Testing the ¢xed hotspot hypothesis using Ar/ Ar age

Testing the ¢xed hotspot hypothesis using 40Ar/39Ar ageprogressions 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 ingeology from a conceptual theory. The azimuths and age progressions of these seamount trails provide the only meansto determine absolute plate motions with respect to an independent reference frame of `fixed' hotspots. However, thepresumed fixity of hotspots is in disagreement with recent paleomagnetic studies and global-circuit plate reconstructionsfor the HawaiianÊmperor seamount trail. In this study, we provide independent evidence suggesting that hotspots arenot fixed relative to each other. We use a straightforward test that compares the observed 40Ar/39Ar age progressionsalong 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 Eulerpoles, or with a new set of Euler poles as derived in this study using discrete seamount locations digitized from thebathymetry maps of Smith and Sandwell [EOS 77 (1996) 315; Science 277 (1997) 1956^1921]. We conclude that therelative motion between hotspots may be required to reconcile the observed age progressions with the predicted platevelocities from their modeled Euler poles. On average, the Pacific hotspots may show motion at 10^60 mm/yr over thelast 100 Myr, partly attributed to individual hotspot motion, whereas systematic motion of these hotspots (due to truepolar 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 under-lie the Earth's lithospheric plates has been most

important in the development of plate tectonics.According to the ¢xed hotspot hypothesis sea-mount trails are formed by volcanism penetratingthe lithospheric plates whilst moving over `hot-spots' of upwelling mantle (e.g. [1,2]). In turn,the azimuths and age progressions of seamounttrails can be used to quantify plate motions withrespect to an independent geospatial referenceframe 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

* Corresponding author. Fax: +1-858-534-8090;E-mail: [email protected]

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Earth and Planetary Science Letters 185 (2001) 237^252

www.elsevier.com/locate/epsl

quanti¢cations plate motions are assumed to beconstant rotations of rigid, non-deforming platesaround ¢xed poles of rotation (i.e. Euler poles)for distinct time periods (i.e. stage poles).Although, there is no doubt that hotspot meltingrepresents the major means of intra-plate volcan-ism, the ¢xity of both hotspots and their associ-ated Euler poles appears unlikely in the context ofa dynamically convecting Earth [5^8]. Recent pa-leomagnetic studies [8^12] and global-circuit platereconstructions [13^19] for the HawaiianÊmper-or seamount trail suggest that the Hawaiian hot-spot may have experienced a motion of 10^40

mm/yr during the Emperor stage pole (80^43Ma).

The major objective of this paper is to furthertest the ¢xed hotspot hypothesis, in this case, bytesting for compatibility between the observed40Ar/39Ar age progressions along seamount trailson the Paci¢c plate (Fig. 1) and the locations ofthe Euler poles describing its absolute plate rota-tions. In this straightforward test, the Euler poleswill be re-determined by minimizing the angulardistances from the `best-¢t' Euler poles to the lo-cations of individual seamounts, as digitized fromthe bathymetric maps of Smith and Sandwell

Fig. 1. Paci¢c hotspot trails according to age range. For reference the currently active hotspots of the Paci¢c (circles) have beenincluded. 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 (seeSection 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 = Musi-cians; NW = North Wake; RL = Ralik; RT = Ratak; SE = Seth; SR = Shatsky Rise; SW = South Wake; TM = Tuamotu; TO = To-kelau; TV = Tuvalu; WW = Wentworth.

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([20,21] ; Appendix 1, EPSL Online BackgroundDataset1). Because the `best-¢t' Euler poles aregeometrically derived using seamount locationsexclusively, the age progressions along seamounttrails (i.e. local plate velocities) provide an inde-pendent check for the angular distance of individ-ual hotspots to the `best-¢t' Euler poles. We willshow that the local Paci¢c plate velocities are notcompatible with the angular plate velocities aspredicted by the `best-¢t' Euler poles ([22] ; thisstudy) or with any previously published Eulerpoles ([3,7,23^28] ; Appendix 2, EPSL OnlineBackground Dataset1 [50^52]). This may indicatethat the presumed ¢xity of hotspots is invalidwithin the limits of these tests ^ allowing for pos-sible motions between individual hotspots of thePaci¢c hotspot system.

2. Least squared derivation of Euler poles usingdiscrete seamount locations

One approach in determining an Euler pole isbased on the measurement of spatial trends inseamount trails. When using these azimuths oneis, however, limited by the small number of avail-able seamount trails. An alternative approach forthe least squared derivation of Euler poles is pre-sented here using the locations of discrete sea-mounts within multiple seamount trails or seg-ments. This purely geometrical approach waspreviously used to determine Euler poles for rel-ative plate motion using digitized points on frac-ture zones [23]. One of its advantages is the in-creased number of possible observations. Anotheradvantage is the improved reliability of the uncer-tainty estimates. More importantly, the derivationof Euler poles is not controlled by the observedage progressions along the studied seamounttrails. The age progressions along seamount trails,therefore, may serve as an independent check tothe location of an Euler pole as based on the ¢xedhotspot hypothesis.

2.1. Formulation of the least squared model

Fig. 2 illustrates the least squared model usedto determine Euler poles for absolute plate mo-tion. The seamount locations within two co-polarseamount trails A and B are plotted as smallcircles around their `best-¢t' Euler pole E. Be-cause the angular distances d between each sea-mount i in seamount trail A and the Euler pole Eare of equal length, their sum of squared devia-tions from the mean angular distance becomeszero. The same relation holds for seamount trailB, and because seamount trails A and B are co-polar, the `best-¢t' Euler pole is de¢ned by a min-imum in their total sum of squared deviations. Itslocation can be derived by an inversion of sea-mount locations using a least squared algorithmwhich minimizes the variance in the calculatedangular distances:

vardij �XMj�1

XN

i�1

1NU�dj

i3djmean�2 �1�

where N is the number of seamounts (independentobservations) per seamount trail and M is thenumber of trails. This variance is equal to thesquared RMS error for the motion of lithospheric

Fig. 2. Geometrical derivation of Euler poles based on thelocation 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 largerthan zero.

1 http://www.elsevier.nl/locate/epsl; mirror site: http://www.elsevier.com/locate/epsl

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plates [29,30]. Analyzing each seamount locationwith reference to the mean angular distance of itsrepresentative seamount trail avoids biasing of theanalysis. The `best-¢t' poles were found by gridsearching in the northern hemisphere. The searchareas were narrowed around these poles in foursubsequent searches using increased grid resolu-tions (2³, 0.5³, 0.1³ and 0.02³). The distributionof the variances is contoured in latitude^longitudespace (Fig. 3).

2.2. Uncertainties and bootstrapping

All seamount locations were retrieved by digi-tization of the predicted bathymetry maps ofSmith and Sandwell ([20,21] ; Appendix 1, EPSLOnline Background Dataset1). The scatter in thelocation of the seamounts perpendicular to theline of age progression is re£ected in the variancefor the calculated angular distances. No scalingwas 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 themost probable least squared solutions and show the `best-¢t' Euler pole at their center point (black circles). These contours arearbitrarily 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 atthe 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 resultsare summarized in Tables 1 and 3. Seamount locations, previously published rotation poles, and a further discussion of the dataare available in Appendices 1^3, EPSL Online Background Dataset1. Abbreviations: EP84 = Epp, 1984 [23]; EP85 = Engebretson etal., 1985 [24]; HP85 = Henderson, 1985 [25]; DpCP85 = Duncan and Clague, 1985 [3] ; LP88 = Lonsdale, 1988 [26]; YpKP93 = Yanand 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 pref-erentially ¢t the longest seamount trails, resultingin an undesired loss of plate motion informationfrom the shorter seamount trails.

The variance about the `best-¢t' Euler pole is ameasure of the goodness of ¢t to the seamountlocations. The contoured variances in Fig. 3,therefore, represent the most likely distributionsof solutions for the Euler poles at 5% intervals.The shape and elongation of these distributionsare largely dependent on the number of sea-mounts, the length of the seamount trails andthe position of these trails with respect to theEuler pole (cf. [29,31]). The con¢dence regionson the 65^95^99% con¢dence levels (Fig. 3, insets)were constructed using a statistical F ratio testfollowing the methodology of Engebretson et al.[29,32,33]. When presuming normal distributions

in a linear system, the F test determines if thevariance of `trial' Euler pole Etrial is signi¢cantlygreater than the minimum variance of the `best-¢t'Euler pole Ebest :

R ��varEtrial3varEbest�UX

pvarEbest

�2�

where X= pN3p equals the degrees of freedomand p is the number of adjustable parameters inthe model (in this case, latitude^longitude, p = 2).The R ratio corresponds to standard F ratio ta-bles at the desired con¢dence level with (p,X) de-grees of freedom.

Application of the bootstrap method was usedto test the robustness of the reconstructed `best-¢t' Euler poles. Alternative `bootstrap' Eulerpoles were calculated ignoring each seamount trail

Fig. 3 (continued).

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and each pair of trails once during the reconstruc-tions, resulting in 1/2M231/2M solutions, whereM is the number of seamount trails. If all mod-eled 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 similarto the `best-¢t' Euler pole at the 99% con¢dencelevel.

Fig. 3 (continued).

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3. Results

The most recent stage pole models include atleast 11 di¡erent Euler poles to describe absolute

Paci¢c plate motion (cf. [28]). Additional poleswere incorporated in these models to improvethe ¢t to the HawaiianÊmperor and Louisvilleseamount trails with possible changes in plate mo-

Fig. 3 (continued).

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tion around 3^5 Ma, 12^15 Ma, 17^20 Ma, and65 Ma. In our study, a ¢rst order stage pole mod-el is investigated following Henderson [25] for thelast 100 Myr (43^0, 80^43 and 100^80 Ma). Thechange in plate motion around 3^5 Ma [28,34,35]is ignored since it seems in disagreement withplate motion of the North American plate [36].Plate motion prior to 100 Ma (110^100, 125^110and 140^125 Ma) follows the stage pole model ofWessel and Kroenke [28]. The results are illus-

trated in the polar plots of Fig. 3 and listed inTable 1 and Table 3; results for Euler poles olderthan 100 Ma are discussed in Appendix 3 of theEPSL Online Background Dataset1 [42,43].

3.1. Euler pole: 43^0 Ma

Seventeen seamount trails were included in thecalculation of the Euler pole (67³07P N, 294³28PE) belonging to the so-called Hawaiian stage pole

Table 1Results from the least squared derivation of Paci¢c plate Euler poles

Euler pole Best-¢t con¢dence regions

Lat. Long. Var M N Longitude Latitude Extreme points

Min Max Min Max Lat. Long. Lat. Long.

Hawaiian stage poleTotal pole best-¢t 67.1 294.5 0.22 21 346 0.65% 292.5 296.3 66.7 67.5 66.9 292.5 67.3 296.4

bootstrap 67.1 294.7 231 0.95% 291.2 297.7 66.4 67.8 66.8 291.2 67.4 297.8scaled 67.9 296.8 0.99% 290.4 298.5 66.2 68.0 66.7 290.4 67.5 298.6

20^0 Ma best-¢t 70.1 302.0 0.15 19 293 0.65% 299.9 304.0 69.7 70.5 69.9 299.8 70.2 304.2bootstrap 70.1 302.0 190 0.95% 298.5 305.6 69.5 70.7 69.7 298.3 70.3 305.8

0.99% 297.6 306.5 69.3 70.9 69.6 297.4 70.5 306.7Emperor stage poleTotal pole best-¢t 18.8 253.6 0.15 8 122 0.65% 252.6 254.6 18.2 19.5 19.2 252.6 18.6 254.6


w/o Emperor best-¢t 25.6 272.4 0.11 7 99 0.65% 274.7 270.2 24.8 26.3 24.7 269.1 26.5 275.7bootstrap 24.9 268.7 28 0.95% 276.3 268.6 24.3 26.8 23.9 266.8 27.0 278.1

0.99% 277.4 267.7 24.0 27.2 23.5 265.3 27.3 279.6w/o Louisville best-¢t 21.4 248.8 0.11 7 100 0.65% 247.9 249.7 20.9 22.0 21.8 247.8 21.1 249.8

bootstrap 21.5 248.4 28 0.95% 247.2 250.4 20.5 22.4 22.1 247.1 20.7 250.50.99% 246.8 250.8 20.2 22.6 22.2 246.6 20.6 251.0

100^80 Ma stage poleTotal pole best-¢t 40.6 259.8 0.10 10 92 0.65% 254.3 264.5 39.7 41.4 41.3 252.0 39.1 268.1


110^100 Ma stage poleTotal pole best-¢t 74.1 101.8 0.13 5 95

scaled 74.5 102.9w/o Mid-Pac best-¢t 75.1 44.8 0.04 3 41

scaled 75.2 44.5125^110 Ma stage poleTotal pole best-¢t 65.3 273.2 0.09 4 47

bootstrap 65.7 268.5scaled 67.2 268.9

140^125 Ma stage poleTotal pole best-¢t 7.7 33.1 0.20 3 41

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 atthe latitude of the Euler pole, (2) the min and max latitude at the longitude of the Euler pole, and (3) the extreme points of theerror regions. These parameters were used to construct the non-ellipsoid error regions in the insets of Fig. 3. M = number of sea-mount trails; N = total number of seamounts for the `best-¢t' pole or the number of solutions for the `bootstrap' pole. Var = var-iance as calculated from Eq. 2.

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between 43 and 0 Ma. This `best-¢t' Euler polehas an overall variance of 0.22 and agrees withthe `mean-bootstrap' pole (67³07P N, 294³40P E).Scaling by the number of seamounts in each trailonly results in a minor shift in the location of the`best-¢t' Euler pole. However, the bootstrap re-sults show two noteworthy deviations: (1) a lon-gitudinal shift of the Euler pole when excludingHawaiian seamounts 43^20 Myr old, and (2) alatitudinal shift when excluding similar seamountsfrom the Louisville seamount trail. The remainingbootstrap poles fall within the 99% con¢denceregion around the total Euler pole. For this rea-son, we calculated a separate Paci¢c plate Eulerpole for the 20^0 Ma Hawaiian stage pole. Thisyields a signi¢cantly changed Euler pole (70³05PN, 301³58P E) with a lower variance (0.15) that isshifted to the north when compared to: (1) the

total Hawaiian Euler pole and (2) all publishedEuler poles. The 43^20 Ma Euler pole was notre-modeled since only two seamount trails (Ha-waii and Louisville) represent this stage pole[37,38] ; this Euler pole is best approximated bythe total pole at 67³07P N, 294³28P E.


The Emperor stage pole (80^43 Ma) was mod-eled using eight seamount trails resulting in a`best-¢t' Euler pole (18³50P N, 253³35P E) with avariance of 0.15. Despite the low variance, thedistribution of bootstrap poles yields a poorly de-¢ned and di¡erent `mean-bootstrap' pole (20³13PN, 256³37P E). When eliminating the Emperor orthe Louisville seamount trails, the models givelower variances (0.11) and better constrained

Table 2Local plate velocities for the Paci¢c plate between 0 and 140 Ma

Data Regression

Seamount trail Age range Calculation type Style Plate velocity(Ma) (mm/yr)

Hawaiian stage poleHawaii [38] 43.4^0 maximum ages YORK 2 92 þ 3Hawaii [38] 12.3^0 YORK 2 96 þ 4Bowie [3] 24.8^0 Linear 67 þ 20Cobb [3] 25.7^0 Linear 57 þ 20Pitcairn [3] 8.1^0.5 Linear 127 þ 55Society [3] 4.5^0 Linear 109 þ 10Austral-Cook [3] 19.6^0 Linear 107 þ 16Caroline [3] 13.9^1.0 Linear 121 þ 39Samoa [3] 27.7^0 Linear 72 þ 23Foundation [44] 21.2^0.9 maximum ages Linear 91.1 þ 2.0Louisville based on [37] 45.5^0.5 recombined ages YORK 2 60.5 þ 2.0Emperor stage poleEmperor [38] 64.7^43.4 YORK 2 72 þ 11Emperor [38] 64.7^19.9 YORK 2 68 þ 3Louisville based on [37] 66.3^0.5 recombined ages YORK 2 61.2 þ 1.2Louisville based on [37] 66.3^35.5 recombined ages YORK 2 64.4 þ 4.8Line [45] 93.4^47.4 Linear 96 þ 4100^80 Ma stage poleMagellan [22] 95.2^87.1 recombined ages YORK 2 47.6 þ 1.6Line [46] 93.4^81.0 YORK 2 66 þ 25Musicians [22] 95.4^82.3 recombined ages YORK 2 55.8 þ 6.4Wentworth [41] 93.4^86.4 2 data points 70125^110 Ma stage poleJapanese [40] 118.1^103.7 recombined ages YORK 2 48.1 þ 4.5

When available the style of data regression, the type of seamount ages included in the age progressions and the standard devia-tions are denoted. The calculations were not forced through the origin; YORK 2 = York, 1969 [53].

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`mean-bootstrap' poles. The pole with the lowestvariance (21³25P N, 248³47P E) was obtained whenexcluding Louisville seamount trail, and is in ac-cordance with its `mean-bootstrap' Euler pole(21³28P N, 248³26P E). This may indicate thatthe azimuth of Louisville Ridge was indeedchanged due to a major o¡set in the Eltanin frac-ture zone between 60 and 80 Ma [37]. Such kine-matic interactions of hotspots with fracture zonesare believed to cause azimuthal deviations up to15^30³ according to studies of the Tuamotu^Pit-cairn hotspot [38] and the Marquesas hotspot[39].


Eight seamount trails yield a `best-¢t' Eulerpole at 40³34P N, 259³47P E for the 100^80 Mastage pole. The variance is low (0.10) but the as-sociated con¢dence regions are more extendedwhen compared to those of the Hawaiian andEmperor Euler poles. This seems an e¡ect of thelimited regional extension of the short seamounttrails included in this calculation. However, mostof the bootstrap poles fall within the 99% con¢-dence region suggesting that the least squaredmodeling resulted in a self-consistent `best-¢t' Eu-ler pole for the 100^80 Ma stage pole.

4. Discussion

Seven stage poles were determined that describethe absolute rotation of the Paci¢c plate over thelast 140 Myr. In this discussion, these `best-¢t'Euler poles will be tested for their compatibilitywith the observed 40Ar/39Ar age progressionsmeasured along co-polar seamount trails. The¢xed hotspot hypothesis predicts that each ofthese age progressions (i.e. local plate velocities ;Table 2) should give comparable estimates for theangular plate velocity. The latter prediction canonly be tested when the Euler poles are derivedindependently from the age progressions along theseamount trails. This was accomplished in thisstudy by using an entirely geometric approachfor the derivation of Euler poles. We thereforecan use the recorded 40Ar/39Ar age progressions

to de¢ne independent distributions for the loca-tion 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 com-patible with the observed local plate velocities(Table 2). These con¢dence regions were con-structed by grid-searching in the northern hemi-sphere while calculating the angular velocities(and their standard deviations) for each trial Eu-ler pole using the age progressions of the modeledseamount trails. This was done using the relation-ship: e=g sin dmeanT, where e is the linear localplate velocity, dmean is the average angular dis-tance of a seamount trail to its Euler pole, andg is the velocity of angular rotation. Wheneverthe modeled angular velocities were similar atthe desired con¢dence level, the Euler poles wereaccepted. The modeled velocity regions, therefore,depict an independent distribution of potentialEuler poles and can be directly contrasted to lo-cations of the geometrically derived `best-¢t' Eulerpoles (Fig. 3).

An inconsistency arises when cross-checking thelocation of the 100^80 Ma Euler pole with thelocal plate velocities derived from the Magellanand Musicians seamount trails (cf. [22]). Neitherthe published Euler poles nor the `best-¢t' Eulerpole 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 poledistribution derived from the seamount locations(Fig. 3) and the calculated velocity region (Fig. 4).This `forced' Euler pole, however, is locatedV35³ away from the `best-¢t' Euler pole at40³34P N, 259³47P E. This observation may indi-cate that the age progressions can only be recon-ciled with the `best-¢t' Euler pole, when allowingfor the relative movement of the Magellan andMusicians hotspots with respect to one another[22].

For the Hawaiian (43^0 Ma) and Emperorstage poles (80^43 Ma) similar tests were con-ducted. The tests for the Hawaiian stage pole in-clude the Emperor, Louisville and Foundationhotspots. 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 theage 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 distributionsshould overlie the locations of the `best-¢t' Euler poles based on seamount locations (circles with 99% con¢dence regions; Table1) or the published Euler poles (hexagonal symbols). Note that, in case of the 43^0 Ma stage pole, the 99% error regions aresmaller than the actual symbols depicting the `best-¢t' Euler poles (circles in squares).

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sively dated by 40Ar/39Ar techniques resulting inan average age progression of 92 þ 3 mm/yr overthe last 43 Myr [38]. The Foundation seamounttrail is de¢ned by small, monogenetic seamountsand yields the most accurate age progression inthe Paci¢c of 91.1 þ 2.0 mm/yr [44]. The Louisvilleseamount trail has an age progression of60.5 þ 2.0 mm/yr; but its accuracy is limited bya low sample density for seamounts youngerthan 43 Ma [37]. From Fig. 4 it follows that theobserved age progressions for the Hawaiian andFoundation seamount trails are compatible withthe `best-¢t' Euler poles and most of the previ-ously published Euler poles at the 65^95% con¢-dence level. The Hawaiian and Foundation hot-spots may, consequently, be considered ¢xed withrespect to each other. The tests including theLouisville seamount trail, however, yield con¢-dence regions that are signi¢cantly di¡erentfrom these Euler poles. For example, an increasein the apparent local plate velocity from 60.5 to 73mm/yr at the Louisville seamount trail would berequired to achieve concordant results in all threecases. If ignoring the low sample density at theLouisville seamount trail, then this discrepancycould be explained by the independent motionof the Louisville hotspot by V12 mm/yr (sub)par-allel to the direction of Paci¢c plate motion. Thisis in accord with the predicted V9 mm/yr motionof the Louisville hotspot [5^7].

The tests for the Emperor stage pole include theEmperor, Louisville and Line hotspots. The Em-peror and Louisville seamount trails have beenwell dated with 40Ar/39Ar techniques and yieldage progressions of 68 þ 3 mm/yr and 61.2 þ 1.2mm/yr, respectively [37,38]. Dating of the LineIslands focused only on the time period between90 and 65 Ma [45]. Nonetheless, an overall ageprogression of 96 þ 4 mm/yr was proposed for itsEmperor stage pole [23,45]. From Fig. 4 it followsthat the Emperor and Louisville seamount trailsmay be in accord with the `best-¢t' Euler poles atthe 95% con¢dence level. The poor resolution isnot only a function of the precision for the ageprogressions, but also results from the similarityin the local plate velocities and the fact that theEmperor and Louisville seamount trails are lo-cated at comparable angular distances to the pre-

ferred Euler pole (72.8 þ 0.3; 80.8 þ 0.5). Bothtests including the Line Islands show marked de-viations from the `best-¢t' Euler poles. The dis-played narrow distributions are the result of thepronouncedly higher local plate velocity at theLine Islands and its shorter angular distance tothe Euler pole (54.1 þ 0.3). Since none of the threetest cases yielded concordant results at the 65%con¢dence level, it seems likely that the Emperor,Louisville and Line hotspots have moved relativeto each other. Alternatively, the uncertainties inthe age progressions (Table 2) may be too precise;they may not entirely re£ect their true geologicaluncertainties, including the prolonged volcanicevolution of individual seamounts, rejuvenationby younger hotspots and uncertainties in the ac-tual location of the hotspot underneath seamounttrails.

4.2. Hotspot motion in velocity space

In Fig. 5 the above tests are plotted in velocityspace displaying possible combinations of hotspotmotion at the 65^95% con¢dence levels. Everycombination of coexistent hotspot motion fallingwithin these con¢dence regions reconciles the ap-parent age progressions with the `best-¢t' Eulerpoles. Fixed hotspots are represented by the ori-gin, whereas hotspot motions anti-parallel to platemotion are represented by negative velocities. Itfollows that the scenarios for hotspot motion rep-resent non-unique solutions. Additional geologi-cal constraints are required to quantitatively re-solve inter-hotspot motions.

Hotspot motion anti-parallel to plate motionshould be prevalent [6] when considering thefact that (whole) mantle convection seems primar-ily 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 ¢xedMusicians hotspot and the motion of the Magel-lan hotspot in the direction of plate motion. Italso may suggest that anti-parallel motion of theMusicians hotspot is between 12 and 24 mm/yr(Fig. 5). This is a minimum estimate given thatthe Magellan hotspot may have experienced anti-parallel hotspot motion as well. Two assumptionsare required: (1) subduction of the Paci¢c plate

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beneath the Asian plate was more important thansubduction of the Kula plate during the 100^80Ma stage pole, and (2) hotspot motion wasaligned to Paci¢c plate motion. Hotspot motionperpendicular to plate motion does not inducechanges in the local plate velocities at co-polarseamount trails. Instead, it would induce changesin the location of the Euler pole. Consistencywithin the modeling results for the 100^80 MaEuler pole implies that the orientations of theMagellan and Musicians seamount trails are notsigni¢cantly di¡erent. The detected discrepancy intheir local plate velocities, thus, may indicate thatthe (major) component of hotspot motion wasparallel to plate motion.

For the Emperor stage pole (Fig. 5) the ageprogressions are incompatible with the ¢xed hot-spot hypothesis ; inter-hotspot motion seems to berequired. The modeled coexistent motion of theLouisville and Emperor hotspots is compatiblewith independently derived estimates from paleo-latitude and global-circuit plate studies (Fig. 5).However, the Line hotspot cannot be reconciledwith these estimates, which suggests an additionalcomponent of hotspot motion, provided that thelocal plate velocity of 96 þ 4 mm/yr [45] is an ac-curate estimate. For the Hawaiian stage pole, theFoundation 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 hotspotsmay not necessarily be ¢xed with respect to thedeep mantle, but only with respect to each other.Other combinations of hotspot motion may alsobe compatible with their observed 40Ar/39Ar ageprogressions and 43^0 Ma Euler pole. Estimatesfrom paleolatitude studies are again comparablewith the presented relation of `true' motion be-tween these hotspots (Fig. 5). The estimates ofSteinberger and O'Connell [6] for the motion ofthe Louisville hotspot (V9 mm/yr) and the Ha-waiian hotspot (V12 mm/yr) are di¡erent sincethey fall slightly below the con¢dence envelopesin Fig. 5.

4.3. Absolute Paci¢c plate motion

Angular plate velocities should be estimated

Fig. 5. Hotspot motion in velocity space. The origin repre-sents truly ¢xed hotspots; positive and negative velocitiesrepresent hotspot motion parallel and anti-parallel to the di-rection of plate motion (in mm/yr). The modeled 65^95%con¢dence envelopes depict all possible combinations of hot-spot motion for two co-polar seamount trails compatiblewith both the improved Euler poles from Table 3 and theobserved age progressions from Table 2 including standarderrors. Independent estimates for the motion of hotspotsbased on paleolatitude studies (65^95% con¢dence boxes)and mantle £ow modeling are added (see diagrams for refer-ences).

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considering the motion of hotspots so that theysolely re£ect plate motions (cf. [7]). To achievesuch estimates, we calculated the angular veloc-ities based on the average angular distance ofthe seamount trail to the modeled `best-¢t' Eulerpole. These calculations include the propagationof errors in the angular distance to the Euler pole(standard deviation) and the age progression(standard error; Table 2). If all calculated angularvelocities for one speci¢c stage pole are similar atthe 65% con¢dence level, then the average angularvelocity represents an estimate for its true angularplate velocity. If no evidence exists for the (rela-tive) ¢xity of co-polar hotspots then minimumangular velocities were estimated. In Table 3 wepresent our preferred stage pole model for thePaci¢c plate over the last 140 Myr including the`best-¢t' Euler poles derived using the geometricmethod and the new estimates for the angularplate velocities.

5. Summary and conclusions

Seamount locations were used to derive Eulerpoles describing the direction of Paci¢c plate mo-tion over the last 140 Myr. This was done byminimizing the angular distances between theseseamounts and the Euler pole with respect to anaverage angular distance for each seamount trail.As a result, this geometric method yields reliableestimates for Euler poles based on seamount lo-cations exclusively. The modeled Euler poles sub-

sequently were used to predict their associatedangular plate velocities and to compare thesewith the observed 40Ar/39Ar age progressions, inorder to test the ¢xed hotspot hypothesis. Onlythe Hawaiian and Foundation hotspots appearto be ¢xed with respect to each other over thelast 20 Myr; in most other cases, the estimatedplate velocities were signi¢cantly di¡erent at the65^95% con¢dence levels. One possible explana-tion is that these discordances are caused by rel-ative motion between hotspots in a direction sub-parallel to plate motion.

The possible motion of hotspots was found tobe consistent with the independent estimates onhotspot motion using the di¡erence in paleolati-tude for the Emperor seamount trail [8^12], glob-al-circuit plate motion models [13^19] and mantle£ow modeling [5^7]. Combining these independ-ent estimates with the relations of hotspot motionin velocity space suggests hotspot motion in theorder of 10^60 mm/yr over the last 100 Myr. Thepossibility for hotspot motion may have contrast-ing implications for mantle geodynamics. Hotspotmotion anti-parallel to plate motion can be ex-plained by the kinematic return £ow in the deepmantle [48] as driven by the slab-pull of subduct-ing lithospheric plates. Hotspot motion parallel toplate motion can only be explained by density-driven mantle convections, but this would requiremuch lower viscosities in the upper mantle [6,49].

We emphasize, however, that age progressionsalong seamount trails still carry signi¢cant geo-logical and analytical uncertainties. Within the

Table 3Preferred stage pole model for the Paci¢c plate

Stage pole Euler pole Rotation

Lat. Long. Var M N Vel Deg Comments

20^0 Ma 70.1 302.0 0.15 19 293 0.881 þ 0.016 17.6 þ 0.3 weighted average Foundation+Hawaii43^20 Ma 67.1 294.5 0.22 21 346 0.502^0.478 13.3^11.0 models 1^3 of Steinberger and O'Connell [6]43^80 Ma 18.8 253.6 0.15 8 122 0.657 þ 0.029 24.3 þ 1.1 minimum Emperor seamount trail100^80 Ma 40.6 259.8 0.10 10 92 0.425 þ 0.014 8.5 þ 0.3 minimum Magellan seamount trail110^100 Ma 75.1 44.8 0.04 3 41 0.44 4.4 average Magellan+Japanese seamount trail125^110 Ma 65.3 273.2 0.09 4 47 0.449 þ 0.042 6.7 þ 0.6 minimum Japanese seamount trail140^125 Ma 7.7 33.1 0.20 3 41 0.49 9.8 Wessel and Kroenke [28]

Vel = angular velocity in ³/Myr; Deg = angular rotation for the total stage pole. Standard deviations on the angular velocities andthe angular rotation were estimated from the standard errors on the observed local plate velocities (Table 2) and the standard de-viations on the angular distance to the Euler pole. For error regions of the `best-¢t' Euler pole and abbreviations see Table 1.

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limits of these data, we concluded here that hot-spots are not necessarily ¢xed with respect to eachother, and that our proposed relative hotspot mo-tions are consistent with independent geodynamicmodels. However, more importantly, we were ableto develop and use quantitative methods to deter-mine uncertainties in stage pole de¢nitions andplate motion models based on age progressionsin linear island chains. Ultimately, such quantita-tive methods will allow us to continue buildingand re¢ning plate motion models as additionaland more accurate data become available.

Acknowledgements

We thank Dave Sandwell for his help withGMT. Jan Wijbrans is thanked for his commentson the manuscript. We thank Gary Acton andBill Harbert for their reviews. This paper is anoutgrowth of A.A.P.K.s Ph.D. thesis at the VrijeUniversiteit in Amsterdam, The Netherlands. Fi-nancial support by the Netherlands Foundationof Earth Sciences Research (GOA-NWO750.60.005), Netherlands Science Foundation(NWO-TALENT grant to A.A.P.K.) and Nation-al Science Foundation (NSF-OCE 91-02183 and97-30394).[RV]

References

[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 platemotions, Am. Assoc. Petrol. Geol. Bull. 56 (1972) 42^43.

[3] R.A. Duncan, D.A. Clague, Paci¢c plate motion recordedby linear volcanic chains, in: A.E.A. Nairn, F.L. Stehli, S.Uyeda (Eds.), The Ocean Basins and Margins, The Paci¢cOcean 7A, Plenum Press, New York, 1985, pp. 89^121.

[4] W.J. Morgan, Hotspot tracks and early rifting of the At-lantic, Tectonophysics 94 (1983) 123^139.

[5] B. Steinberger, R.J. O'Connell, Changes of the Earth'srotation axes owing to advection of mantle density heter-ogeneities, Nature 387 (1997) 169^173.

[6] B. Steinberger, R.J. O'Connell, Advection of plumes inmantle £ow: implications for hotspot motion, mantle vis-cosity and plume distribution, Geophys. J. Int. 132 (1998)412^434.

[7] B. Steinberger, Plumes in a convecting mantle: models

and observations for individual hotspots, J. Geophys.Res. 105 (2000) 11127^11152.

[8] U. Christensen, Fixed hotspots gone with the wind, Na-ture 391 (1998) 739^740.

[9] R.G. Gordon, C.D. Cape, Cenozoic latitudinal shift ofthe Hawaiian hotspot and its implications for true polarwander, Earth Planet. Sci. Lett. 55 (1981) 37^47.

[10] W.W. Sager, U. Bleil, Latitudinal shift of Paci¢c hotspotsduring the late Cretaceous and early Tertiary, Nature 326(1987) 488^490.

[11] J.A. Tarduno, J. Gee, Large-scale motion between Paci¢cand Atlantic hotspots, Nature 378 (1995) 477^480.

[12] J.A. Tarduno, R.D. Cottrel, Paleomagnetic evidence formotion of the Hawaiian hotspot during formation of theEmperor seamounts, Earth Planet. Sci. Lett. 153 (1997)171^180.

[13] P. Molnar, J. Stock, Relative motions of hotspots in thePaci¢c, Atlantic and Indian Oceans since late Cretaceoustime, Nature 327 (1987) 587^591.

[14] G.D. Acton, R.G. Gordon, Paleomagnetic tests of Paci¢cplate reconstructions and implications for motion betweenhotspots, Science 263 (1994) 1246^1254.

[15] S.C. Cande, C.A. Raymond, J. Stock, W.F. Haxby, Geo-physics of the Pitman fracture zone and Paci¢c-Antarcticplate motions during the Cenozoic, Science 270 (1995)947^953.

[16] I.O. Norton, Plate motions in the North Paci¢c: the 43Ma nonevent, Tectonics 14 (1995) 1080^1094.

[17] I.O. Norton, Hotspot tracks and reference frames don'tmix, in: Conference on the History and Dynamics ofGlobal Plate Motions, American Geophysical Union,Marshall, CA, 1997, p. 23.

[18] C.A. Raymond, J.M. Stock, S.C. Cande, Relative hotspotmotion based on global plate reconstructions, in: Confer-ence on the History and Dynamics of Global Plate Mo-tions, American Geophysical Union, Marshall, CA, 1997,p. 25.

[19] V. DiVenere, D.V. Kent, Are the Paci¢c and Indo-Atlan-tic hotspots ¢xed? Testing the plate circuit through Ant-arctica, Earth Planet. Sci. Lett. 170 (1999) 105^117.

[20] W.H.F. Smith, D. Sandwell, Predicted bathymetry. Newglobal sea£oor topography from satellite altimetry, EOS77-46 (1996) 315.

[21] W.H.F. Smith, D. Sandwell, Global sea £oor topographyfrom satellite altimetry and ship depth soundings, Science277 (1997) 1956^1962.

[22] A.A.P. Koppers, H. Staudigel, J.R. Wijbrans, M.S. Prin-gle, The Magellan seamount trail : implications for Creta-ceous hotspot volcanism and absolute Paci¢c plate mo-tion, Earth Planet. Sci. Lett. 163 (1998) 53^68.

[23] D. Epp, Possible perturbations to hotspot traces and im-plications for the origin and structure of the Line Islands,J. Geophys. Res. 89 (1984) 11273^11286.

[24] D. Engebretson, A. Cox, R. Gordon, Relative Motionsbetween Oceanic and Continental Plates in the Paci¢cBasin, Geological Society of America Special Paper 206,1985.

EPSL 5737 2-2-01


[25] L.J. Henderson, Motion of the Paci¢c Plate Relative tothe Hotspots since the Jurrasic and Model of OceanicPlateaus of the Farallon Plate, Ph.D. Thesis, Northwest-ern University, USA, 1985.

[26] P. Lonsdale, Geography and history of the Louisville hot-spot chain in the Southwest Paci¢c, J. Geophys. Res. 93(1988) 3078^3104.

[27] C.Y. Yan, L.W. Kroenke, A plate tectonic reconstructionof the southwest Paci¢c, 0^100 Ma, in: W.H. Berger,L.W. Kroenke, L.A. Mayer et al. (Eds.), Proceedings ofthe 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 relocat-ing hotspots and re¢ning absolute plate motions, Nature387 (1997) 365^369.

[29] D.C. Engebretson, A. Cox, R.G. Gordon, Relative mo-tions between oceanic plates of the Paci¢c Basin, J. Geo-phys. Res. 89 (1984) 10291^10310.

[30] D.M. Jurdy, R.G. Gordon, Global plate motions relativeto the hotspots 64 to 56 Ma, J. Geophys. Res. 89 (1984)9927^9936.

[31] J.M. Stock, P. Molnar, Some geometrical aspects of un-certainties in combined plate tectonics, Geology 11 (1983)697^701.

[32] S. Stein, R.G. Gordon, Statistical tests of additional plateboundaries from plate motion inversions, Earth Planet.Sci. Lett. 69 (1984) 401^412.

[33] W. Harbert, A. Cox, Late Neogene motion of the Paci¢cplate, J. Geophys. Res. 94 (1989) 3052^3064.

[34] A. Cox, D. Engebretson, Change in motion of Paci¢cplate at 5 Myr BP, Nature 313 (1985) 472^474.

[35] P. Wessel, L.W. Kroenke, The geometric relationship be-tween hotspots and seamounts: implications for Paci¢chotspots, Earth Planet. Sci. Lett. 158 (1998) 1^18.

[36] C. DeMets, S. Traylen, Motion of the Rivera plate since10 Ma relative to the Paci¢c and North American platesand 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 theEltanin 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 Ha-waiian-Emperor chain, in: E.L. Winterer, D.M. Hussong,R.W. Decker (Eds.), The Eastern Paci¢c Ocean and Ha-waii, The Geology of North America, Geological Societyof America, Boulder, CO, 1989, pp. 187^287.

[39] D.L. Desonie, R.A. Duncan, J.H. Natland, Temporal andgeochemical variability of volcanic products of the Mar-quesas hotspot, J. Geophys. Res. 98 (1993) 17649^17665.

[40] A.A.P. Koppers, 40Ar/39Ar Geochronology and Isotope

Geochemistry of the West Paci¢c Seamount Province:Implications for Paci¢c Plate Motion and Chemical Geo-dynamics, Ph.D. Thesis, Vrije Universiteit, Amsterdam,1998, 263 pp..

[41] M.S. Pringle, G.B. Dalrymple, Geochronological con-straints on a possible hot spot origin for Hess Rise andthe 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.

[42] E.L. Winterer, C.V. Metzler, Origin and subsidence ofguyots in Mid-Paci¢c mountains, J. Geophys. Res. 89(1984) 9969^9979.

[43] L.W. Kroenke, P. Wessel, Paci¢c plate motion between125 and 90 Ma and the formation of the Ontong Javaplateau, in: Conference on the History and Dynamics ofGlobal Plate Motions, American Geophysical Union,Marshall, CA, 1997, p. 22.

[44] J.M. O'Connor, P. Sto¡ers, J.R. Wijbrans, Migration rateof volcanism along the Foundation chain, SE Paci¢c,Earth Planet. Sci. Lett. 164 (1998) 41^59.

[45] S.O. Schlanger, M.O. Garcia, B.H. Keating, J.J. Naugh-ton, 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.

[46] M.S. Pringle, Age progressive volcanism in the MusiciansSeamounts: a test of the hot spot hypothesis for the lateCretaceous 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, AmericanGeophysical Union, Washington, DC, 1993, pp. 279^305.

[47] R.D. Van der Hilst, S. Widiyantoro, R.L. Engdahl, Evi-dence for deep mantle circulation from global tomogra-phy, Nature 386 (1997) 578^584.

[48] P. Olson, Drifting mantle hotspots, Nature 327 (1987)559^560.

[49] M.A. Richards, Hotspots and the case against a uniformviscosity composition of the mantle, in: R. Sabadini, K.Lambeack (Eds.), Glacial Isostasy, Sea Level and MantleRheology, Kluwer Academic, Dordrecht, 1991, pp. 571^587.

[50] R.D. Jarrard, D.A. Clague, Implications of Paci¢c islandand seamount ages for the origin of volcanic chains, Rev.Geophys. Space Phys. 15 (1977) 57^76.

[51] J.B. Minster, T.H. Jordan, Present-day plate motions,J. Geophys. Res. 83 (1978) 5331^5354.

[52] D.A. Clague, R.D. Jarrard, Tertiary Paci¢c plate motiondeduced from the Hawaiian-Emperor chain, Geol. Soc.Am. Bull. 84 (1973) 1135^1154.

[53] D. York, Least squares ¢tting of a straight line with cor-related errors, Earth Planet. Sci. Lett. 5 (1969) 320^324.

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Testing the ¢xed hotspot hypothesis using Ar/ Ar age