surface begins beneath the crest of the sediment drift. All three lines cross buried seamounts in the age interval between 110 and 120 Ma, suggesting an anomaly in the basement structure, and there is a direct correlation between the pattern of free-air gravity in the region [24] (Fig. 1) and the anomalous depths shown in Fig. 2. Depths shoal abruptly where the lines cross into a region of higher gravity values near the center of the

basin — at 90 Ma on line C1213, and at 92 Ma on line C1504. On line C1214 basement shoals at 89 Ma, where the line crosses an E–W trending branch of the gravity anomaly, but the three “normal” depths from the oldest part of the Argentine Basin are also from line C1214, where it crosses the deep basin to the south of the gravity high (Fig. 1). The cause of the anomalous depths and the associated gravity anomaly is not known, but the correlation is clear. It is interesting to note that similarly shallow depths occur in the same age interval in the region to the north of our study area [2], and in data from the western North Atlantic and North Pacific [5]. In any case, neither of the cooling models nor the flow model under consideration in this study can account for the abrupt shoaling indicated by these data, and they were therefore excluded from our analysis.

3. Theoretical models Shown with the data in Fig. 2 are the PSM and GDH1 plate models [3,5]. The data show a strong linear trend of increasing depth with increasing root-t, with no evidence of the gradual flattening of depths relative to the root-t line that is characteristic of the plate cooling model. Quite to the contrary, the data show slight downward curvature, suggesting that the bathymetry of this region is influenced by more than simple halfspace cooling. For that reason we considered three models to explain the depth=age relation in the southernmost Argentine Basin. The halfspace cooling model [1] assumes that the oceanic lithosphere cools from an initial temperature Tm . The seafloor subsides as the dense boundary layer thickens in proportion to the square root of age: p d.t/ D dr C b t

(1)

where t is the age of the lithosphere in millions of years, dr is the depth of the seafloor at the mid-ocean ridge, and is b the subsidence rate: b D 2²m ÞTm

.=π/1=2 .²m ²w /

Here, ²m is the density of the mantle (at temperature Tm ), ²w is the density of sea water, Þ is the

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p p Fig. p 2. (Top) Sediment load correction versus age. (Bottom) Depth versus age in the Argentine Basin and the best fit of the halfspace ( t) thermal subsidence model to the data. Included for comparison are the plate cooling models from Parsons and Sclater (PSM) [3] and Stein and Stein (GDH1) [5]. The inset shows the distribution of estimated errors in the correction for sediment load.

volume thermal expansion coefficient and  is the thermal diffusivity. In the halfspace model, the thermal boundary layer thickens without limit and Eq. 1 applies to all ages. The plate model differs from the halfspace model in that the thermal boundary layer forms in a layer or “plate” of finite thickness over an isothermal halfspace, so that the thickness of the cooling boundary layer is limited to the thickness of the plate. In its early stages, the thermal evolution of the plate is the same as that of the halfspace and subsidence in both cases is proportional to the square root of age. As age increases, however, the base of the boundary layer approaches the base of the plate, and plate

subsidence flattens relative to the root-t curve as the depth of the seafloor asymptotically approaches a constant. In contrast to the flattening predicted by the plate cooling model, we observe a slight steepening of the gradient (Fig. 2). One way to explain this observation is to postulate an age-dependent variation of the initial temperature Tm and=or density ²m . Variations of these parameters both along and across the Mid-Atlantic Ridge have been proposed to explain regional bathymetric trends [2,13,14,16]. In an ad hoc way, we can introduce age-dependent initial conditions by making thepslope b of the phalfspace model a linear function of t, b D b0 C b1 t. Depth

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is then a quadratic function of p d.t/ D dr C b0 t C b1 t

p

t:

4. Testing the models (2)

A potentially significant limitation of all thermal models is that they are strictly isostatic, and necessarily fail if depths are affected by flow in the asthenosphere. Phipps-Morgan and Smith [10] have proposed that the flattening of the depth=age trend in the Pacific, the asymmetry of the South Atlantic, and the anomalously great depth of the Argentine Basin may be caused by asthenospheric flow. Beneath the western South Atlantic, they suggest, the asthenosphere is underlain by the more stable mesosphere at a depth of about 200 km beneath the ridge. The asthenosphere channel thins as the thickness of the lithosphere increases (by halfspace cooling) away from the ridge. Moreover, this channel is cut off on the west by the thick South American continental lithosphere. Thus, as the South America Plate moves vigorously westward relative to the mesosphere, mantle material consumed by the growth of the lithosphere and the westward extension of the asthenosphere channel must be supplied by an influx of new mantle material from near the ridge. Using lubrication theory, Phipps-Morgan and Smith have shown how flow of this kind might affect the subsidence of the Argentine Basin. In effect, the model suggests that the excess depth of the basin is caused by a pressure deficiency (relative to a state of isostatic equilibrium) beneath the western South Atlantic. A model that combines the effects of halfspace cooling and asthenosphere flow is given by: p (3) d.t/ D dr C b t C To ln Þ.t/ C Þ 1 .t/ 1] p where dr C b t describes the subsidence due to halfspace cooling and S is a constant that p det. scribes the thickening of the lithosphere S p Þ.t/ D .h o S t/= h o is the age-dependent fractional thickness of the asthenosphere channel relative to its initial thickness at the ridge h o . To is the dynamic topography magnitude as defined by Phipps-Morgan and Smith [10]; i.e., To is the sensitivity of the topography to flow in the asthenosphere channel Þ.t/, and is proportional to the viscosity of the asthenosphere and the absolute motion of the plate.

Fitting the halfspace and quadratic models (Eqs. 1 and 2) to the data is a straight forward linear leastsquares procedure. The halfspace-plus-flow model (Eq. 3) is a nonlinear, four-parameter model (dr , b, To and the ratio S= h o ). We fit this model to the data by nonlinear inverse methods, but found that we could not constrain all four parameters. We then took the alternative course of assuming a value for S= h o of 0.0498 [10], in which case Þ.t/ is known, and Eq. 3 is linear in the three parameters dr , b and To . To test the three depth=age models, we made leastsquares fits of each to the full data set (excluding the anomalous depths) shown in Fig. 2, and to two subsets of the data as described below. The results are summarized in Table 2 and Figs. 2 and 3. A potential problem is presented by the fact that the greatest age in our data set is 104 Ma. That age is roughly in the middle of the Cretaceous Normal Super Chron. Ages in the “tail” of our data set (>84 Ma) are thus interpolated, and not directly constrained magnetic lineations. To guard against potential spurious results, we made fits to both the full data set, and to depths with ages less than 84 Ma, where ages are constrained by the Cenozoic reversal sequence. An added benefit of this procedure is that we also test the models using data from seafloor younger than the interval where the shoaling of depths cited above occurs. As indicated in Table 2, these fits yield statistically identical results in each case. In his review Russo noted that there are four data points in the age interval 35–50 Ma that lie above the best-fitting model curves (Figs. 2 and 3). He correctly pointed out that these points might be crucial to our analysis. To test this possibility, we have made an additional fit of each model to data from the age interval 0–84 Ma with those four points deleted. The results are not statistically distinguishable from the other fits (Table 2), and actually show significant improvements in the fits of all three models. All three models fit our data from the southern Argentine Basin very well. In each case, F-tests for statistical significance show that the addition of a third parameter in the quadratic and flow models (Eqs. 2 and 3) is justified by the data.

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Table 2 Summary of statistical parameters Model

Age (Ma)

dr (m)

b=b0 (m Ma-1/2 )

Halfspace model

0–84 0–84 a 0–104

2349 š 64 2361 š 62 2313 š 60

423 š 10 426 š 8 430 š 9

Quadratic fit

0–84 0–84 a 0–104

2791 š 105 2712 š 86 2749 š 95

229 š 40 270 š 33 251 š 34

Halfspace C flow model

0–84 0–84 a 0–104

2683 š 87 2616 š 73 2620 š 80

305 š 21 334 š 22 331 š 21

a Fit

To =b1 (m)

N

S (m)

R2

55 51 61

160 129 157

0.971 0.982 0.976

18 š 4 14 š 3 15 š 3

55 51 61

133 107 130

0.980 0.988 0.984

3998 š 821 3048 š 688 2953 š 592

55 51 61

134 110 133

0.980 0.988 0.983

– – –

with four potentially anomalous points deleted from the data set. See text.

Fig. 3. Depths versus model.

p

age in the Argentine Basin with the best fit to the halfspace model and the fit to the PMS halfspace-plus-flow

5. Discussion The halfspace model fits the data remarkably well, accounting for more than 97% of the variance in the corrected depth to basement in the Argentine Basin (Table 2, Fig. 2). There are, however, two problems with this model. One is the very high subsidence rate (¾430 m Ma 1=2 ). Similarly high rates

observed elsewhere have proven to be difficult to explain [14,22]. In this case, the apparent rate of subsidence is higher than the “normal” rates for the western North Atlantic and North Pacific of about 350 m Ma 1=2 [3,9], and somewhat higher (at the 95% confidence level) than the rates of subsidence obtained from other studies of this region (Table 1). In terms of the model, a subsidence rate of this mag-

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nitude can be explained by an increase in the product ÞTm .=π/1=2 , and=or by a decrease of mantle density ²m . For example, neglecting the potential temperature dependence of Þ and , a 15% increase in Tm combined with a 15% decrease in ²m would account for the high apparent rate of subsidence in the Argentine Basin, but that would imply Tm ¾ 1410ºC and ²m ¾ 2800 kg m 3 , neither of which seems likely. Another problem with the fit to the halfspace model (Fig. 2) is that there is a small degree of systematic misfit between the model and the data; the best-fitting halfspace model (Fig. 2) underestimates depths for ages less than about 16 Ma and more than about 64 Ma, while it overestimates depths to the seafloor in the age range between 16 and 64 Ma. This systematic misfit suggests that an additional degree of freedom (another parameter) might be required to explain the data. As noted above, one way to add degrees of freedom to the model is to allow the properties of the mantle Þ, , ²m and=or the initial temperature Tm to vary with age. The quadratic model (Eq. 2), in which the initial conditions are assumed to vary with age also fits the data very well, accounting for more than 98% of the variance of corrected seafloor depths. However, the thermal subsidence rate varies from near 250 to about 550 m Ma 1=2 , a range of values that requires an implausibly large variation of mantle density or temperature. Further, the model is entirely ad hoc; there is no independent evidence for such a large variation of either mantle density or temperature in the region. Finally, Kane and Hayes [14] and Stein and Stein [16] have both proposed a systematic difference of mantle temperature to explain the asymmetry of the South Atlantic, but this model suggests an age-dependent variation of initial conditions at the ridge over the last 100 Ma. The quadratic model would therefore seem to be inconsistent with the observed asymmetry of the South Atlantic [10,14]. An alternative to the purely thermal models is one that includes flow in the asthenosphere, as proposed by Phipps-Morgan and Smith [10]. The excellent fit of the combined halfspace and flow models (Eq. 3, Table 2) to the data is shown, with the fit to the halfspace model in Fig. 3. F tests indicates that the addition of the third parameter is justified by the

improvement in the standard error of the estimate in each case. The systematic misfit is eliminated, and the thermal subsidence rate b is near 330 š 20 m Ma 1=2 , a value that is in better agreement with average subsidence rates [2,9]. Moreover, though it is not very well resolved by this data set, the best-fitting dynamic topography magnitude To ¾ 3000 š 600 m, agrees well with the value of 3300 m estimated by Phipps-Morgan and Smith [10]. The PMS halfspace-plus-flow model fits out data very well, but in view of the previous challenge to the validity of the PMS flow model by Stein and Stein [16], it is particularly important to test our results as rigorously as possible. One problem for this model is that the depth=age trend of our data differs from those of other studies of this region, as evidenced by the difference in the best-fitting halfspace model parameters (Tables 1 and 2). One possibility is that our data set is spurious — somehow not representative of the region. That seems unlikely in light of the fact that the ship tracks we have used are fairly well separated, and the flow model fits all three subsets of the data (Table 2, Fig. 3). Moreover, the results we obtained by analyzing the data from lines C1214 and C1504 taken separately are not statistically distinguishable from the fits made to the data set as a whole. Line C1213 does not span a large enough range of age to be treated separately, but it is clear that the data from that line are compatible with the data from the other two lines. Hence our data show a consistent pattern across a corridor several hundred kilometers wide (Fig. 1). An alternative explanation is that where other studies [2,10,13,14] have used all of the bathymetry data from the region, we have made a line-by-line evaluation and eliminated depths that are associated with the local free-air gravity high, thereby avoiding a potential bias toward shallow depths that may affect other data sets. Of course we prefer the latter explanation. Two lines of evidence that tend to support the PMS flow model are that the mantle temperature is slightly lower than “normal” and the viscosity of the asthenosphere that we estimate from To is consistent with the mantle temperature and the rheological properties of olivine. Given a typical set of constants (Þ D 3:5 ð 10 5 ,  D 8 ð 10 7 m2 s 1 , ²m D 3300 kg m 3 , ²w D 1000 kg m 3 ), Tm ¾ 3:5b. Tm for plate models is near 1350ºC, while the subsidence

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rate for typical halfspace models is commonly 350 m Ma 1=2 , with Tm ¾ 1225ºC. Our thermal subsidence rate of ¾ 330 š 20 m Ma 1=2 corresponds to Tm ¾ 1150 š 70ºC. While this value is not statistically distinguishable from 1225ºC, it is lower, as we might expect for a region that has not been thermally rejuvenated by mantle plumes. The viscosity of the asthenosphere can be estimated from the dynamic topography magnitude To [10]. Using the South American plate parameters given by Phipps-Morgan and Smith [10] (Ua D 30 mm=y, Ur D 20 mm=y) our best-fitting values of To (Table 2) yield viscosities in the range 3 4 ð 1019 Pa s. This range of viscosities is slightly higher than the estimated viscosity of the asthenosphere beneath ocean basins based on plate dynamic models of 5 ð 1017 and 5 ð 1018 Pa s [25,26], presumably at temperatures of 1225 to 1350ºC. Adjusting our estimated viscosity of 4 ð 1019 Pa s at 1150ºC for the effect of temperature using a dry olivine flow law [27], we estimate that the viscosity would be 5 ð 1018 Pa s at 1225ºC and 2 ð 1017 Pa s at 1350ºC, in excellent agreement with the viscosities estimated from the plate dynamic models. The foregoing discussion shows that PMS flow model for the Argentine Basin is not demonstrably inconsistent with the temperature or viscosity of the asthenosphere derived from other studies, but the ultimate test of any model derives from its predictive power. Stein and Stein [16] have noted that the PMS model is thermally equivalent to the halfspace model. Hence the heat flow q as a function of age is predicted by q D kTm .πt/ 1=2 , where k is the thermal conductivity. Taking Tm D 1150 š 70ºC, and k D 3:14 W m 1 K 1 , the PMS model predicts the heat flow in the southernmost Argentine Basin to be .435 š 26/t 1=2 mW m 2 . Very few measurements of heat flow in the Argentine Basin south of 40ºS have been reported; a compilation by Hayes [28] includes just the nineteen individual measurements that are compared with the predicted heat flow for the region in Fig. 4. While there is considerable scatter in the measured heat flow, there is also a clear concentration of points that follows an apparent cooling trend through the data field that is in excellent agreement with the trend predicted from our fit to the PMS flow model.

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Fig. 4. Observed heat flow versus heat flow predicted by the PMS flow model in the southern Argentine Basin.

6. Conclusions Our analysis of primary seafloor depth data from the southern Argentine Basin shows no evidence of “flattening” predicted by the plate cooling model. Excluding the shallow basement depths associated with the region of elevated free-air gravity that occupies its central-western part, a halfspace or root-t cooling model explains 98% of the variance of depth in the basin. The results of this and other studies [2,10,13,14] thus tend to confirm the hypothesis of Heestand and Crough [12] that the flattening of depth=age trends observed elsewhere is related to thermal rejuvenation of the lithosphere by mantle plumes. However, the rate of subsidence required by the best-fitting halfspace model is unreasonably high, and there is a significant, though small, degree of systematic misfit between the model and the observations. A thermal model in which initial conditions vary with age fits the data, but also requires an unreasonably large variation of mantle temperature over the last 100 Ma. Thus no simple thermal subsidence model is sufficient to explain the relationship between depth and age in the Argentine Basin. The combined halfspace-cooling-plus-flow model proposed by Phipps-Morgan and Smith [10] explains more than 98% of the variance of depth in the southern Argentine Basin, and the model parameters suggest that the temperature of the mantle beneath the basin is slightly lower than normal, as might be expected in a region that has not been affected by hot spots. Moreover, the viscosity of the asthenosphere that we infer from the model is consistent with the lower temperature of the mantle and with other

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estimates of the viscosity of the mantle under ocean basins. Most important is the fact that the PMS flow model accurately predicts the variation of heat flow with age in the region. Hence, though Stein and Stein [16] have demonstrated that the PMS flow model fails to explain the variation of depth with age in the western North Atlantic, and argued that the PMS flow model is not a viable global alternative to the plate thermal models such as GDH1, quite the reverse is true of the Argentine Basin, where the depth=age and heat flow=age data are consistent with the PMS model, but the depth=age data show no evidence of plate cooling. A line of evidence that the bathymetry of this region is influenced by dynamic effects on a smaller scale is the fact that shallow depths in the center of the basin that cannot be explained by either simple cooling or flow models are associated with a region of elevated free-air gravity values. Our results thus suggest that the large-scale bathymetry of the Argentine Basin is affected not only by the combined halfspace thermal subsidence and large-scale flow in the asthenosphere, but also by local dynamic features.

Acknowledgements We are indebted to Philip Rabinowitz for providing the primary data for this study. Thoughtful reviews by R. Russo, C Stein and an anonymous reviewer contributed significantly to the paper. [CL]

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