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39Ar age progressions along seamount trails
Earth and Planetary Science Letters 185 (2001) 237^252 www.elsevier.com/locate/epsl
Testing the ¢xed hotspot hypothesis using 40Ar/39 Ar age progressions along seamount trails Anthony A.P. Koppers a; *, Jason Phipps Morgan a , Jason W. Morgan b , Hubert Staudigel a a
Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0225, USA b Geosciences Department, Princeton University, Princeton, NJ 08544-1003, USA Received 21 August 2000; received in revised form 8 December 2000; accepted 10 December 2000
Abstract Hotspots and their associated intra-plate volcanism producing seamount trails have become an accepted fact in geology from a conceptual theory. The azimuths and age progressions of these seamount trails provide the only means to determine absolute plate motions with respect to an independent reference frame of `fixed' hotspots. However, the presumed fixity of hotspots is in disagreement with recent paleomagnetic studies and global-circuit plate reconstructions for the Hawaiian^Emperor seamount trail. In this study, we provide independent evidence suggesting that hotspots are not fixed relative to each other. We use a straightforward test that compares the observed 40 Ar/39 Ar age progressions along Pacific seamount trails (0^140 Myr) with the Pacific plate velocities as predicted by their poles of plate rotation (i.e. Euler poles). In most of these comparisons, the age progressions were found incompatible with published Euler poles, or with a new set of Euler poles as derived in this study using discrete seamount locations digitized from the bathymetry maps of Smith and Sandwell [EOS 77 (1996) 315; Science 277 (1997) 1956^1921]. We conclude that the relative motion between hotspots may be required to reconcile the observed age progressions with the predicted plate velocities from their modeled Euler poles. On average, the Pacific hotspots may show motion at 10^60 mm/yr over the last 100 Myr, partly attributed to individual hotspot motion, whereas systematic motion of these hotspots (due to true polar wander) may account for the remainder. ß 2001 Elsevier Science B.V. All rights reserved. Keywords: hot spots; movement; plate tectonics; Ar-40/Ar-39; geochronology; seamounts; Paci¢c Plate
1. Introduction The assumption that stationary hotspots underlie the Earth's lithospheric plates has been most
* Corresponding author. Fax: +1-858-534-8090; E-mail: [email protected]
important in the development of plate tectonics. According to the ¢xed hotspot hypothesis seamount trails are formed by volcanism penetrating the lithospheric plates whilst moving over `hotspots' of upwelling mantle (e.g. [1,2]). In turn, the azimuths and age progressions of seamount trails can be used to quantify plate motions with respect to an independent geospatial reference frame of hotspots in the mantle [3,4]. In such
0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 3 8 7 - 3
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Fig. 1. Paci¢c hotspot trails according to age range. For reference the currently active hotspots of the Paci¢c (circles) have been included. Most of the 0^43 Ma seamount trails can be associated with these hotspots, except for the Tuamotu seamount trails. Note that for the Hawaiian, Louisville, Easter, and Guadalupe seamount trails we have omitted seamounts younger to 5 Ma (see Section 3 for explanation). Abbreviations: AN = Anewetak; EM = Emperor; GL = Gilbert; HR = Hess Rise; IT = Ita Mai Tai; JP = Japanese; LI = Line Islands; LK = Liliuokalani; LV = Louisville; MA = Magellan; MP = Mid Paci¢c Mountains; MU = Musicians; NW = North Wake; RL = Ralik; RT = Ratak; SE = Seth; SR = Shatsky Rise; SW = South Wake; TM = Tuamotu; TO = Tokelau; TV = Tuvalu; WW = Wentworth.
quanti¢cations plate motions are assumed to be constant rotations of rigid, non-deforming plates around ¢xed poles of rotation (i.e. Euler poles) for distinct time periods (i.e. stage poles). Although, there is no doubt that hotspot melting represents the major means of intra-plate volcanism, the ¢xity of both hotspots and their associated Euler poles appears unlikely in the context of a dynamically convecting Earth [5^8]. Recent paleomagnetic studies [8^12] and global-circuit plate reconstructions [13^19] for the Hawaiian^Emperor seamount trail suggest that the Hawaiian hotspot may have experienced a motion of 10^40
mm/yr during the Emperor stage pole (80^43 Ma). The major objective of this paper is to further test the ¢xed hotspot hypothesis, in this case, by testing for compatibility between the observed 40 Ar/39 Ar age progressions along seamount trails on the Paci¢c plate (Fig. 1) and the locations of the Euler poles describing its absolute plate rotations. In this straightforward test, the Euler poles will be re-determined by minimizing the angular distances from the `best-¢t' Euler poles to the locations of individual seamounts, as digitized from the bathymetric maps of Smith and Sandwell
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([20,21]; Appendix 1, EPSL Online Background Dataset1 ). Because the `best-¢t' Euler poles are geometrically derived using seamount locations exclusively, the age progressions along seamount trails (i.e. local plate velocities) provide an independent check for the angular distance of individual hotspots to the `best-¢t' Euler poles. We will show that the local Paci¢c plate velocities are not compatible with the angular plate velocities as predicted by the `best-¢t' Euler poles ([22]; this study) or with any previously published Euler poles ([3,7,23^28]; Appendix 2, EPSL Online Background Dataset1 [50^52]). This may indicate that the presumed ¢xity of hotspots is invalid within the limits of these tests ^ allowing for possible motions between individual hotspots of the Paci¢c hotspot system. 2. Least squared derivation of Euler poles using discrete seamount locations One approach in determining an Euler pole is based on the measurement of spatial trends in seamount trails. When using these azimuths one is, however, limited by the small number of available seamount trails. An alternative approach for the least squared derivation of Euler poles is presented here using the locations of discrete seamounts within multiple seamount trails or segments. This purely geometrical approach was previously used to determine Euler poles for relative plate motion using digitized points on fracture zones [23]. One of its advantages is the increased number of possible observations. Another advantage is the improved reliability of the uncertainty estimates. More importantly, the derivation of Euler poles is not controlled by the observed age progressions along the studied seamount trails. The age progressions along seamount trails, therefore, may serve as an independent check to the location of an Euler pole as based on the ¢xed hotspot hypothesis.
1
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mirror
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Fig. 2. Geometrical derivation of Euler poles based on the location of individual seamounts. Trial pole E depicts the `best-¢t' Euler pole, whereas trial pole EP depicts a `mis¢t' pole with a sum of squared deviations signi¢cantly larger than zero.
2.1. Formulation of the least squared model Fig. 2 illustrates the least squared model used to determine Euler poles for absolute plate motion. The seamount locations within two co-polar seamount trails A and B are plotted as small circles around their `best-¢t' Euler pole E. Because the angular distances d between each seamount i in seamount trail A and the Euler pole E are of equal length, their sum of squared deviations from the mean angular distance becomes zero. The same relation holds for seamount trail B, and because seamount trails A and B are copolar, the `best-¢t' Euler pole is de¢ned by a minimum in their total sum of squared deviations. Its location can be derived by an inversion of seamount locations using a least squared algorithm which minimizes the variance in the calculated angular distances: vard ij
M X N X 1 j1
N i1
U d ji 3d jmean 2
1
where N is the number of seamounts (independent observations) per seamount trail and M is the number of trails. This variance is equal to the squared RMS error for the motion of lithospheric
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plates [29,30]. Analyzing each seamount location with reference to the mean angular distance of its representative seamount trail avoids biasing of the analysis. The `best-¢t' poles were found by grid searching in the northern hemisphere. The search areas were narrowed around these poles in four subsequent searches using increased grid resolutions (2³, 0.5³, 0.1³ and 0.02³). The distribution of the variances is contoured in latitude^longitude space (Fig. 3).
2.2. Uncertainties and bootstrapping All seamount locations were retrieved by digitization of the predicted bathymetry maps of Smith and Sandwell ([20,21]; Appendix 1, EPSL Online Background Dataset1 ). The scatter in the location of the seamounts perpendicular to the line of age progression is re£ected in the variance for the calculated angular distances. No scaling was performed because scaling by the number of
Fig. 3. Improved `best-¢t' Euler poles for absolute Paci¢c plate motion. Contours in the polar plots draw the distributions of the most probable least squared solutions and show the `best-¢t' Euler pole at their center point (black circles). These contours are arbitrarily set at 5% of the minimal variance; outer contours therefore represent variances 25% higher than that for the `best-¢t' pole. Published rotation poles (hexagonal symbols) are included together with the location of the processed seamount locations. The seamount trails are identi¢ed in the legends. Contours in the insets display con¢dence regions based on statistical F tests at the 65^95^99% con¢dence levels. The insets also display the `best-¢t' Euler poles obtained by the bootstrap method (open circles), its mean (gray squares), the 99% con¢dence ellipse around this mean (dark gray line), and alternative models. Modeling results are summarized in Tables 1 and 3. Seamount locations, previously published rotation poles, and a further discussion of the data are available in Appendices 1^3, EPSL Online Background Dataset1 . Abbreviations: EP84 = Epp, 1984 [23]; EP85 = Engebretson et al., 1985 [24]; HP85 = Henderson, 1985 [25]; DpCP85 = Duncan and Clague, 1985 [3]; LP88 = Lonsdale, 1988 [26]; YpKP93 = Yan and Kroenke, 1993 [27]; WpKP97 = Wessel and Kroenke, 1997 [28]; MP97 = Morgan (unpublished); SP00 = Steinberger, 2000 [7].
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seamounts (or seamount trail length) would preferentially ¢t the longest seamount trails, resulting in an undesired loss of plate motion information from the shorter seamount trails. The variance about the `best-¢t' Euler pole is a measure of the goodness of ¢t to the seamount locations. The contoured variances in Fig. 3, therefore, represent the most likely distributions of solutions for the Euler poles at 5% intervals. The shape and elongation of these distributions are largely dependent on the number of seamounts, the length of the seamount trails and the position of these trails with respect to the Euler pole (cf. [29,31]). The con¢dence regions on the 65^95^99% con¢dence levels (Fig. 3, insets) were constructed using a statistical F ratio test following the methodology of Engebretson et al. [29,32,33]. When presuming normal distributions
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in a linear system, the F test determines if the variance of `trial' Euler pole Etrial is signi¢cantly greater than the minimum variance of the `best-¢t' Euler pole Ebest : X varE trial 3varE best U p R 2 varE best where X = pN3p equals the degrees of freedom and p is the number of adjustable parameters in the model (in this case, latitude^longitude, p = 2). The R ratio corresponds to standard F ratio tables at the desired con¢dence level with (p,X) degrees of freedom. Application of the bootstrap method was used to test the robustness of the reconstructed `best¢t' Euler poles. Alternative `bootstrap' Euler poles were calculated ignoring each seamount trail
Fig. 3 (continued).
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and each pair of trails once during the reconstructions, resulting in 1/2M2 31/2M solutions, where M is the number of seamount trails. If all modeled seamount trails belong to the same stage pole
and M is su¤ciently large, the location of the `mean-bootstrap' pole is expected to be similar to the `best-¢t' Euler pole at the 99% con¢dence level.
Fig. 3 (continued).
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3. Results The most recent stage pole models include at least 11 di¡erent Euler poles to describe absolute
243
Paci¢c plate motion (cf. [28]). Additional poles were incorporated in these models to improve the ¢t to the Hawaiian^Emperor and Louisville seamount trails with possible changes in plate mo-
Fig. 3 (continued).
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Table 1 Results from the least squared derivation of Paci¢c plate Euler poles Euler pole Lat. Long. Hawaiian stage pole Total pole best-¢t bootstrap scaled 20^0 Ma best-¢t bootstrap
67.1 67.1 67.9 70.1 70.1
294.5 294.7 296.8 302.0 302.0
Emperor stage pole Total pole best-¢t bootstrap scaled w/o Emperor best-¢t bootstrap
18.8 20.2 19.9 25.6 24.9
253.6 256.6 252.5 272.4 268.7
w/o Louisville
best-¢t bootstrap
100^80 Ma stage pole Total pole best-¢t bootstrap scaled 110^100 Ma stage pole Total pole best-¢t scaled w/o Mid-Pac best-¢t scaled 125^110 Ma stage pole Total pole best-¢t bootstrap scaled 140^125 Ma stage pole Total pole best-¢t
Best-¢t con¢dence regions Var
M
N
0.22
21
346 231
0.15
19
293 190
0.15
8
122 36
0.11
7
99 28
21.4 248.8 21.5 248.4
0.11
7
100 28
40.6 259.8 40.2 258.1 39.4 254.5
0.10
10
92 55
74.1 101.8 74.5 102.9 75.1 44.8 75.2 44.5
0.13
5
95
0.04
3
41
0.09
4
47
0.20
3
41
65.3 273.2 65.7 268.5 67.2 268.9 7.7
33.1
Longitude
Latitude
Min
Max
Min Max Lat. Long.
Extreme points Lat. Long.
0.65% 0.95% 0.99% 0.65% 0.95% 0.99%
292.5 291.2 290.4 299.9 298.5 297.6
296.3 297.7 298.5 304.0 305.6 306.5
66.7 66.4 66.2 69.7 69.5 69.3
67.5 67.8 68.0 70.5 70.7 70.9
66.9 66.8 66.7 69.9 69.7 69.6
292.5 291.2 290.4 299.8 298.3 297.4
67.3 67.4 67.5 70.2 70.3 70.5
296.4 297.8 298.6 304.2 305.8 306.7
0.65% 0.95% 0.99% 0.65% 0.95% 0.99% 0.65% 0.95% 0.99%
252.6 251.9 251.5 274.7 276.3 277.4 247.9 247.2 246.8
254.6 255.3 255.8 270.2 268.6 267.7 249.7 250.4 250.8
18.2 17.8 17.5 24.8 24.3 24.0 20.9 20.5 20.2
19.5 19.9 20.2 26.3 26.8 27.2 22.0 22.4 22.6
19.2 19.4 19.3 24.7 23.9 23.5 21.8 22.1 22.2
252.6 251.9 251.4 269.1 266.8 265.3 247.8 247.1 246.6
18.6 18.3 18.3 26.5 27.0 27.3 21.1 20.7 20.6
254.6 255.3 255.8 275.7 278.1 279.6 249.8 250.5 251.0
0.65% 0.95% 0.99%
254.3 249.8 246.7
264.5 267.6 269.4
39.7 41.4 41.3 252.0 39.1 42.0 41.6 246.9 38.7 42.4 41.6 243.9
39.1 268.1 37.7 274.3 36.6 278.1
For the `best-¢t' pole the 65^95^99% con¢dence regions are de¢ned based on F ratio tests by: (1) the min and max longitude at the latitude of the Euler pole, (2) the min and max latitude at the longitude of the Euler pole, and (3) the extreme points of the error regions. These parameters were used to construct the non-ellipsoid error regions in the insets of Fig. 3. M = number of seamount trails; N = total number of seamounts for the `best-¢t' pole or the number of solutions for the `bootstrap' pole. Var = variance as calculated from Eq. 2.
tion around 3^5 Ma, 12^15 Ma, 17^20 Ma, and 65 Ma. In our study, a ¢rst order stage pole model is investigated following Henderson [25] for the last 100 Myr (43^0, 80^43 and 100^80 Ma). The change in plate motion around 3^5 Ma [28,34,35] is ignored since it seems in disagreement with plate motion of the North American plate [36]. Plate motion prior to 100 Ma (110^100, 125^110 and 140^125 Ma) follows the stage pole model of Wessel and Kroenke [28]. The results are illus-
trated in the polar plots of Fig. 3 and listed in Table 1 and Table 3; results for Euler poles older than 100 Ma are discussed in Appendix 3 of the EPSL Online Background Dataset1 [42,43]. 3.1. Euler pole: 43^0 Ma Seventeen seamount trails were included in the calculation of the Euler pole (67³07P N, 294³28P E) belonging to the so-called Hawaiian stage pole
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Table 2 Local plate velocities for the Paci¢c plate between 0 and 140 Ma Data Seamount trail Hawaiian stage pole Hawaii [38] Hawaii [38] Bowie [3] Cobb [3] Pitcairn [3] Society [3] Austral-Cook [3] Caroline [3] Samoa [3] Foundation [44] Louisville based on [37] Emperor stage pole Emperor [38] Emperor [38] Louisville based on [37] Louisville based on [37] Line [45] 100^80 Ma stage pole Magellan [22] Line [46] Musicians [22] Wentworth [41] 125^110 Ma stage pole Japanese [40]
Regression Age range (Ma) 43.4^0 12.3^0 24.8^0 25.7^0 8.1^0.5 4.5^0 19.6^0 13.9^1.0 27.7^0 21.2^0.9 45.5^0.5
Calculation type
Style
Plate velocity (mm/yr)
maximum ages
YORK 2 YORK 2 Linear Linear Linear Linear Linear Linear Linear Linear YORK 2
92 þ 3 96 þ 4 67 þ 20 57 þ 20 127 þ 55 109 þ 10 107 þ 16 121 þ 39 72 þ 23 91.1 þ 2.0 60.5 þ 2.0
YORK YORK YORK YORK Linear
2 2 2 2
72 þ 11 68 þ 3 61.2 þ 1.2 64.4 þ 4.8 96 þ 4
YORK 2 YORK 2 YORK 2
47.6 þ 1.6 66 þ 25 55.8 þ 6.4 70
YORK 2
48.1 þ 4.5
maximum ages recombined ages
64.7^43.4 64.7^19.9 66.3^0.5 66.3^35.5 93.4^47.4
recombined ages recombined ages
95.2^87.1 93.4^81.0 95.4^82.3 93.4^86.4
recombined ages recombined ages 2 data points
118.1^103.7
recombined ages
When available the style of data regression, the type of seamount ages included in the age progressions and the standard deviations are denoted. The calculations were not forced through the origin; YORK 2 = York, 1969 [53].
between 43 and 0 Ma. This `best-¢t' Euler pole has an overall variance of 0.22 and agrees with the `mean-bootstrap' pole (67³07P N, 294³40P E). Scaling by the number of seamounts in each trail only results in a minor shift in the location of the `best-¢t' Euler pole. However, the bootstrap results show two noteworthy deviations: (1) a longitudinal shift of the Euler pole when excluding Hawaiian seamounts 43^20 Myr old, and (2) a latitudinal shift when excluding similar seamounts from the Louisville seamount trail. The remaining bootstrap poles fall within the 99% con¢dence region around the total Euler pole. For this reason, we calculated a separate Paci¢c plate Euler pole for the 20^0 Ma Hawaiian stage pole. This yields a signi¢cantly changed Euler pole (70³05P N, 301³58P E) with a lower variance (0.15) that is shifted to the north when compared to: (1) the
total Hawaiian Euler pole and (2) all published Euler poles. The 43^20 Ma Euler pole was not re-modeled since only two seamount trails (Hawaii and Louisville) represent this stage pole [37,38]; this Euler pole is best approximated by the total pole at 67³07P N, 294³28P E. 3.2. Euler pole: 80^43 Ma The Emperor stage pole (80^43 Ma) was modeled using eight seamount trails resulting in a `best-¢t' Euler pole (18³50P N, 253³35P E) with a variance of 0.15. Despite the low variance, the distribution of bootstrap poles yields a poorly de¢ned and di¡erent `mean-bootstrap' pole (20³13P N, 256³37P E). When eliminating the Emperor or the Louisville seamount trails, the models give lower variances (0.11) and better constrained
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`mean-bootstrap' poles. The pole with the lowest variance (21³25P N, 248³47P E) was obtained when excluding Louisville seamount trail, and is in accordance with its `mean-bootstrap' Euler pole (21³28P N, 248³26P E). This may indicate that the azimuth of Louisville Ridge was indeed changed due to a major o¡set in the Eltanin fracture zone between 60 and 80 Ma [37]. Such kinematic interactions of hotspots with fracture zones are believed to cause azimuthal deviations up to 15^30³ according to studies of the Tuamotu^Pitcairn hotspot [38] and the Marquesas hotspot [39]. 3.3. Euler pole: 100^80 Ma Eight seamount trails yield a `best-¢t' Euler pole at 40³34P N, 259³47P E for the 100^80 Ma stage pole. The variance is low (0.10) but the associated con¢dence regions are more extended when compared to those of the Hawaiian and Emperor Euler poles. This seems an e¡ect of the limited regional extension of the short seamount trails included in this calculation. However, most of the bootstrap poles fall within the 99% con¢dence region suggesting that the least squared modeling resulted in a self-consistent `best-¢t' Euler pole for the 100^80 Ma stage pole. 4. Discussion Seven stage poles were determined that describe the absolute rotation of the Paci¢c plate over the last 140 Myr. In this discussion, these `best-¢t' Euler poles will be tested for their compatibility with the observed 40 Ar/39 Ar age progressions measured along co-polar seamount trails. The ¢xed hotspot hypothesis predicts that each of these age progressions (i.e. local plate velocities; Table 2) should give comparable estimates for the angular plate velocity. The latter prediction can only be tested when the Euler poles are derived independently from the age progressions along the seamount trails. This was accomplished in this study by using an entirely geometric approach for the derivation of Euler poles. We therefore can use the recorded 40 Ar/39 Ar age progressions
to de¢ne independent distributions for the location of these seven Euler poles. 4.1. Test of the ¢xed hotspot hypothesis In Fig. 4 the 65^95% con¢dence regions (open^ closed circles) depict which Euler poles are compatible with the observed local plate velocities (Table 2). These con¢dence regions were constructed by grid-searching in the northern hemisphere while calculating the angular velocities (and their standard deviations) for each trial Euler pole using the age progressions of the modeled seamount trails. This was done using the relationship : e = g sin dmean T, where e is the linear local plate velocity, dmean is the average angular distance of a seamount trail to its Euler pole, and g is the velocity of angular rotation. Whenever the modeled angular velocities were similar at the desired con¢dence level, the Euler poles were accepted. The modeled velocity regions, therefore, depict an independent distribution of potential Euler poles and can be directly contrasted to locations of the geometrically derived `best-¢t' Euler poles (Fig. 3). An inconsistency arises when cross-checking the location of the 100^80 Ma Euler pole with the local plate velocities derived from the Magellan and Musicians seamount trails (cf. [22]). Neither the published Euler poles nor the `best-¢t' Euler pole agree with the modeled velocity region (Fig. 4). We may de¢ne a `forced' Euler pole (29³ N, 297³ E) from the intersection of the Euler pole distribution derived from the seamount locations (Fig. 3) and the calculated velocity region (Fig. 4). This `forced' Euler pole, however, is located V35³ away from the `best-¢t' Euler pole at 40³34P N, 259³47P E. This observation may indicate that the age progressions can only be reconciled with the `best-¢t' Euler pole, when allowing for the relative movement of the Magellan and Musicians hotspots with respect to one another [22]. For the Hawaiian (43^0 Ma) and Emperor stage poles (80^43 Ma) similar tests were conducted. The tests for the Hawaiian stage pole include the Emperor, Louisville and Foundation hotspots. The Hawaiian chain has been inten-
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Fig. 4. Testing the ¢xed hotspot hypothesis. These diagrams display independent distributions of Euler poles calculated from the age progressions in two co-polar seamount trails accepting the ¢xed hotspot hypothesis. Open and closed circles represent 65% and 95% con¢dence levels, respectively. If the tested hotspots are truly ¢xed with respect to each other, then these distributions should overlie the locations of the `best-¢t' Euler poles based on seamount locations (circles with 99% con¢dence regions; Table 1) or the published Euler poles (hexagonal symbols). Note that, in case of the 43^0 Ma stage pole, the 99% error regions are smaller than the actual symbols depicting the `best-¢t' Euler poles (circles in squares).
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sively dated by 40 Ar/39 Ar techniques resulting in an average age progression of 92 þ 3 mm/yr over the last 43 Myr [38]. The Foundation seamount trail is de¢ned by small, monogenetic seamounts and yields the most accurate age progression in the Paci¢c of 91.1 þ 2.0 mm/yr [44]. The Louisville seamount trail has an age progression of 60.5 þ 2.0 mm/yr; but its accuracy is limited by a low sample density for seamounts younger than 43 Ma [37]. From Fig. 4 it follows that the observed age progressions for the Hawaiian and Foundation seamount trails are compatible with the `best-¢t' Euler poles and most of the previously published Euler poles at the 65^95% con¢dence level. The Hawaiian and Foundation hotspots may, consequently, be considered ¢xed with respect to each other. The tests including the Louisville seamount trail, however, yield con¢dence regions that are signi¢cantly di¡erent from these Euler poles. For example, an increase in the apparent local plate velocity from 60.5 to 73 mm/yr at the Louisville seamount trail would be required to achieve concordant results in all three cases. If ignoring the low sample density at the Louisville seamount trail, then this discrepancy could be explained by the independent motion of the Louisville hotspot by V12 mm/yr (sub)parallel to the direction of Paci¢c plate motion. This is in accord with the predicted V9 mm/yr motion of the Louisville hotspot [5^7]. The tests for the Emperor stage pole include the Emperor, Louisville and Line hotspots. The Emperor and Louisville seamount trails have been well dated with 40 Ar/39 Ar techniques and yield age progressions of 68 þ 3 mm/yr and 61.2 þ 1.2 mm/yr, respectively [37,38]. Dating of the Line Islands focused only on the time period between 90 and 65 Ma [45]. Nonetheless, an overall age progression of 96 þ 4 mm/yr was proposed for its Emperor stage pole [23,45]. From Fig. 4 it follows that the Emperor and Louisville seamount trails may be in accord with the `best-¢t' Euler poles at the 95% con¢dence level. The poor resolution is not only a function of the precision for the age progressions, but also results from the similarity in the local plate velocities and the fact that the Emperor and Louisville seamount trails are located at comparable angular distances to the pre-
ferred Euler pole (72.8 þ 0.3; 80.8 þ 0.5). Both tests including the Line Islands show marked deviations from the `best-¢t' Euler poles. The displayed narrow distributions are the result of the pronouncedly higher local plate velocity at the Line Islands and its shorter angular distance to the Euler pole (54.1 þ 0.3). Since none of the three test cases yielded concordant results at the 65% con¢dence level, it seems likely that the Emperor, Louisville and Line hotspots have moved relative to each other. Alternatively, the uncertainties in the age progressions (Table 2) may be too precise; they may not entirely re£ect their true geological uncertainties, including the prolonged volcanic evolution of individual seamounts, rejuvenation by younger hotspots and uncertainties in the actual location of the hotspot underneath seamount trails. 4.2. Hotspot motion in velocity space In Fig. 5 the above tests are plotted in velocity space displaying possible combinations of hotspot motion at the 65^95% con¢dence levels. Every combination of coexistent hotspot motion falling within these con¢dence regions reconciles the apparent age progressions with the `best-¢t' Euler poles. Fixed hotspots are represented by the origin, whereas hotspot motions anti-parallel to plate motion are represented by negative velocities. It follows that the scenarios for hotspot motion represent non-unique solutions. Additional geological constraints are required to quantitatively resolve inter-hotspot motions. Hotspot motion anti-parallel to plate motion should be prevalent [6] when considering the fact that (whole) mantle convection seems primarily driven by subduction over the last 100 Myr (e.g. [47]). For the 100^80 Ma stage pole (Fig. 5) this may rule out the scenario based on a ¢xed Musicians hotspot and the motion of the Magellan hotspot in the direction of plate motion. It also may suggest that anti-parallel motion of the Musicians hotspot is between 12 and 24 mm/yr (Fig. 5). This is a minimum estimate given that the Magellan hotspot may have experienced antiparallel hotspot motion as well. Two assumptions are required: (1) subduction of the Paci¢c plate
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Fig. 5. Hotspot motion in velocity space. The origin represents truly ¢xed hotspots; positive and negative velocities represent hotspot motion parallel and anti-parallel to the direction of plate motion (in mm/yr). The modeled 65^95% con¢dence envelopes depict all possible combinations of hotspot motion for two co-polar seamount trails compatible with both the improved Euler poles from Table 3 and the observed age progressions from Table 2 including standard errors. Independent estimates for the motion of hotspots based on paleolatitude studies (65^95% con¢dence boxes) and mantle £ow modeling are added (see diagrams for references).
249
beneath the Asian plate was more important than subduction of the Kula plate during the 100^80 Ma stage pole, and (2) hotspot motion was aligned to Paci¢c plate motion. Hotspot motion perpendicular to plate motion does not induce changes in the local plate velocities at co-polar seamount trails. Instead, it would induce changes in the location of the Euler pole. Consistency within the modeling results for the 100^80 Ma Euler pole implies that the orientations of the Magellan and Musicians seamount trails are not signi¢cantly di¡erent. The detected discrepancy in their local plate velocities, thus, may indicate that the (major) component of hotspot motion was parallel to plate motion. For the Emperor stage pole (Fig. 5) the age progressions are incompatible with the ¢xed hotspot hypothesis ; inter-hotspot motion seems to be required. The modeled coexistent motion of the Louisville and Emperor hotspots is compatible with independently derived estimates from paleolatitude and global-circuit plate studies (Fig. 5). However, the Line hotspot cannot be reconciled with these estimates, which suggests an additional component of hotspot motion, provided that the local plate velocity of 96 þ 4 mm/yr [45] is an accurate estimate. For the Hawaiian stage pole, the Foundation and Hawaiian hotspots may obey the ¢xed hotspot hypothesis because their 95% con¢dence envelope intersects the origin in Fig. 5. Note that the Foundation and Hawaiian hotspots may not necessarily be ¢xed with respect to the deep mantle, but only with respect to each other. Other combinations of hotspot motion may also be compatible with their observed 40 Ar/39 Ar age progressions and 43^0 Ma Euler pole. Estimates from paleolatitude studies are again comparable with the presented relation of `true' motion between these hotspots (Fig. 5). The estimates of Steinberger and O'Connell [6] for the motion of the Louisville hotspot (V9 mm/yr) and the Hawaiian hotspot (V12 mm/yr) are di¡erent since they fall slightly below the con¢dence envelopes in Fig. 5. 4.3. Absolute Paci¢c plate motion Angular plate velocities should be estimated
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Table 3 Preferred stage pole model for the Paci¢c plate Stage pole 20^0 Ma 43^20 Ma 43^80 Ma 100^80 Ma 110^100 Ma 125^110 Ma 140^125 Ma
Euler pole
Rotation
Lat.
Long.
Var
70.1 67.1 18.8 40.6 75.1 65.3 7.7
302.0 294.5 253.6 259.8 44.8 273.2 33.1
0.15 0.22 0.15 0.10 0.04 0.09 0.20
M 19 21 8 10 3 4 3
N
Vel
Deg
Comments
293 346 122 92 41 47 41
0.881 þ 0.016 0.502^0.478 0.657 þ 0.029 0.425 þ 0.014 0.44 0.449 þ 0.042 0.49
17.6 þ 0.3 13.3^11.0 24.3 þ 1.1 8.5 þ 0.3 4.4 6.7 þ 0.6 9.8
weighted average Foundation+Hawaii models 1^3 of Steinberger and O'Connell [6] minimum Emperor seamount trail minimum Magellan seamount trail average Magellan+Japanese seamount trail minimum Japanese seamount trail Wessel and Kroenke [28]
Vel = angular velocity in ³/Myr; Deg = angular rotation for the total stage pole. Standard deviations on the angular velocities and the angular rotation were estimated from the standard errors on the observed local plate velocities (Table 2) and the standard deviations on the angular distance to the Euler pole. For error regions of the `best-¢t' Euler pole and abbreviations see Table 1.
considering the motion of hotspots so that they solely re£ect plate motions (cf. [7]). To achieve such estimates, we calculated the angular velocities based on the average angular distance of the seamount trail to the modeled `best-¢t' Euler pole. These calculations include the propagation of errors in the angular distance to the Euler pole (standard deviation) and the age progression (standard error; Table 2). If all calculated angular velocities for one speci¢c stage pole are similar at the 65% con¢dence level, then the average angular velocity represents an estimate for its true angular plate velocity. If no evidence exists for the (relative) ¢xity of co-polar hotspots then minimum angular velocities were estimated. In Table 3 we present our preferred stage pole model for the Paci¢c plate over the last 140 Myr including the `best-¢t' Euler poles derived using the geometric method and the new estimates for the angular plate velocities. 5. Summary and conclusions Seamount locations were used to derive Euler poles describing the direction of Paci¢c plate motion over the last 140 Myr. This was done by minimizing the angular distances between these seamounts and the Euler pole with respect to an average angular distance for each seamount trail. As a result, this geometric method yields reliable estimates for Euler poles based on seamount locations exclusively. The modeled Euler poles sub-
sequently were used to predict their associated angular plate velocities and to compare these with the observed 40 Ar/39 Ar age progressions, in order to test the ¢xed hotspot hypothesis. Only the Hawaiian and Foundation hotspots appear to be ¢xed with respect to each other over the last 20 Myr; in most other cases, the estimated plate velocities were signi¢cantly di¡erent at the 65^95% con¢dence levels. One possible explanation is that these discordances are caused by relative motion between hotspots in a direction subparallel to plate motion. The possible motion of hotspots was found to be consistent with the independent estimates on hotspot motion using the di¡erence in paleolatitude for the Emperor seamount trail [8^12], global-circuit plate motion models [13^19] and mantle £ow modeling [5^7]. Combining these independent estimates with the relations of hotspot motion in velocity space suggests hotspot motion in the order of 10^60 mm/yr over the last 100 Myr. The possibility for hotspot motion may have contrasting implications for mantle geodynamics. Hotspot motion anti-parallel to plate motion can be explained by the kinematic return £ow in the deep mantle [48] as driven by the slab-pull of subducting lithospheric plates. Hotspot motion parallel to plate motion can only be explained by densitydriven mantle convections, but this would require much lower viscosities in the upper mantle [6,49]. We emphasize, however, that age progressions along seamount trails still carry signi¢cant geological and analytical uncertainties. Within the
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limits of these data, we concluded here that hotspots are not necessarily ¢xed with respect to each other, and that our proposed relative hotspot motions are consistent with independent geodynamic models. However, more importantly, we were able to develop and use quantitative methods to determine uncertainties in stage pole de¢nitions and plate motion models based on age progressions in linear island chains. Ultimately, such quantitative methods will allow us to continue building and re¢ning plate motion models as additional and more accurate data become available.
[8] [9] [10] [11] [12]
[13]
Acknowledgements We thank Dave Sandwell for his help with GMT. Jan Wijbrans is thanked for his comments on the manuscript. We thank Gary Acton and Bill Harbert for their reviews. This paper is an outgrowth of A.A.P.K.s Ph.D. thesis at the Vrije Universiteit in Amsterdam, The Netherlands. Financial support by the Netherlands Foundation of Earth Sciences Research (GOA-NWO 750.60.005), Netherlands Science Foundation (NWO-TALENT grant to A.A.P.K.) and National Science Foundation (NSF-OCE 91-02183 and 97-30394).[RV]
[14]
References
[19]
[1] J.T. Wilson, A possible origin of the Hawaiian Islands, Can. J. Phys. 41 (1963) 863^870. [2] W.J. Morgan, Deep mantle convection plumes and plate motions, Am. Assoc. Petrol. Geol. Bull. 56 (1972) 42^43. [3] R.A. Duncan, D.A. Clague, Paci¢c plate motion recorded by linear volcanic chains, in: A.E.A. Nairn, F.L. Stehli, S. Uyeda (Eds.), The Ocean Basins and Margins, The Paci¢c Ocean 7A, Plenum Press, New York, 1985, pp. 89^121. [4] W.J. Morgan, Hotspot tracks and early rifting of the Atlantic, Tectonophysics 94 (1983) 123^139. [5] B. Steinberger, R.J. O'Connell, Changes of the Earth's rotation axes owing to advection of mantle density heterogeneities, Nature 387 (1997) 169^173. [6] B. Steinberger, R.J. O'Connell, Advection of plumes in mantle £ow: implications for hotspot motion, mantle viscosity and plume distribution, Geophys. J. Int. 132 (1998) 412^434. [7] B. Steinberger, Plumes in a convecting mantle: models
[15]
[16] [17]
[18]
[20] [21] [22]
[23] [24]
251
and observations for individual hotspots, J. Geophys. Res. 105 (2000) 11127^11152. U. Christensen, Fixed hotspots gone with the wind, Nature 391 (1998) 739^740. R.G. Gordon, C.D. Cape, Cenozoic latitudinal shift of the Hawaiian hotspot and its implications for true polar wander, Earth Planet. Sci. Lett. 55 (1981) 37^47. W.W. Sager, U. Bleil, Latitudinal shift of Paci¢c hotspots during the late Cretaceous and early Tertiary, Nature 326 (1987) 488^490. J.A. Tarduno, J. Gee, Large-scale motion between Paci¢c and Atlantic hotspots, Nature 378 (1995) 477^480. J.A. Tarduno, R.D. Cottrel, Paleomagnetic evidence for motion of the Hawaiian hotspot during formation of the Emperor seamounts, Earth Planet. Sci. Lett. 153 (1997) 171^180. P. Molnar, J. Stock, Relative motions of hotspots in the Paci¢c, Atlantic and Indian Oceans since late Cretaceous time, Nature 327 (1987) 587^591. G.D. Acton, R.G. Gordon, Paleomagnetic tests of Paci¢c plate reconstructions and implications for motion between hotspots, Science 263 (1994) 1246^1254. S.C. Cande, C.A. Raymond, J. Stock, W.F. Haxby, Geophysics of the Pitman fracture zone and Paci¢c-Antarctic plate motions during the Cenozoic, Science 270 (1995) 947^953. I.O. Norton, Plate motions in the North Paci¢c: the 43 Ma nonevent, Tectonics 14 (1995) 1080^1094. I.O. Norton, Hotspot tracks and reference frames don't mix, in: Conference on the History and Dynamics of Global Plate Motions, American Geophysical Union, Marshall, CA, 1997, p. 23. C.A. Raymond, J.M. Stock, S.C. Cande, Relative hotspot motion based on global plate reconstructions, in: Conference on the History and Dynamics of Global Plate Motions, American Geophysical Union, Marshall, CA, 1997, p. 25. V. DiVenere, D.V. Kent, Are the Paci¢c and Indo-Atlantic hotspots ¢xed? Testing the plate circuit through Antarctica, Earth Planet. Sci. Lett. 170 (1999) 105^117. W.H.F. Smith, D. Sandwell, Predicted bathymetry. New global sea£oor topography from satellite altimetry, EOS 77-46 (1996) 315. W.H.F. Smith, D. Sandwell, Global sea £oor topography from satellite altimetry and ship depth soundings, Science 277 (1997) 1956^1962. A.A.P. Koppers, H. Staudigel, J.R. Wijbrans, M.S. Pringle, The Magellan seamount trail: implications for Cretaceous hotspot volcanism and absolute Paci¢c plate motion, Earth Planet. Sci. Lett. 163 (1998) 53^68. D. Epp, Possible perturbations to hotspot traces and implications for the origin and structure of the Line Islands, J. Geophys. Res. 89 (1984) 11273^11286. D. Engebretson, A. Cox, R. Gordon, Relative Motions between Oceanic and Continental Plates in the Paci¢c Basin, Geological Society of America Special Paper 206, 1985.
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[25] L.J. Henderson, Motion of the Paci¢c Plate Relative to the Hotspots since the Jurrasic and Model of Oceanic Plateaus of the Farallon Plate, Ph.D. Thesis, Northwestern University, USA, 1985. [26] P. Lonsdale, Geography and history of the Louisville hotspot chain in the Southwest Paci¢c, J. Geophys. Res. 93 (1988) 3078^3104. [27] C.Y. Yan, L.W. Kroenke, A plate tectonic reconstruction of the southwest Paci¢c, 0^100 Ma, in: W.H. Berger, L.W. Kroenke, L.A. Mayer et al. (Eds.), Proceedings of the Ocean Drilling Program, Scienti¢c Results: 130. Ocean Drilling Program, College Station, TX, 1993, pp. 697^709. [28] P. Wessel, L. Kroenke, A geometric technique for relocating hotspots and re¢ning absolute plate motions, Nature 387 (1997) 365^369. [29] D.C. Engebretson, A. Cox, R.G. Gordon, Relative motions between oceanic plates of the Paci¢c Basin, J. Geophys. Res. 89 (1984) 10291^10310. [30] D.M. Jurdy, R.G. Gordon, Global plate motions relative to the hotspots 64 to 56 Ma, J. Geophys. Res. 89 (1984) 9927^9936. [31] J.M. Stock, P. Molnar, Some geometrical aspects of uncertainties in combined plate tectonics, Geology 11 (1983) 697^701. [32] S. Stein, R.G. Gordon, Statistical tests of additional plate boundaries from plate motion inversions, Earth Planet. Sci. Lett. 69 (1984) 401^412. [33] W. Harbert, A. Cox, Late Neogene motion of the Paci¢c plate, J. Geophys. Res. 94 (1989) 3052^3064. [34] A. Cox, D. Engebretson, Change in motion of Paci¢c plate at 5 Myr BP, Nature 313 (1985) 472^474. [35] P. Wessel, L.W. Kroenke, The geometric relationship between hotspots and seamounts: implications for Paci¢c hotspots, Earth Planet. Sci. Lett. 158 (1998) 1^18. [36] C. DeMets, S. Traylen, Motion of the Rivera plate since 10 Ma relative to the Paci¢c and North American plates and the mantle, Tectonophysics 318 (2000) 119^159. [37] A.B. Watts, J.K. Weissel, R.A. Duncan, R.L. Larson, Origin of the Louisville ridge and its relationship to the Eltanin fracture zone system, J. Geophys. Res. 93 (1988) 3051^3077. [38] D.A. Clague, G.B. Dalrymple, T.L. Wright, F.W. Klein, R.Y. Koyanagi, R.W. Decker, D.M. Thomas, The Hawaiian-Emperor chain, in: E.L. Winterer, D.M. Hussong, R.W. Decker (Eds.), The Eastern Paci¢c Ocean and Hawaii, The Geology of North America, Geological Society of America, Boulder, CO, 1989, pp. 187^287. [39] D.L. Desonie, R.A. Duncan, J.H. Natland, Temporal and geochemical variability of volcanic products of the Marquesas hotspot, J. Geophys. Res. 98 (1993) 17649^17665. [40] A.A.P. Koppers, 40 Ar/39 Ar Geochronology and Isotope
[41]
[42] [43]
[44] [45]
[46]
[47] [48] [49]
[50] [51] [52] [53]
Geochemistry of the West Paci¢c Seamount Province: Implications for Paci¢c Plate Motion and Chemical Geodynamics, Ph.D. Thesis, Vrije Universiteit, Amsterdam, 1998, 263 pp.. M.S. Pringle, G.B. Dalrymple, Geochronological constraints on a possible hot spot origin for Hess Rise and the Wentworth Seamount Chain, in: M.S. Pringle, W.W. Sager, W.V. Sliter, S. Stein (Eds.), The Mesozoic Paci¢c: Geology, Tectonics, and Volcanism, Monograph 77, American Geophysical Union, Washington, DC, 1993, pp. 279^305. E.L. Winterer, C.V. Metzler, Origin and subsidence of guyots in Mid-Paci¢c mountains, J. Geophys. Res. 89 (1984) 9969^9979. L.W. Kroenke, P. Wessel, Paci¢c plate motion between 125 and 90 Ma and the formation of the Ontong Java plateau, in: Conference on the History and Dynamics of Global Plate Motions, American Geophysical Union, Marshall, CA, 1997, p. 22. J.M. O'Connor, P. Sto¡ers, J.R. Wijbrans, Migration rate of volcanism along the Foundation chain, SE Paci¢c, Earth Planet. Sci. Lett. 164 (1998) 41^59. S.O. Schlanger, M.O. Garcia, B.H. Keating, J.J. Naughton, W.W. Sager, J.A. Haggerty, J.A. Philpotts, R.A. Duncan, Geology and Geochronology of the Line Islands, J. Geophys. Res. 89 (1984) 11261^11272. M.S. Pringle, Age progressive volcanism in the Musicians Seamounts: a test of the hot spot hypothesis for the late Cretaceous Paci¢c, in: M.S. Pringle, W.W. Sager, W.V. Sliter, S. Stein (Eds.), The Mesozoic Paci¢c: Geology, Tectonics, and Volcanism, Monograph 77, American Geophysical Union, Washington, DC, 1993, pp. 279^305. R.D. Van der Hilst, S. Widiyantoro, R.L. Engdahl, Evidence for deep mantle circulation from global tomography, Nature 386 (1997) 578^584. P. Olson, Drifting mantle hotspots, Nature 327 (1987) 559^560. M.A. Richards, Hotspots and the case against a uniform viscosity composition of the mantle, in: R. Sabadini, K. Lambeack (Eds.), Glacial Isostasy, Sea Level and Mantle Rheology, Kluwer Academic, Dordrecht, 1991, pp. 571^ 587. R.D. Jarrard, D.A. Clague, Implications of Paci¢c island and seamount ages for the origin of volcanic chains, Rev. Geophys. Space Phys. 15 (1977) 57^76. J.B. Minster, T.H. Jordan, Present-day plate motions, J. Geophys. Res. 83 (1978) 5331^5354. D.A. Clague, R.D. Jarrard, Tertiary Paci¢c plate motion deduced from the Hawaiian-Emperor chain, Geol. Soc. Am. Bull. 84 (1973) 1135^1154. D. York, Least squares ¢tting of a straight line with correlated errors, Earth Planet. Sci. Lett. 5 (1969) 320^324.
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Testing the ¢xed hotspot hypothesis using 40Ar/39 Ar age progressions along seamount trails Anthony A.P. Koppers a; *, Jason Phipps Morgan a , Jason W. Morgan b , Hubert Staudigel a a
Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0225, USA b Geosciences Department, Princeton University, Princeton, NJ 08544-1003, USA Received 21 August 2000; received in revised form 8 December 2000; accepted 10 December 2000
Abstract Hotspots and their associated intra-plate volcanism producing seamount trails have become an accepted fact in geology from a conceptual theory. The azimuths and age progressions of these seamount trails provide the only means to determine absolute plate motions with respect to an independent reference frame of `fixed' hotspots. However, the presumed fixity of hotspots is in disagreement with recent paleomagnetic studies and global-circuit plate reconstructions for the Hawaiian^Emperor seamount trail. In this study, we provide independent evidence suggesting that hotspots are not fixed relative to each other. We use a straightforward test that compares the observed 40 Ar/39 Ar age progressions along Pacific seamount trails (0^140 Myr) with the Pacific plate velocities as predicted by their poles of plate rotation (i.e. Euler poles). In most of these comparisons, the age progressions were found incompatible with published Euler poles, or with a new set of Euler poles as derived in this study using discrete seamount locations digitized from the bathymetry maps of Smith and Sandwell [EOS 77 (1996) 315; Science 277 (1997) 1956^1921]. We conclude that the relative motion between hotspots may be required to reconcile the observed age progressions with the predicted plate velocities from their modeled Euler poles. On average, the Pacific hotspots may show motion at 10^60 mm/yr over the last 100 Myr, partly attributed to individual hotspot motion, whereas systematic motion of these hotspots (due to true polar wander) may account for the remainder. ß 2001 Elsevier Science B.V. All rights reserved. Keywords: hot spots; movement; plate tectonics; Ar-40/Ar-39; geochronology; seamounts; Paci¢c Plate
1. Introduction The assumption that stationary hotspots underlie the Earth's lithospheric plates has been most
* Corresponding author. Fax: +1-858-534-8090; E-mail: [email protected]
important in the development of plate tectonics. According to the ¢xed hotspot hypothesis seamount trails are formed by volcanism penetrating the lithospheric plates whilst moving over `hotspots' of upwelling mantle (e.g. [1,2]). In turn, the azimuths and age progressions of seamount trails can be used to quantify plate motions with respect to an independent geospatial reference frame of hotspots in the mantle [3,4]. In such
0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 3 8 7 - 3
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Fig. 1. Paci¢c hotspot trails according to age range. For reference the currently active hotspots of the Paci¢c (circles) have been included. Most of the 0^43 Ma seamount trails can be associated with these hotspots, except for the Tuamotu seamount trails. Note that for the Hawaiian, Louisville, Easter, and Guadalupe seamount trails we have omitted seamounts younger to 5 Ma (see Section 3 for explanation). Abbreviations: AN = Anewetak; EM = Emperor; GL = Gilbert; HR = Hess Rise; IT = Ita Mai Tai; JP = Japanese; LI = Line Islands; LK = Liliuokalani; LV = Louisville; MA = Magellan; MP = Mid Paci¢c Mountains; MU = Musicians; NW = North Wake; RL = Ralik; RT = Ratak; SE = Seth; SR = Shatsky Rise; SW = South Wake; TM = Tuamotu; TO = Tokelau; TV = Tuvalu; WW = Wentworth.
quanti¢cations plate motions are assumed to be constant rotations of rigid, non-deforming plates around ¢xed poles of rotation (i.e. Euler poles) for distinct time periods (i.e. stage poles). Although, there is no doubt that hotspot melting represents the major means of intra-plate volcanism, the ¢xity of both hotspots and their associated Euler poles appears unlikely in the context of a dynamically convecting Earth [5^8]. Recent paleomagnetic studies [8^12] and global-circuit plate reconstructions [13^19] for the Hawaiian^Emperor seamount trail suggest that the Hawaiian hotspot may have experienced a motion of 10^40
mm/yr during the Emperor stage pole (80^43 Ma). The major objective of this paper is to further test the ¢xed hotspot hypothesis, in this case, by testing for compatibility between the observed 40 Ar/39 Ar age progressions along seamount trails on the Paci¢c plate (Fig. 1) and the locations of the Euler poles describing its absolute plate rotations. In this straightforward test, the Euler poles will be re-determined by minimizing the angular distances from the `best-¢t' Euler poles to the locations of individual seamounts, as digitized from the bathymetric maps of Smith and Sandwell
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([20,21]; Appendix 1, EPSL Online Background Dataset1 ). Because the `best-¢t' Euler poles are geometrically derived using seamount locations exclusively, the age progressions along seamount trails (i.e. local plate velocities) provide an independent check for the angular distance of individual hotspots to the `best-¢t' Euler poles. We will show that the local Paci¢c plate velocities are not compatible with the angular plate velocities as predicted by the `best-¢t' Euler poles ([22]; this study) or with any previously published Euler poles ([3,7,23^28]; Appendix 2, EPSL Online Background Dataset1 [50^52]). This may indicate that the presumed ¢xity of hotspots is invalid within the limits of these tests ^ allowing for possible motions between individual hotspots of the Paci¢c hotspot system. 2. Least squared derivation of Euler poles using discrete seamount locations One approach in determining an Euler pole is based on the measurement of spatial trends in seamount trails. When using these azimuths one is, however, limited by the small number of available seamount trails. An alternative approach for the least squared derivation of Euler poles is presented here using the locations of discrete seamounts within multiple seamount trails or segments. This purely geometrical approach was previously used to determine Euler poles for relative plate motion using digitized points on fracture zones [23]. One of its advantages is the increased number of possible observations. Another advantage is the improved reliability of the uncertainty estimates. More importantly, the derivation of Euler poles is not controlled by the observed age progressions along the studied seamount trails. The age progressions along seamount trails, therefore, may serve as an independent check to the location of an Euler pole as based on the ¢xed hotspot hypothesis.
1
http://www.elsevier.nl/locate/epsl; www.elsevier.com/locate/epsl
mirror
site:
http://
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Fig. 2. Geometrical derivation of Euler poles based on the location of individual seamounts. Trial pole E depicts the `best-¢t' Euler pole, whereas trial pole EP depicts a `mis¢t' pole with a sum of squared deviations signi¢cantly larger than zero.
2.1. Formulation of the least squared model Fig. 2 illustrates the least squared model used to determine Euler poles for absolute plate motion. The seamount locations within two co-polar seamount trails A and B are plotted as small circles around their `best-¢t' Euler pole E. Because the angular distances d between each seamount i in seamount trail A and the Euler pole E are of equal length, their sum of squared deviations from the mean angular distance becomes zero. The same relation holds for seamount trail B, and because seamount trails A and B are copolar, the `best-¢t' Euler pole is de¢ned by a minimum in their total sum of squared deviations. Its location can be derived by an inversion of seamount locations using a least squared algorithm which minimizes the variance in the calculated angular distances: vard ij
M X N X 1 j1
N i1
U d ji 3d jmean 2
1
where N is the number of seamounts (independent observations) per seamount trail and M is the number of trails. This variance is equal to the squared RMS error for the motion of lithospheric
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plates [29,30]. Analyzing each seamount location with reference to the mean angular distance of its representative seamount trail avoids biasing of the analysis. The `best-¢t' poles were found by grid searching in the northern hemisphere. The search areas were narrowed around these poles in four subsequent searches using increased grid resolutions (2³, 0.5³, 0.1³ and 0.02³). The distribution of the variances is contoured in latitude^longitude space (Fig. 3).
2.2. Uncertainties and bootstrapping All seamount locations were retrieved by digitization of the predicted bathymetry maps of Smith and Sandwell ([20,21]; Appendix 1, EPSL Online Background Dataset1 ). The scatter in the location of the seamounts perpendicular to the line of age progression is re£ected in the variance for the calculated angular distances. No scaling was performed because scaling by the number of
Fig. 3. Improved `best-¢t' Euler poles for absolute Paci¢c plate motion. Contours in the polar plots draw the distributions of the most probable least squared solutions and show the `best-¢t' Euler pole at their center point (black circles). These contours are arbitrarily set at 5% of the minimal variance; outer contours therefore represent variances 25% higher than that for the `best-¢t' pole. Published rotation poles (hexagonal symbols) are included together with the location of the processed seamount locations. The seamount trails are identi¢ed in the legends. Contours in the insets display con¢dence regions based on statistical F tests at the 65^95^99% con¢dence levels. The insets also display the `best-¢t' Euler poles obtained by the bootstrap method (open circles), its mean (gray squares), the 99% con¢dence ellipse around this mean (dark gray line), and alternative models. Modeling results are summarized in Tables 1 and 3. Seamount locations, previously published rotation poles, and a further discussion of the data are available in Appendices 1^3, EPSL Online Background Dataset1 . Abbreviations: EP84 = Epp, 1984 [23]; EP85 = Engebretson et al., 1985 [24]; HP85 = Henderson, 1985 [25]; DpCP85 = Duncan and Clague, 1985 [3]; LP88 = Lonsdale, 1988 [26]; YpKP93 = Yan and Kroenke, 1993 [27]; WpKP97 = Wessel and Kroenke, 1997 [28]; MP97 = Morgan (unpublished); SP00 = Steinberger, 2000 [7].
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seamounts (or seamount trail length) would preferentially ¢t the longest seamount trails, resulting in an undesired loss of plate motion information from the shorter seamount trails. The variance about the `best-¢t' Euler pole is a measure of the goodness of ¢t to the seamount locations. The contoured variances in Fig. 3, therefore, represent the most likely distributions of solutions for the Euler poles at 5% intervals. The shape and elongation of these distributions are largely dependent on the number of seamounts, the length of the seamount trails and the position of these trails with respect to the Euler pole (cf. [29,31]). The con¢dence regions on the 65^95^99% con¢dence levels (Fig. 3, insets) were constructed using a statistical F ratio test following the methodology of Engebretson et al. [29,32,33]. When presuming normal distributions
241
in a linear system, the F test determines if the variance of `trial' Euler pole Etrial is signi¢cantly greater than the minimum variance of the `best-¢t' Euler pole Ebest : X varE trial 3varE best U p R 2 varE best where X = pN3p equals the degrees of freedom and p is the number of adjustable parameters in the model (in this case, latitude^longitude, p = 2). The R ratio corresponds to standard F ratio tables at the desired con¢dence level with (p,X) degrees of freedom. Application of the bootstrap method was used to test the robustness of the reconstructed `best¢t' Euler poles. Alternative `bootstrap' Euler poles were calculated ignoring each seamount trail
Fig. 3 (continued).
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and each pair of trails once during the reconstructions, resulting in 1/2M2 31/2M solutions, where M is the number of seamount trails. If all modeled seamount trails belong to the same stage pole
and M is su¤ciently large, the location of the `mean-bootstrap' pole is expected to be similar to the `best-¢t' Euler pole at the 99% con¢dence level.
Fig. 3 (continued).
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3. Results The most recent stage pole models include at least 11 di¡erent Euler poles to describe absolute
243
Paci¢c plate motion (cf. [28]). Additional poles were incorporated in these models to improve the ¢t to the Hawaiian^Emperor and Louisville seamount trails with possible changes in plate mo-
Fig. 3 (continued).
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Table 1 Results from the least squared derivation of Paci¢c plate Euler poles Euler pole Lat. Long. Hawaiian stage pole Total pole best-¢t bootstrap scaled 20^0 Ma best-¢t bootstrap
67.1 67.1 67.9 70.1 70.1
294.5 294.7 296.8 302.0 302.0
Emperor stage pole Total pole best-¢t bootstrap scaled w/o Emperor best-¢t bootstrap
18.8 20.2 19.9 25.6 24.9
253.6 256.6 252.5 272.4 268.7
w/o Louisville
best-¢t bootstrap
100^80 Ma stage pole Total pole best-¢t bootstrap scaled 110^100 Ma stage pole Total pole best-¢t scaled w/o Mid-Pac best-¢t scaled 125^110 Ma stage pole Total pole best-¢t bootstrap scaled 140^125 Ma stage pole Total pole best-¢t
Best-¢t con¢dence regions Var
M
N
0.22
21
346 231
0.15
19
293 190
0.15
8
122 36
0.11
7
99 28
21.4 248.8 21.5 248.4
0.11
7
100 28
40.6 259.8 40.2 258.1 39.4 254.5
0.10
10
92 55
74.1 101.8 74.5 102.9 75.1 44.8 75.2 44.5
0.13
5
95
0.04
3
41
0.09
4
47
0.20
3
41
65.3 273.2 65.7 268.5 67.2 268.9 7.7
33.1
Longitude
Latitude
Min
Max
Min Max Lat. Long.
Extreme points Lat. Long.
0.65% 0.95% 0.99% 0.65% 0.95% 0.99%
292.5 291.2 290.4 299.9 298.5 297.6
296.3 297.7 298.5 304.0 305.6 306.5
66.7 66.4 66.2 69.7 69.5 69.3
67.5 67.8 68.0 70.5 70.7 70.9
66.9 66.8 66.7 69.9 69.7 69.6
292.5 291.2 290.4 299.8 298.3 297.4
67.3 67.4 67.5 70.2 70.3 70.5
296.4 297.8 298.6 304.2 305.8 306.7
0.65% 0.95% 0.99% 0.65% 0.95% 0.99% 0.65% 0.95% 0.99%
252.6 251.9 251.5 274.7 276.3 277.4 247.9 247.2 246.8
254.6 255.3 255.8 270.2 268.6 267.7 249.7 250.4 250.8
18.2 17.8 17.5 24.8 24.3 24.0 20.9 20.5 20.2
19.5 19.9 20.2 26.3 26.8 27.2 22.0 22.4 22.6
19.2 19.4 19.3 24.7 23.9 23.5 21.8 22.1 22.2
252.6 251.9 251.4 269.1 266.8 265.3 247.8 247.1 246.6
18.6 18.3 18.3 26.5 27.0 27.3 21.1 20.7 20.6
254.6 255.3 255.8 275.7 278.1 279.6 249.8 250.5 251.0
0.65% 0.95% 0.99%
254.3 249.8 246.7
264.5 267.6 269.4
39.7 41.4 41.3 252.0 39.1 42.0 41.6 246.9 38.7 42.4 41.6 243.9
39.1 268.1 37.7 274.3 36.6 278.1
For the `best-¢t' pole the 65^95^99% con¢dence regions are de¢ned based on F ratio tests by: (1) the min and max longitude at the latitude of the Euler pole, (2) the min and max latitude at the longitude of the Euler pole, and (3) the extreme points of the error regions. These parameters were used to construct the non-ellipsoid error regions in the insets of Fig. 3. M = number of seamount trails; N = total number of seamounts for the `best-¢t' pole or the number of solutions for the `bootstrap' pole. Var = variance as calculated from Eq. 2.
tion around 3^5 Ma, 12^15 Ma, 17^20 Ma, and 65 Ma. In our study, a ¢rst order stage pole model is investigated following Henderson [25] for the last 100 Myr (43^0, 80^43 and 100^80 Ma). The change in plate motion around 3^5 Ma [28,34,35] is ignored since it seems in disagreement with plate motion of the North American plate [36]. Plate motion prior to 100 Ma (110^100, 125^110 and 140^125 Ma) follows the stage pole model of Wessel and Kroenke [28]. The results are illus-
trated in the polar plots of Fig. 3 and listed in Table 1 and Table 3; results for Euler poles older than 100 Ma are discussed in Appendix 3 of the EPSL Online Background Dataset1 [42,43]. 3.1. Euler pole: 43^0 Ma Seventeen seamount trails were included in the calculation of the Euler pole (67³07P N, 294³28P E) belonging to the so-called Hawaiian stage pole
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Table 2 Local plate velocities for the Paci¢c plate between 0 and 140 Ma Data Seamount trail Hawaiian stage pole Hawaii [38] Hawaii [38] Bowie [3] Cobb [3] Pitcairn [3] Society [3] Austral-Cook [3] Caroline [3] Samoa [3] Foundation [44] Louisville based on [37] Emperor stage pole Emperor [38] Emperor [38] Louisville based on [37] Louisville based on [37] Line [45] 100^80 Ma stage pole Magellan [22] Line [46] Musicians [22] Wentworth [41] 125^110 Ma stage pole Japanese [40]
Regression Age range (Ma) 43.4^0 12.3^0 24.8^0 25.7^0 8.1^0.5 4.5^0 19.6^0 13.9^1.0 27.7^0 21.2^0.9 45.5^0.5
Calculation type
Style
Plate velocity (mm/yr)
maximum ages
YORK 2 YORK 2 Linear Linear Linear Linear Linear Linear Linear Linear YORK 2
92 þ 3 96 þ 4 67 þ 20 57 þ 20 127 þ 55 109 þ 10 107 þ 16 121 þ 39 72 þ 23 91.1 þ 2.0 60.5 þ 2.0
YORK YORK YORK YORK Linear
2 2 2 2
72 þ 11 68 þ 3 61.2 þ 1.2 64.4 þ 4.8 96 þ 4
YORK 2 YORK 2 YORK 2
47.6 þ 1.6 66 þ 25 55.8 þ 6.4 70
YORK 2
48.1 þ 4.5
maximum ages recombined ages
64.7^43.4 64.7^19.9 66.3^0.5 66.3^35.5 93.4^47.4
recombined ages recombined ages
95.2^87.1 93.4^81.0 95.4^82.3 93.4^86.4
recombined ages recombined ages 2 data points
118.1^103.7
recombined ages
When available the style of data regression, the type of seamount ages included in the age progressions and the standard deviations are denoted. The calculations were not forced through the origin; YORK 2 = York, 1969 [53].
between 43 and 0 Ma. This `best-¢t' Euler pole has an overall variance of 0.22 and agrees with the `mean-bootstrap' pole (67³07P N, 294³40P E). Scaling by the number of seamounts in each trail only results in a minor shift in the location of the `best-¢t' Euler pole. However, the bootstrap results show two noteworthy deviations: (1) a longitudinal shift of the Euler pole when excluding Hawaiian seamounts 43^20 Myr old, and (2) a latitudinal shift when excluding similar seamounts from the Louisville seamount trail. The remaining bootstrap poles fall within the 99% con¢dence region around the total Euler pole. For this reason, we calculated a separate Paci¢c plate Euler pole for the 20^0 Ma Hawaiian stage pole. This yields a signi¢cantly changed Euler pole (70³05P N, 301³58P E) with a lower variance (0.15) that is shifted to the north when compared to: (1) the
total Hawaiian Euler pole and (2) all published Euler poles. The 43^20 Ma Euler pole was not re-modeled since only two seamount trails (Hawaii and Louisville) represent this stage pole [37,38]; this Euler pole is best approximated by the total pole at 67³07P N, 294³28P E. 3.2. Euler pole: 80^43 Ma The Emperor stage pole (80^43 Ma) was modeled using eight seamount trails resulting in a `best-¢t' Euler pole (18³50P N, 253³35P E) with a variance of 0.15. Despite the low variance, the distribution of bootstrap poles yields a poorly de¢ned and di¡erent `mean-bootstrap' pole (20³13P N, 256³37P E). When eliminating the Emperor or the Louisville seamount trails, the models give lower variances (0.11) and better constrained
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`mean-bootstrap' poles. The pole with the lowest variance (21³25P N, 248³47P E) was obtained when excluding Louisville seamount trail, and is in accordance with its `mean-bootstrap' Euler pole (21³28P N, 248³26P E). This may indicate that the azimuth of Louisville Ridge was indeed changed due to a major o¡set in the Eltanin fracture zone between 60 and 80 Ma [37]. Such kinematic interactions of hotspots with fracture zones are believed to cause azimuthal deviations up to 15^30³ according to studies of the Tuamotu^Pitcairn hotspot [38] and the Marquesas hotspot [39]. 3.3. Euler pole: 100^80 Ma Eight seamount trails yield a `best-¢t' Euler pole at 40³34P N, 259³47P E for the 100^80 Ma stage pole. The variance is low (0.10) but the associated con¢dence regions are more extended when compared to those of the Hawaiian and Emperor Euler poles. This seems an e¡ect of the limited regional extension of the short seamount trails included in this calculation. However, most of the bootstrap poles fall within the 99% con¢dence region suggesting that the least squared modeling resulted in a self-consistent `best-¢t' Euler pole for the 100^80 Ma stage pole. 4. Discussion Seven stage poles were determined that describe the absolute rotation of the Paci¢c plate over the last 140 Myr. In this discussion, these `best-¢t' Euler poles will be tested for their compatibility with the observed 40 Ar/39 Ar age progressions measured along co-polar seamount trails. The ¢xed hotspot hypothesis predicts that each of these age progressions (i.e. local plate velocities; Table 2) should give comparable estimates for the angular plate velocity. The latter prediction can only be tested when the Euler poles are derived independently from the age progressions along the seamount trails. This was accomplished in this study by using an entirely geometric approach for the derivation of Euler poles. We therefore can use the recorded 40 Ar/39 Ar age progressions
to de¢ne independent distributions for the location of these seven Euler poles. 4.1. Test of the ¢xed hotspot hypothesis In Fig. 4 the 65^95% con¢dence regions (open^ closed circles) depict which Euler poles are compatible with the observed local plate velocities (Table 2). These con¢dence regions were constructed by grid-searching in the northern hemisphere while calculating the angular velocities (and their standard deviations) for each trial Euler pole using the age progressions of the modeled seamount trails. This was done using the relationship : e = g sin dmean T, where e is the linear local plate velocity, dmean is the average angular distance of a seamount trail to its Euler pole, and g is the velocity of angular rotation. Whenever the modeled angular velocities were similar at the desired con¢dence level, the Euler poles were accepted. The modeled velocity regions, therefore, depict an independent distribution of potential Euler poles and can be directly contrasted to locations of the geometrically derived `best-¢t' Euler poles (Fig. 3). An inconsistency arises when cross-checking the location of the 100^80 Ma Euler pole with the local plate velocities derived from the Magellan and Musicians seamount trails (cf. [22]). Neither the published Euler poles nor the `best-¢t' Euler pole agree with the modeled velocity region (Fig. 4). We may de¢ne a `forced' Euler pole (29³ N, 297³ E) from the intersection of the Euler pole distribution derived from the seamount locations (Fig. 3) and the calculated velocity region (Fig. 4). This `forced' Euler pole, however, is located V35³ away from the `best-¢t' Euler pole at 40³34P N, 259³47P E. This observation may indicate that the age progressions can only be reconciled with the `best-¢t' Euler pole, when allowing for the relative movement of the Magellan and Musicians hotspots with respect to one another [22]. For the Hawaiian (43^0 Ma) and Emperor stage poles (80^43 Ma) similar tests were conducted. The tests for the Hawaiian stage pole include the Emperor, Louisville and Foundation hotspots. The Hawaiian chain has been inten-
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Fig. 4. Testing the ¢xed hotspot hypothesis. These diagrams display independent distributions of Euler poles calculated from the age progressions in two co-polar seamount trails accepting the ¢xed hotspot hypothesis. Open and closed circles represent 65% and 95% con¢dence levels, respectively. If the tested hotspots are truly ¢xed with respect to each other, then these distributions should overlie the locations of the `best-¢t' Euler poles based on seamount locations (circles with 99% con¢dence regions; Table 1) or the published Euler poles (hexagonal symbols). Note that, in case of the 43^0 Ma stage pole, the 99% error regions are smaller than the actual symbols depicting the `best-¢t' Euler poles (circles in squares).
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sively dated by 40 Ar/39 Ar techniques resulting in an average age progression of 92 þ 3 mm/yr over the last 43 Myr [38]. The Foundation seamount trail is de¢ned by small, monogenetic seamounts and yields the most accurate age progression in the Paci¢c of 91.1 þ 2.0 mm/yr [44]. The Louisville seamount trail has an age progression of 60.5 þ 2.0 mm/yr; but its accuracy is limited by a low sample density for seamounts younger than 43 Ma [37]. From Fig. 4 it follows that the observed age progressions for the Hawaiian and Foundation seamount trails are compatible with the `best-¢t' Euler poles and most of the previously published Euler poles at the 65^95% con¢dence level. The Hawaiian and Foundation hotspots may, consequently, be considered ¢xed with respect to each other. The tests including the Louisville seamount trail, however, yield con¢dence regions that are signi¢cantly di¡erent from these Euler poles. For example, an increase in the apparent local plate velocity from 60.5 to 73 mm/yr at the Louisville seamount trail would be required to achieve concordant results in all three cases. If ignoring the low sample density at the Louisville seamount trail, then this discrepancy could be explained by the independent motion of the Louisville hotspot by V12 mm/yr (sub)parallel to the direction of Paci¢c plate motion. This is in accord with the predicted V9 mm/yr motion of the Louisville hotspot [5^7]. The tests for the Emperor stage pole include the Emperor, Louisville and Line hotspots. The Emperor and Louisville seamount trails have been well dated with 40 Ar/39 Ar techniques and yield age progressions of 68 þ 3 mm/yr and 61.2 þ 1.2 mm/yr, respectively [37,38]. Dating of the Line Islands focused only on the time period between 90 and 65 Ma [45]. Nonetheless, an overall age progression of 96 þ 4 mm/yr was proposed for its Emperor stage pole [23,45]. From Fig. 4 it follows that the Emperor and Louisville seamount trails may be in accord with the `best-¢t' Euler poles at the 95% con¢dence level. The poor resolution is not only a function of the precision for the age progressions, but also results from the similarity in the local plate velocities and the fact that the Emperor and Louisville seamount trails are located at comparable angular distances to the pre-
ferred Euler pole (72.8 þ 0.3; 80.8 þ 0.5). Both tests including the Line Islands show marked deviations from the `best-¢t' Euler poles. The displayed narrow distributions are the result of the pronouncedly higher local plate velocity at the Line Islands and its shorter angular distance to the Euler pole (54.1 þ 0.3). Since none of the three test cases yielded concordant results at the 65% con¢dence level, it seems likely that the Emperor, Louisville and Line hotspots have moved relative to each other. Alternatively, the uncertainties in the age progressions (Table 2) may be too precise; they may not entirely re£ect their true geological uncertainties, including the prolonged volcanic evolution of individual seamounts, rejuvenation by younger hotspots and uncertainties in the actual location of the hotspot underneath seamount trails. 4.2. Hotspot motion in velocity space In Fig. 5 the above tests are plotted in velocity space displaying possible combinations of hotspot motion at the 65^95% con¢dence levels. Every combination of coexistent hotspot motion falling within these con¢dence regions reconciles the apparent age progressions with the `best-¢t' Euler poles. Fixed hotspots are represented by the origin, whereas hotspot motions anti-parallel to plate motion are represented by negative velocities. It follows that the scenarios for hotspot motion represent non-unique solutions. Additional geological constraints are required to quantitatively resolve inter-hotspot motions. Hotspot motion anti-parallel to plate motion should be prevalent [6] when considering the fact that (whole) mantle convection seems primarily driven by subduction over the last 100 Myr (e.g. [47]). For the 100^80 Ma stage pole (Fig. 5) this may rule out the scenario based on a ¢xed Musicians hotspot and the motion of the Magellan hotspot in the direction of plate motion. It also may suggest that anti-parallel motion of the Musicians hotspot is between 12 and 24 mm/yr (Fig. 5). This is a minimum estimate given that the Magellan hotspot may have experienced antiparallel hotspot motion as well. Two assumptions are required: (1) subduction of the Paci¢c plate
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Fig. 5. Hotspot motion in velocity space. The origin represents truly ¢xed hotspots; positive and negative velocities represent hotspot motion parallel and anti-parallel to the direction of plate motion (in mm/yr). The modeled 65^95% con¢dence envelopes depict all possible combinations of hotspot motion for two co-polar seamount trails compatible with both the improved Euler poles from Table 3 and the observed age progressions from Table 2 including standard errors. Independent estimates for the motion of hotspots based on paleolatitude studies (65^95% con¢dence boxes) and mantle £ow modeling are added (see diagrams for references).
249
beneath the Asian plate was more important than subduction of the Kula plate during the 100^80 Ma stage pole, and (2) hotspot motion was aligned to Paci¢c plate motion. Hotspot motion perpendicular to plate motion does not induce changes in the local plate velocities at co-polar seamount trails. Instead, it would induce changes in the location of the Euler pole. Consistency within the modeling results for the 100^80 Ma Euler pole implies that the orientations of the Magellan and Musicians seamount trails are not signi¢cantly di¡erent. The detected discrepancy in their local plate velocities, thus, may indicate that the (major) component of hotspot motion was parallel to plate motion. For the Emperor stage pole (Fig. 5) the age progressions are incompatible with the ¢xed hotspot hypothesis ; inter-hotspot motion seems to be required. The modeled coexistent motion of the Louisville and Emperor hotspots is compatible with independently derived estimates from paleolatitude and global-circuit plate studies (Fig. 5). However, the Line hotspot cannot be reconciled with these estimates, which suggests an additional component of hotspot motion, provided that the local plate velocity of 96 þ 4 mm/yr [45] is an accurate estimate. For the Hawaiian stage pole, the Foundation and Hawaiian hotspots may obey the ¢xed hotspot hypothesis because their 95% con¢dence envelope intersects the origin in Fig. 5. Note that the Foundation and Hawaiian hotspots may not necessarily be ¢xed with respect to the deep mantle, but only with respect to each other. Other combinations of hotspot motion may also be compatible with their observed 40 Ar/39 Ar age progressions and 43^0 Ma Euler pole. Estimates from paleolatitude studies are again comparable with the presented relation of `true' motion between these hotspots (Fig. 5). The estimates of Steinberger and O'Connell [6] for the motion of the Louisville hotspot (V9 mm/yr) and the Hawaiian hotspot (V12 mm/yr) are di¡erent since they fall slightly below the con¢dence envelopes in Fig. 5. 4.3. Absolute Paci¢c plate motion Angular plate velocities should be estimated
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Table 3 Preferred stage pole model for the Paci¢c plate Stage pole 20^0 Ma 43^20 Ma 43^80 Ma 100^80 Ma 110^100 Ma 125^110 Ma 140^125 Ma
Euler pole
Rotation
Lat.
Long.
Var
70.1 67.1 18.8 40.6 75.1 65.3 7.7
302.0 294.5 253.6 259.8 44.8 273.2 33.1
0.15 0.22 0.15 0.10 0.04 0.09 0.20
M 19 21 8 10 3 4 3
N
Vel
Deg
Comments
293 346 122 92 41 47 41
0.881 þ 0.016 0.502^0.478 0.657 þ 0.029 0.425 þ 0.014 0.44 0.449 þ 0.042 0.49
17.6 þ 0.3 13.3^11.0 24.3 þ 1.1 8.5 þ 0.3 4.4 6.7 þ 0.6 9.8
weighted average Foundation+Hawaii models 1^3 of Steinberger and O'Connell [6] minimum Emperor seamount trail minimum Magellan seamount trail average Magellan+Japanese seamount trail minimum Japanese seamount trail Wessel and Kroenke [28]
Vel = angular velocity in ³/Myr; Deg = angular rotation for the total stage pole. Standard deviations on the angular velocities and the angular rotation were estimated from the standard errors on the observed local plate velocities (Table 2) and the standard deviations on the angular distance to the Euler pole. For error regions of the `best-¢t' Euler pole and abbreviations see Table 1.
considering the motion of hotspots so that they solely re£ect plate motions (cf. [7]). To achieve such estimates, we calculated the angular velocities based on the average angular distance of the seamount trail to the modeled `best-¢t' Euler pole. These calculations include the propagation of errors in the angular distance to the Euler pole (standard deviation) and the age progression (standard error; Table 2). If all calculated angular velocities for one speci¢c stage pole are similar at the 65% con¢dence level, then the average angular velocity represents an estimate for its true angular plate velocity. If no evidence exists for the (relative) ¢xity of co-polar hotspots then minimum angular velocities were estimated. In Table 3 we present our preferred stage pole model for the Paci¢c plate over the last 140 Myr including the `best-¢t' Euler poles derived using the geometric method and the new estimates for the angular plate velocities. 5. Summary and conclusions Seamount locations were used to derive Euler poles describing the direction of Paci¢c plate motion over the last 140 Myr. This was done by minimizing the angular distances between these seamounts and the Euler pole with respect to an average angular distance for each seamount trail. As a result, this geometric method yields reliable estimates for Euler poles based on seamount locations exclusively. The modeled Euler poles sub-
sequently were used to predict their associated angular plate velocities and to compare these with the observed 40 Ar/39 Ar age progressions, in order to test the ¢xed hotspot hypothesis. Only the Hawaiian and Foundation hotspots appear to be ¢xed with respect to each other over the last 20 Myr; in most other cases, the estimated plate velocities were signi¢cantly di¡erent at the 65^95% con¢dence levels. One possible explanation is that these discordances are caused by relative motion between hotspots in a direction subparallel to plate motion. The possible motion of hotspots was found to be consistent with the independent estimates on hotspot motion using the di¡erence in paleolatitude for the Emperor seamount trail [8^12], global-circuit plate motion models [13^19] and mantle £ow modeling [5^7]. Combining these independent estimates with the relations of hotspot motion in velocity space suggests hotspot motion in the order of 10^60 mm/yr over the last 100 Myr. The possibility for hotspot motion may have contrasting implications for mantle geodynamics. Hotspot motion anti-parallel to plate motion can be explained by the kinematic return £ow in the deep mantle [48] as driven by the slab-pull of subducting lithospheric plates. Hotspot motion parallel to plate motion can only be explained by densitydriven mantle convections, but this would require much lower viscosities in the upper mantle [6,49]. We emphasize, however, that age progressions along seamount trails still carry signi¢cant geological and analytical uncertainties. Within the
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limits of these data, we concluded here that hotspots are not necessarily ¢xed with respect to each other, and that our proposed relative hotspot motions are consistent with independent geodynamic models. However, more importantly, we were able to develop and use quantitative methods to determine uncertainties in stage pole de¢nitions and plate motion models based on age progressions in linear island chains. Ultimately, such quantitative methods will allow us to continue building and re¢ning plate motion models as additional and more accurate data become available.
[8] [9] [10] [11] [12]
[13]
Acknowledgements We thank Dave Sandwell for his help with GMT. Jan Wijbrans is thanked for his comments on the manuscript. We thank Gary Acton and Bill Harbert for their reviews. This paper is an outgrowth of A.A.P.K.s Ph.D. thesis at the Vrije Universiteit in Amsterdam, The Netherlands. Financial support by the Netherlands Foundation of Earth Sciences Research (GOA-NWO 750.60.005), Netherlands Science Foundation (NWO-TALENT grant to A.A.P.K.) and National Science Foundation (NSF-OCE 91-02183 and 97-30394).[RV]
[14]
References
[19]
[1] J.T. Wilson, A possible origin of the Hawaiian Islands, Can. J. Phys. 41 (1963) 863^870. [2] W.J. Morgan, Deep mantle convection plumes and plate motions, Am. Assoc. Petrol. Geol. Bull. 56 (1972) 42^43. [3] R.A. Duncan, D.A. Clague, Paci¢c plate motion recorded by linear volcanic chains, in: A.E.A. Nairn, F.L. Stehli, S. Uyeda (Eds.), The Ocean Basins and Margins, The Paci¢c Ocean 7A, Plenum Press, New York, 1985, pp. 89^121. [4] W.J. Morgan, Hotspot tracks and early rifting of the Atlantic, Tectonophysics 94 (1983) 123^139. [5] B. Steinberger, R.J. O'Connell, Changes of the Earth's rotation axes owing to advection of mantle density heterogeneities, Nature 387 (1997) 169^173. [6] B. Steinberger, R.J. O'Connell, Advection of plumes in mantle £ow: implications for hotspot motion, mantle viscosity and plume distribution, Geophys. J. Int. 132 (1998) 412^434. [7] B. Steinberger, Plumes in a convecting mantle: models
[15]
[16] [17]
[18]
[20] [21] [22]
[23] [24]
251
and observations for individual hotspots, J. Geophys. Res. 105 (2000) 11127^11152. U. Christensen, Fixed hotspots gone with the wind, Nature 391 (1998) 739^740. R.G. Gordon, C.D. Cape, Cenozoic latitudinal shift of the Hawaiian hotspot and its implications for true polar wander, Earth Planet. Sci. Lett. 55 (1981) 37^47. W.W. Sager, U. Bleil, Latitudinal shift of Paci¢c hotspots during the late Cretaceous and early Tertiary, Nature 326 (1987) 488^490. J.A. Tarduno, J. Gee, Large-scale motion between Paci¢c and Atlantic hotspots, Nature 378 (1995) 477^480. J.A. Tarduno, R.D. Cottrel, Paleomagnetic evidence for motion of the Hawaiian hotspot during formation of the Emperor seamounts, Earth Planet. Sci. Lett. 153 (1997) 171^180. P. Molnar, J. Stock, Relative motions of hotspots in the Paci¢c, Atlantic and Indian Oceans since late Cretaceous time, Nature 327 (1987) 587^591. G.D. Acton, R.G. Gordon, Paleomagnetic tests of Paci¢c plate reconstructions and implications for motion between hotspots, Science 263 (1994) 1246^1254. S.C. Cande, C.A. Raymond, J. Stock, W.F. Haxby, Geophysics of the Pitman fracture zone and Paci¢c-Antarctic plate motions during the Cenozoic, Science 270 (1995) 947^953. I.O. Norton, Plate motions in the North Paci¢c: the 43 Ma nonevent, Tectonics 14 (1995) 1080^1094. I.O. Norton, Hotspot tracks and reference frames don't mix, in: Conference on the History and Dynamics of Global Plate Motions, American Geophysical Union, Marshall, CA, 1997, p. 23. C.A. Raymond, J.M. Stock, S.C. Cande, Relative hotspot motion based on global plate reconstructions, in: Conference on the History and Dynamics of Global Plate Motions, American Geophysical Union, Marshall, CA, 1997, p. 25. V. DiVenere, D.V. Kent, Are the Paci¢c and Indo-Atlantic hotspots ¢xed? Testing the plate circuit through Antarctica, Earth Planet. Sci. Lett. 170 (1999) 105^117. W.H.F. Smith, D. Sandwell, Predicted bathymetry. New global sea£oor topography from satellite altimetry, EOS 77-46 (1996) 315. W.H.F. Smith, D. Sandwell, Global sea £oor topography from satellite altimetry and ship depth soundings, Science 277 (1997) 1956^1962. A.A.P. Koppers, H. Staudigel, J.R. Wijbrans, M.S. Pringle, The Magellan seamount trail: implications for Cretaceous hotspot volcanism and absolute Paci¢c plate motion, Earth Planet. Sci. Lett. 163 (1998) 53^68. D. Epp, Possible perturbations to hotspot traces and implications for the origin and structure of the Line Islands, J. Geophys. Res. 89 (1984) 11273^11286. D. Engebretson, A. Cox, R. Gordon, Relative Motions between Oceanic and Continental Plates in the Paci¢c Basin, Geological Society of America Special Paper 206, 1985.
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A.A.P. Koppers et al. / Earth and Planetary Science Letters 185 (2001) 237^252
[25] L.J. Henderson, Motion of the Paci¢c Plate Relative to the Hotspots since the Jurrasic and Model of Oceanic Plateaus of the Farallon Plate, Ph.D. Thesis, Northwestern University, USA, 1985. [26] P. Lonsdale, Geography and history of the Louisville hotspot chain in the Southwest Paci¢c, J. Geophys. Res. 93 (1988) 3078^3104. [27] C.Y. Yan, L.W. Kroenke, A plate tectonic reconstruction of the southwest Paci¢c, 0^100 Ma, in: W.H. Berger, L.W. Kroenke, L.A. Mayer et al. (Eds.), Proceedings of the Ocean Drilling Program, Scienti¢c Results: 130. Ocean Drilling Program, College Station, TX, 1993, pp. 697^709. [28] P. Wessel, L. Kroenke, A geometric technique for relocating hotspots and re¢ning absolute plate motions, Nature 387 (1997) 365^369. [29] D.C. Engebretson, A. Cox, R.G. Gordon, Relative motions between oceanic plates of the Paci¢c Basin, J. Geophys. Res. 89 (1984) 10291^10310. [30] D.M. Jurdy, R.G. Gordon, Global plate motions relative to the hotspots 64 to 56 Ma, J. Geophys. Res. 89 (1984) 9927^9936. [31] J.M. Stock, P. Molnar, Some geometrical aspects of uncertainties in combined plate tectonics, Geology 11 (1983) 697^701. [32] S. Stein, R.G. Gordon, Statistical tests of additional plate boundaries from plate motion inversions, Earth Planet. Sci. Lett. 69 (1984) 401^412. [33] W. Harbert, A. Cox, Late Neogene motion of the Paci¢c plate, J. Geophys. Res. 94 (1989) 3052^3064. [34] A. Cox, D. Engebretson, Change in motion of Paci¢c plate at 5 Myr BP, Nature 313 (1985) 472^474. [35] P. Wessel, L.W. Kroenke, The geometric relationship between hotspots and seamounts: implications for Paci¢c hotspots, Earth Planet. Sci. Lett. 158 (1998) 1^18. [36] C. DeMets, S. Traylen, Motion of the Rivera plate since 10 Ma relative to the Paci¢c and North American plates and the mantle, Tectonophysics 318 (2000) 119^159. [37] A.B. Watts, J.K. Weissel, R.A. Duncan, R.L. Larson, Origin of the Louisville ridge and its relationship to the Eltanin fracture zone system, J. Geophys. Res. 93 (1988) 3051^3077. [38] D.A. Clague, G.B. Dalrymple, T.L. Wright, F.W. Klein, R.Y. Koyanagi, R.W. Decker, D.M. Thomas, The Hawaiian-Emperor chain, in: E.L. Winterer, D.M. Hussong, R.W. Decker (Eds.), The Eastern Paci¢c Ocean and Hawaii, The Geology of North America, Geological Society of America, Boulder, CO, 1989, pp. 187^287. [39] D.L. Desonie, R.A. Duncan, J.H. Natland, Temporal and geochemical variability of volcanic products of the Marquesas hotspot, J. Geophys. Res. 98 (1993) 17649^17665. [40] A.A.P. Koppers, 40 Ar/39 Ar Geochronology and Isotope
[41]
[42] [43]
[44] [45]
[46]
[47] [48] [49]
[50] [51] [52] [53]
Geochemistry of the West Paci¢c Seamount Province: Implications for Paci¢c Plate Motion and Chemical Geodynamics, Ph.D. Thesis, Vrije Universiteit, Amsterdam, 1998, 263 pp.. M.S. Pringle, G.B. Dalrymple, Geochronological constraints on a possible hot spot origin for Hess Rise and the Wentworth Seamount Chain, in: M.S. Pringle, W.W. Sager, W.V. Sliter, S. Stein (Eds.), The Mesozoic Paci¢c: Geology, Tectonics, and Volcanism, Monograph 77, American Geophysical Union, Washington, DC, 1993, pp. 279^305. E.L. Winterer, C.V. Metzler, Origin and subsidence of guyots in Mid-Paci¢c mountains, J. Geophys. Res. 89 (1984) 9969^9979. L.W. Kroenke, P. Wessel, Paci¢c plate motion between 125 and 90 Ma and the formation of the Ontong Java plateau, in: Conference on the History and Dynamics of Global Plate Motions, American Geophysical Union, Marshall, CA, 1997, p. 22. J.M. O'Connor, P. Sto¡ers, J.R. Wijbrans, Migration rate of volcanism along the Foundation chain, SE Paci¢c, Earth Planet. Sci. Lett. 164 (1998) 41^59. S.O. Schlanger, M.O. Garcia, B.H. Keating, J.J. Naughton, W.W. Sager, J.A. Haggerty, J.A. Philpotts, R.A. Duncan, Geology and Geochronology of the Line Islands, J. Geophys. Res. 89 (1984) 11261^11272. M.S. Pringle, Age progressive volcanism in the Musicians Seamounts: a test of the hot spot hypothesis for the late Cretaceous Paci¢c, in: M.S. Pringle, W.W. Sager, W.V. Sliter, S. Stein (Eds.), The Mesozoic Paci¢c: Geology, Tectonics, and Volcanism, Monograph 77, American Geophysical Union, Washington, DC, 1993, pp. 279^305. R.D. Van der Hilst, S. Widiyantoro, R.L. Engdahl, Evidence for deep mantle circulation from global tomography, Nature 386 (1997) 578^584. P. Olson, Drifting mantle hotspots, Nature 327 (1987) 559^560. M.A. Richards, Hotspots and the case against a uniform viscosity composition of the mantle, in: R. Sabadini, K. Lambeack (Eds.), Glacial Isostasy, Sea Level and Mantle Rheology, Kluwer Academic, Dordrecht, 1991, pp. 571^ 587. R.D. Jarrard, D.A. Clague, Implications of Paci¢c island and seamount ages for the origin of volcanic chains, Rev. Geophys. Space Phys. 15 (1977) 57^76. J.B. Minster, T.H. Jordan, Present-day plate motions, J. Geophys. Res. 83 (1978) 5331^5354. D.A. Clague, R.D. Jarrard, Tertiary Paci¢c plate motion deduced from the Hawaiian-Emperor chain, Geol. Soc. Am. Bull. 84 (1973) 1135^1154. D. York, Least squares ¢tting of a straight line with correlated errors, Earth Planet. Sci. Lett. 5 (1969) 320^324.
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