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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B07104, doi:10.1029/2008JB005584, 2008

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Linking the Late Cretaceous to Paleogene Pacific plate and the Atlantic bordering continents using plate circuits and paleomagnetic data Pavel V. Doubrovine1 and John A. Tarduno1 Received 11 January 2008; accepted 31 March 2008; published 19 July 2008.

[1] Late Cretaceous to Paleogene paleomagnetic data from the Pacific plate (the

Emperor Seamounts) can be compared with data from the Atlantic bordering continents through the use of plate circuit reconstructions. Here we summarize the uncertainties in all data sets and present formal tests. We report agreement between Late Cretaceous Pacific paleomagnetic data and predictions based on the estimates of non-Pacific pole positions from synthetic apparent polar wander paths. This congruency points to the veracity of the plate circuits and the accuracy of the paleomagnetic estimates. In contrast to the agreement seen for the Late Cretaceous, small discrepancies are observed in the comparisons of the Pacific Paleogene data and predictions from synthetic apparent polar wander paths. Such a disparity in a younger time interval is unexpected, given the agreement of the Late Cretaceous data. The possibility that minor, temporally variable nondipole field components contribute to the discrepancy cannot be completely discounted. However, an alternative and more straightforward explanation is suggested by further comparisons of the mean non-Pacific paleomagnetic data and the highest-quality poles that contribute to the means. In particular, we note that (1) the Pacific Paleogene data are in full agreement with coeval poles from North America meeting strict reliability criteria and (2) the non-Pacific Paleogene poles of synthetic apparent polar wander paths are dominated by results from the North Atlantic Igneous Province (NAIP), but taken as a whole, the NAIP data fail a paleomagnetic reversal test. Hence, minor discrepancies between Paleocene paleomagnetic data from the Pacific and Atlantic hemispheres may point to limitations of the latter, which incorporate a relatively large number of older, lowerquality data. These findings call for renewed data collections utilizing comprehensive rock magnetic and paleomagnetic (demagnetization) procedures to improve resolution of Paleocene non-Pacific data. The uncertainties of the Pacific paleolatitude data and the non-Pacific reference poles are larger than the differences related to the use of the two alternative plate circuits (through East to West Antarctica and through Australia to the Lord Howe Rise) that link the Atlantic and Pacific hemispheres. While no preference can thus be given to either plate circuit, their overall consistency with paleomagnetic data suggests that they can be used to investigate long-term motion of the Pacific plate since Late Cretaceous times. Citation: Doubrovine, P. V., and J. A. Tarduno (2008), Linking the Late Cretaceous to Paleogene Pacific plate and the Atlantic bordering continents using plate circuits and paleomagnetic data, J. Geophys. Res., 113, B07104, doi:10.1029/2008JB005584.

1. Introduction [2] Relative motion between lithospheric plates in the past can be accurately quantified when two plates share a common spreading ridge boundary and the history of seafloor spreading can be determined using the identifications of marine magnetic anomalies and fracture zones. Because no such record exists between the Pacific plate 1 Department of Earth and Environmental Sciences, University of Rochester, Rochester, New York, USA.

Copyright 2008 by the American Geophysical Union. 0148-0227/08/2008JB005584$09.00

and the majority of circum-Pacific plates (with the exception of the Antarctic plate separated from the Pacific plate by a spreading ridge which has been active since the Late Cretaceous), plate circuit calculations must be used to define relative motion. [3] There are two alternative plate circuits proposed for reconstruction of the motion of the Pacific plate (Figure 1). The first plate circuit uses the traditional route through Antarctica and combines reconstructions of the motion of the Pacific plate relative to West Antarctica and West Antarctica relative to East Antarctica [e.g., Molnar and Atwater, 1973; Raymond et al., 2000]. The corresponding kinematic model will be referred to as the ‘‘East-West

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DOUBROVINE AND TARDUNO: PACIFIC PLATE CIRCUITS

Figure 1. Map of the southwestern Pacific region showing the paths of alternative plate circuits. The reconstructions included in the East-West Antarctica plate circuit are schematically shown by black arrows; those of the Australia-Lord Howe Rise are shown by white arrows (see text). Seafloor ages are from Mu¨ller et al. [2008]. Antarctica plate circuit.’’ The second model was proposed by Steinberger et al. [2004] as an alternative to the EastWest Antarctica circuit for times before chron 20o (43 Ma). This circuit involves reconstruction of the Pacific plate (Campbell Plateau) relative to the Lord Howe

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Rise, the Lord Howe Rise relative to Australia, and Australia relative to East Antarctica (Figure 1). This kinematic model will be referred to as the ‘‘Australia-Lord Howe Rise circuit.’’ [4] Paleogene motions between the tectonic elements that comprise the southwestern Pacific region have been considerably refined in recent years [e.g., Cande et al., 1995; Gaina et al., 1998; Cande et al., 2000]. These improvements have provided much better constraints on the relative motions among the Pacific, Antarctic and Australian plates. However, the two competing plate circuit models suggest contrasting scenarios for the tectonic evolution of the southwestern Pacific. [5] Here we examine the two plate circuit models by comparing Pacific paleomagnetic data with non-Pacific reference paleomagnetic poles reconstructed through the plate circuits. We present rotation parameters for the motion between the Pacific, East Antarctic and North American plates which are based on the most recent reconstructions and include an analysis of rotation uncertainties. These rotation parameters will be used to transfer the reference paleomagnetic poles to the Pacific plate and formal paleomagnetic consistency tests will be presented. We then discuss the implications of the tests for (1) the resolution of the global paleomagnetic data and the structure (i.e., dipole versus nondipole) of the Late Cretaceous to Paleogene time-averaged geomagnetic field and (2) the veracity of the plate motion models.

2. Kinematic Models 2.1. Sources of Plate Circuit Reconstructions [6] Finite rotations describing relative motion between the Pacific plate and East Antarctica, Africa and North America were calculated by combining the reconstructions through the two alternative plate circuits described below. The rotation parameters for individual reconstructions in the plate circuits were compiled from the literature which are

Table 1. Sources of Plate Circuit Reconstructions Rotations PAC-WANT WANT-EANT

Cande and Stock [2004b] Cande et al. [1995] Steinberger et al. [2004] Cande et al. [2000] Cande and Stock [2004a]

LHR-PAC

Sutherland [1995]

LHR-AUS

Gaina et al. [1998]

EANT-AUS EANT-AFR AFR-NA

Chronsa

Typeb

2Ay, 3Ay, 5o, 6o, 8o, 13o 20y, 21o, 24o, 27, 30r 33y, 34y Present – 8o: no motion 13o 20o, 24o (extrapolated) 27 (extrapolated) 27 – 34y: no motion 20r (closure fit) 20r – 34y: no motion Present – 23r: no motion 24o, 25y, 26o, 27o, 28y, 29y 30y, 31y, 32y, 33y, 33o, 34y 2Ay, 3Ay, 5o, 8o, 10o, 12o, 13o, 17o 20o, 21y, 24o, 27y, 32y, 33o, 34y 2Ay, 5y, 6y, 8y, 13y, 18y, 20y, 21y, 24y, 30y, 32y, 33y, 33ry, 34y 6, 13, 18, 20, 21, 25, 30r 32, 33y, 33o, 34y

cov cov -

Reference

Cande and Stock [2004b] Tikku and Cande [2000] Nankivell [1997] McQuarrie et al. [2003] Klitgord and Schouten [1986]

a

cov ell cov cov cov cov ell purs -

All chrons are normal polarity chrons except those denoted by the ‘‘r.’’ The ‘‘y’’ and ‘‘o’’ denote the young and old edges of the chron, respectively. Types of reconstruction uncertainty are as follows: cov, Chang’s [1988] covariance matrix; ell, 95% confidence ellipsoid for the rotation pseudovector; purs, partial uncertainty rotations; dashes, uncertainties were not reported. See auxiliary materials for definitions. b

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referenced in Table 1. Because special effort was made to propagate the reconstruction uncertainty through a plate circuit (i.e., to quantify the uncertainties of combined rotations, see section 2.2), the preference was given to the most recent reconstructions in which the uncertainties of the rotation parameters were estimated through a formal statistical analysis. The geomagnetic polarity timescale of Ogg and Smith [2004] (GPTS2004) was used throughout to assign absolute ages. 2.1.1. East-West Antarctica Plate Circuit [7] The main uncertainty in the reconstruction through Antarctica is the possibility for additional unquantified deformation between West Antarctica and the East Antarctic craton from Paleocene to early middle Eocene times [e.g., Steinberger et al., 2004]. It is generally agreed that the rotations of Cande et al. [2000] for chrons 13o (34 Ma) and 20o (42 Ma), which are based on data from the Adare Basin and closure of the East Antarctica-West AntarcticaAustralia plate circuit, accurately represent the motion between West and East Antarctica from middle Eocene to late Oligocene times. However, the earlier phase of extension between chrons 27 and 24o (62– 54 Ma) suggested by Cande and Stock [2004a] is not well constrained. [8] The assumption used by Cande and Stock [2004a] is that the direction of the motion for this earlier phase of extension was the same as that after chron 20o. However, at least one major plate reorganization (e.g., the cessation of spreading in the Tasman Sea at 52 Ma, followed by the opening of the Emerald and South Tasman Ocean Crust (STOC) basins at 45 Ma) occurred between these times. This may have affected plate motion in the entire region, including the relative motion between West and East Antarctica. Nevertheless, Cande and Stock [2004a] considered the amount of the early extension small compared to the later phase which stated around chron 20o and resulted in the opening of the Adare Trough [Cande et al., 2000]. No motion between West and East Antarctica is assumed prior to chron 27 (62 Ma). [9] For the Pacific-West Antarctica motion we used the rotations of Cande et al. [1995], which are based on marine geophysical data (identifications of marine magnetic anomalies and fracture zones) from the southwestern Pacific Ocean east of the Emerald Fracture Zone. Magnetic anomalies as old as anomaly 33 (73.6– 79.5 Ma) were mapped in this region, and a set of finite rotations (with estimated uncertainties) up to chron 30r time was calculated using the fitting criterion of Hellinger [1981] and the statistical method of Royer and Chang [1991]. (The magnetic anomaly corresponding to chron 30r, a short interval of reversed polarity between chrons 30 and 31, was referred to as ‘‘Anomaly 31’’ in the original publication of Cande et al. [1995].) [10] This kinematic model was recently updated by Cande and Stock [2004a, 2004b], who included additional geophysical data collected in the region since 1995. However, because the uncertainties were not published for the updated rotations ‘‘older’’ than chron 13o (33.7 Ma) [Cande and Stock, 2004a] and because the new solutions for the times before chron 13o are very close to those of Cande et al. [1995], we decided to use the rotations of Cande and Stock [2004b] for chron 13o and younger and the rotations

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of Cande et al. [1995] for chrons 20y– 30r (Table 1). For times before chron 30r (67.8 Ma), we used the chron 33y (73.6 Ma) and chron 34y (84 Ma) rotation parameters published by Steinberger et al. [2004]. No estimate of the reconstruction uncertainty is available for these rotations. [11] For the motion between East and West Antarctica we used the rotations of Cande et al. [2000] and Cande and Stock [2004a]. This model is partially based on the magnetic anomaly and fracture zone data from the western Ross Sea (which record the East-West Antarctica motion between chrons 20o and 8o, 43 to 26 Ma), and partially on the considerations of closure for the Australia-East AntarcticaWest Antarctica plate circuit. [12] Only one rotation (chron 13o, 33.7 Ma) was calculated using the formal statistical analysis [Cande et al., 2000]. The reconstruction parameters for older time (chrons 20o/24o and 27) were estimated from the considerations of paleogeography (closure of the Australia-East AntarcticaWest Antarctica circuit and juxtaposition of the Lord Howe Rise and Campbell Plateau) using extrapolations from the chron 13o rotation. The extrapolation assumes that the Euler pole for the motion of West Antarctica relative to East Antarctica remained stationary between chrons 27 and 8o (62 to 26 Ma) [Cande et al., 2000; Cande and Stock, 2004a, 2004b]. No attempt was made to estimate the uncertainties of the extrapolated rotations. 2.1.2. Australia-Lord Howe Rise Plate Circuit [13] The reconstruction through Australia and the Lord Howe Rise (LHR) is based on the closure fit between the Lord Howe Rise and the Campbell Plateau [Sutherland, 1995]. It is generally assumed that the LHR was a part of the Pacific plate during the opening of the Tasman Sea (between Australia and the LHR), which ceased shortly after chron 24 (52 Ma), and the magnetic anomalies in the Tasman Sea record the motion between the Pacific and Australian plates [e.g., Cande and Stock, 2004a]. However, between 52 and 45 Ma a boundary probably existed between the LHR and the Pacific plate, otherwise the Australian and Pacific plates would have coalesced into a single plate. Cande and Stock [2004a] suggested that this boundary was cutting across the Challenger Plateau at the southeastern end of the LHR and that the motion on this boundary was probably slow and dominantly strike slip. The Australia-Lord Howe Rise plate circuit reconstruction assumes that the LHR remained fixed to the Campbell Plateau (and hence to the Pacific plate) before the opening of the Emerald and STOC basins, which started approximately 45 Ma ago, ignoring the motion between the LHR and the Pacific plate during the 52– 45 Ma period. [14] The separation of the Lord Howe Rise from Australia started at 90 Ma and ceased shortly after chron 24y (52.6 Ma). The LHR-Australia finite rotations were calculated by Gaina et al. [1998] back to chron 33y (73.6 Ma) from the identifications of magnetic anomalies and fracture zones in the Tasman Sea. The uncertainties were estimated by the method of Royer and Chang [1991]. Rotations for chrons 33o (79.5 Ma) and 34y (84 Ma) were calculated assuming that the chron 33y – 32y stage pole remained stable since chron 34y. Error estimates are not available for these two older rotations [Gaina et al., 1998].

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[15] Another episode of rifting involving the Lord Howe Rise occurred in Eocene time. The rifting, followed by seafloor spreading, resulted in separation between the LHR (on the Australian plate) and the Campbell Plateau (on the Pacific plate) and opening of the Emerald and South Tasman Ocean Crust basins southwest of New Zealand. The oldest magnetic anomaly identified in these basins corresponds to chron 18 (38 –39.5 Ma) [e.g., Keller, 2003]. [16] The age of inception of the LHR-Pacific boundary was loosely constrained to the middle Eocene (45 ± 5 Ma) on the basis of stratigraphic data from southern New Zealand and extrapolation of the spreading rates in the Emerald – STOC basins [Sutherland, 1995; Steinberger et al., 2004]. The nominal 45 Ma age assigned by Sutherland [1995] corresponds to the older end of chron 20r (42.8 – 45.3 Ma), suggesting that rifting postdated chron 21. [17] Sutherland [1995] derived a finite rotation for the total LHR-Pacific motion by fitting the rifted margins of the Emerald and STOC basins (the Resolution and southwest Campbell rift margins, respectively) and estimated its uncertainty using the constraints from regional geology of New Zealand and satellite gravity data. Keller [2003] used recent geophysical data and formal statistical analysis to define a set of finite rotations from chron 11o (30.2 Ma) to 18o (39.5 Ma), and a prerift closure fit similar to that of Sutherland [1995]. However, the covariance matrix (section 2.2) for the prerift reconstruction presented in [Keller, 2003] is apparently erroneous because its decomposition shows one negative eigenvalue, which is impossible by the very definition of covariance matrix. Therefore, we decided to use the reconstruction of Sutherland [1995], which appears more conservative. [18] For the Australia-East Antarctica reconstructions we used finite rotations of Cande and Stock [2004b] for chrons 17o and younger (37.7 Ma), and rotations of Tikku and Cande [2000] for chrons 20o and older (42.7 – 84 Ma, Table 1). Both sets of rotation parameters are well constrained by geophysical data from the southeastern Indian Ocean; the rotation parameters and their uncertainties calculated using the Royer and Chang [1991] method were published for all reconstruction ages. [19] As in the study of Steinberger et al. [2004], we switch the Australia-Lord Howe Rise plate circuit to the East-West Antarctica circuit at chron 20o (43 Ma), and interpolate the rotations for times between chrons 21y and 20o. For times younger than chron 20o, the two plate circuit models are identical. 2.1.3. Common Reconstructions [20] Once the Pacific plate is reconstructed to East Antarctica, the remaining chain of the relative plate motion is the same in both models: the reconstructions between East Antarctica and Africa, Africa and North America, etc., are added to the Pacific-East Antarctica rotations to compute the motion of the Pacific plate relative to the continents bordering the Atlantic and Indian oceans. [21] For the East Antarctica-Africa motion we used the revised three-plate solution of Nankivell [1997], which is constrained by data from the southern Atlantic and the southwest Indian oceans and by the closure of the East Antarctica-Africa-South America plate circuit. [22] The method used by Nankivell [1997] to derive finite rotations is an extension of the procedure developed by

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Shaw and Cande [1990], which is based on the fitting of the observed magnetic and fracture zone picks to the synthetic flow lines computed iteratively from the kinematic model. The uncertainties of the model parameters (finite rotations) were estimated from the observed misfits between the synthetic flow lines and the actual picks (see the study of Nankivell [1997] for further details). The uncertainties were presented as three-dimensional 95% confidence ellipsoids for the rotation pseudovectors (section 2.2) for all rotations back to chron 34y (Table 1). [23] Rotation parameters of McQuarrie et al. [2003] were used for the reconstructions between Africa and North America back to chron 30r (67.8 Ma). The rotations are based on locations of magnetic anomalies and fracture zones in the central Atlantic [Klitgord and Schouten, 1986]. For each rotation, the uncertainties were reported as partial uncertainty rotations [e.g., Stock and Molnar, 1983; Molnar and Stock, 1985] (section 2.2). For older times (before chron 30r), we used the rotation parameters of Klitgord and Schouten [1986], for which uncertainties were not estimated (Table 1). 2.2. Reconstruction Method [24] Before combining the rotations through the two plate circuits, two technical problems had to be addressed. The first issue was to parameterize the reconstruction uncertainties for all reconstructions used in plate circuit calculations in a similar manner, so that it would be possible to calculate the uncertainties of combined rotations. [25] Chang et al. [1990] discussed various parameterizations of the rotation uncertainty and showed that the use of the moving exponential parameterization is the most computationally efficient and statistically robust way to analyze the rotation uncertainty. The difference between the estimated rotation A^ and the true (unknown) rotation A0 is expressed as A^ ¼ A0 FðhÞ

ð1Þ

where F(h) is a small right-hand rule rotation about vector h by khk radians. The covariance matrix of vector h is estimated from data and used to construct the confidence region for the unknown rotation (see the auxiliary material Text S1 for further details).1 [26] The majority of reconstructions listed in Table 1 include the uncertainties parameterized using Chang’s [1988] covariance matrices. The uncertainties of the remaining reconstructions, which have been expressed using different parameterizations (i.e., partial uncertainty rotations [McQuarrie et al., 2003] and 95% confidence ellipsoids of rotation pseudovectors [Sutherland, 1995; Nankivell, 1997], Table 1), were converted into the ‘‘approximate’’ covariance matrices using the formulations given in the auxiliary materials. [27] The second problem arises because different published sets of rotations (individual plate pair reconstructions) were calculated for different ages (chrons in Table 1). Because ‘‘noncoeval’’ rotations cannot be combined directly,

1 Auxiliary materials are available in the HTML. doi:10.1029/ 2008JB005584.

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it was necessary to recalculate some of the rotations using a single set of ages common for all plate circuit reconstructions. [28] Here we adopted the following procedure. Absolute ages were assigned to the finite rotations using the identifications of magnetic polarity chrons (Table 1) according to the most recent calibration of the geomagnetic polarity timescale (GPTS2004) [Ogg and Smith, 2004]. For each particular plate circuit, a single list of ages was compiled, including all reconstruction ages from the individual plate pair reconstructions. If a particular age from this list was missing in the original set of finite rotations for an individual plate pair reconstruction, the finite rotation for this age was calculated using linear interpolation between the two original rotations corresponding to the closest ages bracketing the age of interest. The interpolation procedure is based on the calculation of a stage rotation and assumes steady plate motion during the time interval between the two bracketing ages. The uncertainty of the interpolated rotation was estimated from the uncertainties of the original rotations using the equations presented in the auxiliary materials. [29] When it was assumed that no motion had occurred between two plates during a certain time interval (e.g., between chrons 21y– 34y for the LHR-Pacific motion, or between chrons 27– 34y for the East-West Antarctica motion, Table 1), both the ‘‘interpolated’’ rotations (for the ages within the interval) and their uncertainties were set to those of the ‘‘younger’’ rotation. [30 ] Because the East-West Antarctica rotations for chrons 20o/24o and 27 were extrapolated from the chron 13o rotation [Cande et al., 2000; Cande and Stock, 2004b], we chose to set the uncertainties of the interpolated rotations between chrons 13o and 27 to that of the chron 13o rotation. Recognizing that this uncertainty may not be applicable for the older reconstructions, we nevertheless believe that it provides at least a minimum ‘‘inherited value’’ for the extrapolated rotation uncertainty. [31] Uncertainties were not available for some rotations corresponding to the reconstruction ages older than chron 30r (Table 1) and no attempt was made to estimate them. The covariance matrices for these rotations were set to zero. Thus, the uncertainties of the combined rotations for times before chron 30r are underestimated in both plate circuit reconstructions. [32] For each reconstruction age, finite rotations (original or interpolated) were combined and the uncertainty of the combined rotation was calculated using the method described by Royer and Chang [1991]. If a plate circuit consists of n plates (n 1 plate boundaries), the combined rotation can be expressed as A^1!n ¼ A^ðn1Þ!n A^ðn2Þ!ðn1Þ A^2!3 A^1!2

ð2Þ

where A^1!n is the rotation matrix corresponding to the finite rotation which reconstructs plate 1 (moving plate) to plate n (fixed plate), A^1!2 is the rotation of plate 1 to plate 2, A^2!3 is the rotation of plate 2 to plate 3, and so on. The ‘‘hat’’ symbol is used to denote the estimated rotations.

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[33] The estimate of covariance matrix for the combined rotation is calculated using the following recursion [e.g., Chang et al., 1990]: covðh1!3 Þ ¼ A^T1!2 covðh2!3 Þ A^1!2 þ covðh1!2 Þ covðh1!4 Þ ¼ A^T covðh3!4 Þ A^1!3 þ covðh1!3 Þ 1!3

:::

covðh1!n Þ ¼ A^T1!ðn1Þ cov hðn1Þ!n A^1!ðn1Þ þ cov h1!ðn1Þ ð3Þ

where A^1!i (i = 2,. . ., n 1) is the rotation which reconstructs plate 1 to plate i. [34] The calculations of the combined rotations and their uncertainties were performed using a computer program based on the ADDROT algorithm of Royer and Chang [1991] described by Kirkwood et al. [1999]. Because the uncertainties of combined rotations usually included covariance matrices estimated through interpolation, or converted from partial uncertainty rotations or error ellipsoids of ^ (for the rotations originally estimated rotation vectors, all k using the spherical regression method) were treated as known values (see Kirkwood et al. [1999] for the discussion of the ‘‘known kappa’’ assumption). The resulting finite rotations and estimated uncertainties for the motion between the Pacific, East Antarctic and North American plates are presented in auxiliary Tables A1 – A8.

3. Paleomagnetic Consistency Tests 3.1. Pacific Paleolatitude Data [35] Arguably the most reliable Late Cretaceous to Early Eocene paleomagnetic data for the Pacific plate come from the basalt sections recovered from the four Emperor seamounts in the northwestern Pacific Ocean: Koko (49.2 Ma), Nintoku (55.5 Ma), Suiko (60.9 Ma) and Detroit (75.8– 80 Ma) [Kono, 1980; Tarduno and Cottrell, 1997; Tarduno et al., 2003; Doubrovine and Tarduno, 2004]. Because the basalts were cored using rotary drilling, with no control on the azimuthal orientation of samples, only paleomagnetic inclinations and paleolatitude data are available from these sections (Table 2). [36] In the original publications [Tarduno and Cottrell, 1997; Tarduno et al., 2003; Doubrovine and Tarduno, 2004], a paleolatitude was calculated from a site-mean inclination, estimated from the inclinations of independent directional groups using the maximum likelihood method of McFadden and Reid [1982] (IMLE in Table 2). (The inclination group is defined as a group of adjacent lava flows with indistinguishable flow-mean inclinations. Each inclination group is assumed to represent a single, independent cooling unit, which records a ‘‘spot reading’’ of the geomagnetic field.) [37] This approach assumes that the group-mean directions are Fisher distributed. However, data on paleosecular variation of geomagnetic field (PSV) from recent lavas [McElhinny and McFadden, 1997; Tanaka, 1999] and theoretical PSV models [e.g., Kono, 1997; Tauxe and Kent, 2004] suggest that distributions of virtual geomagnetic poles (VGPs) are approximately Fisherian while the corresponding distributions of paleomagnetic directions

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Table 2. Pacific Paleolatitude Data From the Emperor Seamountsa Seamount Koko Nintoku Suiko Detroit Detroit-y Detroit-o

Age (Ma) 49.2 55.5 60.9 78 75.8 80.0

± 0.2 ± 0.6 ± 0.3 ± 0.6 ± 0.9

ls (°N)

fs (°E)

34.926 41.333 44.777 51.198 51.147 51.451

172.146 170.378 170.021 167.859 167.765 168.337

n

IMLE (deg)

lMLE (deg)

^k

^ K

S (deg)

17 22 40 36 26 10

38.3+6.9 9.3 44.3+10.1 6.3 44.9+6.9 3.5 53.9+3.2 6.4 53.2+4.4 8.1 55.7+7.7 6.2

22.0+5.3 5.9 27.0+6.1 7.5 27.0+3.4 4.4 35.0+3.6 5.0 34.4+4.8 6.4 36.6+6.7 7.6

18.9+15.2 10.7 14.2+9.7 7.2 17.9+8.8 7.0 24.6+12.7 10.1 20.5+12.8 9.7 50.2+55.8 35.1

38.7+31.1 22.0 19.6+13.5 10.0 29.7+14.6 11.7 27.9+14.5 11.5 23.9+15.0 11.4 46.8+52.1 32.8

13.0+6.8 3.3 18.3+7.9 4.2 14.9+4.2 2.7 15.3+4.7 2.9 16.6+6.3 3.6 11.8+9.8 3.7

a Parameters are as follows: Age, radiometric age estimate ±2s uncertainty; ls, fs, present day site latitude and longitude, respectively; n, the number of independent inclination units; IMLE, ^k maximum likelihood estimates (MLE) of inclination and of directional precision parameter (±95% confidence limits), ^ MLEs of paleolatitude and of polar precision parameter, respectively, assuming respectively, assuming that the directions are Fisher distributed; lMLE, K, that the VGPs are Fisher distributed; S, angular dispersion of VGPs. The ‘‘Detroit’’ is the combined estimate from the Detroit basalts; the ‘‘Detroit-y’’ denotes younger basalts collected at ODP sites 883, 1203 and 1204; the ‘‘Detroit-o’’ denotes older basalts from ODP Site 884. References for radiometric ages are Tarduno et al. [2003], Duncan and Keller [2004], Sharp and Clague [2006], and Keller et al. [1995]. References for paleomagnetic data are Tarduno et al. [2003], Kono [1980], Doubrovine and Tarduno [2004], and Tarduno and Cottrell [1997].

are not. Consequently, it is usually assumed that VGPs rather than field directions are Fisher distributed. Therefore, we recalculated the paleolatitudes by first defining the group-mean virtual geomagnetic latitudes (VGLs) l ¼ arctan

1 tan I 2

ð4Þ

where I is the group-mean inclination, and then using the VGLs as input data for the McFadden and Reid [1982] procedure to calculate the maximum likelihood estimate (MLE) of paleolatitude (lMLE). This estimate is based on the assumption that the parental VGPs (corresponding to the individual group-mean directions) are Fisherian. [38] The values of lMLE for Koko, Nintoku and Detroit seamounts (Table 2) do not differ significantly from the original estimates of Tarduno et al. [2003], Tarduno and Cottrell [1997] and Doubrovine and Tarduno [2004]. Because of the 4 Ma age difference between the basalts collected at the three nearby sites at the summit region (Ocean Drilling Program (ODP) sites 883, 1203 and 1204) and those from the lower eastern flank of Detroit Seamount (ODP Site 884), we also calculated the lMLE separately for the younger and older basalt groups. These two estimates are indistinguishable from the combined lMLE (Table 2) and from the earlier estimate of Doubrovine and Tarduno [2004]. The group-mean inclination data of Kono [1980] were treated in the same way, i.e., using the McFadden and Reid [1982] method independently for inclinations and VGLs. The resulting lMLE for Suiko is almost exactly the same (a 0.1° difference) as the value reported by Kono [1980]. [39] A useful byproduct of the VGL analysis is an estimate of the precision parameter of the VGP distribution ^ which does not rely on the approximate conversions (K), from the directional to polar space used in previous studies [e.g., Doubrovine and Tarduno, 2004]. The angular disper^ using sion of VGPs can be estimated from K rffiffiffiffi 2 S¼ ^ K

ð5Þ

where S is expressed in radians. This estimate is a very good ^ (e.g., K ^ > 10 [Cox, approximation for large values of K 1970]).

[40] The values of S shown in Table 2 are in excellent agreement with previously published estimates, and compare favorably with the values predicted from the paleosecular variation model (model G) of McFadden et al. [1991] for the 40– 85 Ma period. The predicted S = 12.2° for Koko, 13.4° for Nintoku and Suiko, and 15.2° to 15.8° for Detroit (corresponding to l = 34.4° to 36.6°, respectively). This suggests that the basalt sections adequately sampled the secular variation of the geomagnetic field. [41] The only exception, as was also noted by Tarduno et al. [2003], is the Nintoku Seamount section, which shows the S value significantly higher than the model prediction. However, if we include the uncertainties of the model parameters and paleolatitude, the observed and predicted dispersions are not distinguishable. Also, the geologic evidence for time sampled by the Nintoku basalts and the statistical properties of the inclination data strongly suggests the mean inclination represents the time-averaged field [Tarduno et al., 2003]. This may point to the limitations of the reference data [McFadden et al., 1991], which cover large time intervals unevenly and hence may miss higher frequency variations in S. 3.2. Comparisons With Synthetic Reference Poles [42] Two different approaches were used for the selection of non-Pacific reference poles. The first approach relies on two recent compilations of synthetic apparent polar wander paths (APWPs) published by Besse and Courtillot [2002] and Torsvik et al. [2001a]. The second and arguably more conservative approach uses the most reliable poles from paleomagnetic case studies for single lithospheric plates; these will be fully discussed in section 3.3. 3.2.1. Synthetic Poles [43] The technique of computing synthetic APWPs was proposed by Besse and Courtillot [1991] and involves the reconstruction of paleomagnetic poles from several lithospheric plates into a common reference frame, usually anchored to one of the major plates (e.g., the African plate). Only poles meeting certain minimum reliability criteria (e.g., those with the reliability factor Q 3 [Van der Voo, 1993]) are included in the synthetic APWP calculation. Once the poles have been rotated into a common reference frame, the APWP is calculated using a sliding window technique (sometimes referred to as the running mean method), in which a time window (usually 10 Ma or 20 Ma long) is moved back in time at fixed increments

6 of 24


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Table 3. Synthetic Reference Polesa Age (Ma) 49.9 55.0 60.7 75.4 79.1 50.0 55.0 60.0 75.0 80.0

lp (°N)

fp (°E)

N

A95 (deg)

Poles of Besse and Courtillot [2002]b 85.1 156.4 17 4.2 85.3 181.7 22 4.1 84.3 211.5 24 4.3 86.7 245.7 10 7.3 80.9 292.0 9 6.9 Poles of Torsvik et al. [2001a]c 77.82 169.48 27 77.08 172.98 32 75.78 174.27 26 71.70 194.85 8 72.30 184.77 11

2.93 2.52 2.69 6.22 5.37

^ K 76.0 58.1 48.9 45.8 58.1 90.9d 102.6d 112.1d 80.3d 73.3d

a Parameters are as follows: Age, nominal age assigned to the mean pole; lp, fp, the mean pole latitude and longitude, respectively; N number of individual poles used to calculate the mean; A95, circular uncertainty of the ^ Fisherian precision parameter. mean pole at the 95% confidence level; K, b East Antarctic reference frame. c North American reference frame. d ^ values calculated from A95. The K

auxiliary materials for its definition). The semiaxes of the 95% confidence ellipse for the rotated pole (a95 and b95, expressed in radians, a95 b95) are calculated from the two ^ (n 1 and n 2, n 1 n 2) using nonzero eigenvalues of cov(Ap) a95 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c20:05 ½2 n 1

b95 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c20:05 ½2 n 2

^ ¼ AM ^ ðpÞcovðhÞM ðpÞT A^T cov Ap

ð6Þ

where A^ is the rotation matrix, p is the unit vector ^ is the rotated corresponding to the initial pole position, Ap pole, cov(h) is the estimated covariance matrix for the ^ and M(p) is a skew-symmetric matrix (see the rotation A,

ð7Þ

where c20.05[2] is the critical value of the c2 distribution with 2 degrees of freedom. (Note that the third eigenvalue of ^ corresponds to the eigenvector Ap ^ and is always cov(Ap) zero.) The orientation of the confidence ellipse (i.e., the azimuth of the major axis) is defined by the direction of the eigenvector corresponding to the largest eigenvalue (n 1). [48] The ‘‘intrinsic’’ uncertainty of a paleomagnetic pole (A95, expressed in radians) can be reasonably well approximated by

A95

(e.g., 5 Ma), and all poles within the window are averaged using Fisherian statistics. [44] Besse and Courtillot [2002] used paleomagnetic data from all major lithospheric plates, with the exception of the Pacific plate, and the kinematic models of Royer et al. [1992] for Atlantic and Indian Oceans. The synthetic APWPs calculated at 10 Ma steps with a 20 Ma window, and at 5 Ma increments with a 10 Ma window, were tabulated for the eight major plates, including East Antarctica. Because of the better time resolution (which allowed the comparison with all Pacific paleolatitudes listed in Table 2), poles calculated at 5 Ma steps with the 10 Ma window, with the nominal ages (mean ages) closest to the ages of the five basalt sections from the Emperor Seamounts, were used for the comparison (Table 3). [45] Torsvik et al. [2001a] combined data from North America and Eurasia only and used their own kinematic model for the closure of the North Atlantic Ocean. The synthetic APWP was calculated in North American coordinates using a 20 Ma sliding window at 5 Ma increments. The poles selected from this APWP are given in Table 3. 3.2.2. Transformation to the Pacific Reference Frame [46] Reference poles were transferred to the Pacific plate using the two plate circuit models defined in section 2. The individual two-plate reconstructions within each circuit were interpolated to the nominal ages of the reference poles (as described in the auxiliary materials), and then combined using the formulations given in section 2.2. The finite rotations and the estimated uncertainties are presented in auxiliary Tables A9 –A12. [47] The reconstruction uncertainty of the rotated poles was calculated using the following relationship [Royer and Chang, 1991]:

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sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c20:05 ½2 ¼ ^ KN

ð8Þ

^ = (N 1)/(N R) is the estimate of the Fisher where K precision parameter, and N is the number of the VGPs (or study-mean poles in the case of synthetic APWPs) used to calculate the pole. This approximation is applicable only if ^ and N are large, which is usually the case. Hence, the K semiaxes of the total 95% confidence ellipse for the rotated pole, which includes both the reconstruction uncertainty and A95, can be calculated as a*95 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a295 þ A295

b*95 ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b295 þ A295

ð9Þ

The orientation of this ellipse is the same as that of the reconstruction uncertainty ellipse. 3.2.3. Synthetic Reference Poles in Pacific Coordinates [49] The synthetic poles of Besse and Courtillot [2002] and Torsvik et al. [2001a] were transferred from East Antarctica and North America, respectively, using the rotation parameters given in auxiliary Tables A9 – A12. The rotated poles are shown in Figure 2; their positions and the reconstruction uncertainties are presented in auxiliary Tables A13 and A14. [50] Although the rotations in the two alternative plate circuit reconstruction differ significantly, the rotated position of any single pole is not greatly affected by the choice of plate circuit. The differences are on the order of 1° to 1.5° for the Paleocene and Eocene poles and 1° to 2.5° for the Late Cretaceous poles, well below the A95 limits. The reconstruction uncertainties of the transferred poles are generally within a 0.5° – 1.5° range (auxiliary Tables A13 and A14). Because the values of a295 and b295 are almost negligible compared to those of A295, the incorporation of the reconstruction uncertainty does not significantly increase confidence limits of the rotated poles. [51] As was mentioned in section 2.2, the rotation uncertainties are underestimated for Late Cretaceous times. On the other hand, the A95 of the Late Cretaceous poles are the

7 of 24

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Figure 2. Synthetic poles of Besse and Courtillot [2002] and Torsvik et al. [2001a] rotated to the Pacific plate. The ellipses show the total 95% confidence uncertainty of the rotated poles. Bold solid lines show the colatitudes of the Pacific seamounts, dashed lines correspond to their 95% confidence limits. Dotdashed lines in Figure 2c show the 95% confidence of the Suiko colatitude from Cox and Gordon [1984]. Gray lines in Figures 2d and 2e show the combined Detroit colatitude and its uncertainty (see text). largest, so the incorporation of the reconstruction uncertainty has virtually no effect on the size of the confidence region. Thus, the results of the consistency test for the Late Cretaceous data are not expected to be significantly affected by the underestimation of the rotation uncertainty. 3.2.4. Formal Statistical Test [52] The 95% confidence bands of colatitude shown in Figure 2 can be viewed as the confidence regions for the Pacific paleomagnetic poles, which would be defined had the declination data been available. In the cases when a reference pole is within the colatitude band (e.g., Figures 2d and 2e), it is safe to conclude that the Pacific and the nonPacific data do not show substantial discrepancies at the 5% significance level. Conversely, if the colatitude bands and confidence ellipses do not overlap, it can be concluded that the discrepancy is significant. In the remaining cases, a formal statistical test is needed to decide whether the

latitudes estimated from the Pacific paleomagnetic data and those predicted by the reference poles are distinct. [53] If VGPs (or mean poles contributing to a synthetic reference pole) are Fisher distributed with the precision parameter K, the probability density function for colatitude (q = 90° l) of a particular site is given by [e.g., Kono, 1980; Clark, 1983] f ðqÞ ¼

K expðK cos q cos q0 ÞI0 ðK sin q sin q0 Þ sin q ð10Þ 2 sinh K

where q0 is the true colatitude and

8 of 24

1 I0 ð xÞ ¼ 2p

Z

2p

expð x cos fÞdf 0

ð11Þ


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is the modified Bessel function of the first kind of zero order. Except for a site exactly at the paleoequator (q0 = 90° = p/2 radians), the distribution is asymmetric about q0 and skewed in such way that the ordinary mean

[56] Under the null hypothesis, t0 is approximately distributed as Student’s t with a number of degrees of freedom df ¼

q¼

N 1 X qi N i¼1

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þ N22

2

ðS12 =N1 Þ N1 1

ð12Þ

S2 2

S12 N1

þ

ðS22 =N2 Þ

2

N2 1

or, if equal variances are assumed, df ¼ N1 þ N2 2

is biased toward the equator, meaning that the expected value of q is closer to p/2 than q0 (E(q) > q0 when q0 < p/2; E(q) < q0 when q0 > p/2). [54] If K is large, 2 sinh K exp K and the deviation from the true colatitude (q q0) will be small with high probability, so that cos(q q0) 1 (q q0)2/2 and sin q sin q0. If the true site paleocolatitude is not polar, so that K sin2 q0 1 (meaning that the portion of the pole distribution folded about the axis passing through the Earth’s center and the site is insubstantial), then expð K sin q0 sin qÞ I0 ð K sin q0 sin qÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pK sin q0 sin q

ð13Þ

Substituting these approximations into equation (10), we obtain " # rffiffiffiffiffiffi K K ðq q0 Þ2 exp f ðqÞ 2 2p

ð14Þ

Hence, as K sin2q0 ! 1 , the exact distribution becomes approximately normal with mean q0 and variance 1/K. [55] When approximation (14) is acceptable, the equatorial bias of the mean is negligible (E(q) q0) and the standard Student’s t test can be used to determine whether two population means are unequal. The statistics for testing the null hypothesis that two colatitude samples are from the populations sharing a common mean (H0:q01 = q02) is q1 q2 ffi t 0 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffi S12 S22 þ N1 N2

ð15Þ

where the subscripts 1 and 2 refer to the first and second sample, respectively, and S2 ¼

N 2 1 1 X qi q ¼ ^ N 1 K i¼1

ð16Þ

is the sample variance. If the two populations are assumed to have equal variances (K1 = K2), it is appropriate to replace the sample variances in equation (15) by the pooled variance

Sp2 ¼

S12 ðN1 1Þ þ S22 ðN2 1Þ N1 þ N2 2

ð18Þ

ð19Þ

The null hypothesis can be rejected at an a significance level if jt0j > ta/2[df], where ta/2[df] is the critical value of the t distribution with df degrees of freedom. [57] Because the ‘‘approximation to normality’’ discussed above is essentially based on the asymptotic expansion of I0(K sin q0 sin q), it requires a very large value of K sin2q0 to be sufficiently accurate. Over a typical range of the precision parameter controlled by the secular variation of geomagnetic field, e.g., K = 15– 50 [McFadden et al., 1991], the equatorial bias for low to intermediate latitudes is small, but not negligible, ranging from 0.5° to 1.5° for midlatitudes [Clark and Morrison, 1983]. Furthermore, because the bias in the mean depends on K, the means of the two colatitude populations with the same q0 but different K are not equal, so that the hypothesis that m1 = m2 (which is tested using the statistics given by equation (15)) is not equivalent to the hypothesis that q01 = q02. [58] The bias can however be corrected [e.g., Clark and Morrison, 1983] and the test can be modified accordingly to account for unequal biases. An unbiased estimate of colatitude (i.e., the bias-corrected mean, ^q) is obtained by iteratively solving the following equation ^q ¼ q d ^q

ð20Þ

where d(^q) is the bias function defined as Z

p

d ðq0 Þ ¼ E ðqÞ q0 ¼

ðq q0 Þ f ðqÞdq;

ð21Þ

0

which can be evaluated by numerical integration. ^ is [59] Because K is unknown, the estimate value (K) used to calculate the value of d(^q). This is justified for large ^ is close to the samples, when it is safe to assume that the K true precision parameter. Alternatively, K can be prescribed using global PSV data, as has been proposed by Cox and Gordon [1984]. However, most PSV models are defined using recent (e.g., 0 – 5 Ma) paleomagnetic data and may be not appropriate for earlier times. The only available PSV model for the Late Cretaceous-Paleogene time of McFadden et al. [1991] is based on binning the data which unevenly cover a 45 Ma long time interval (40– 85 Ma), and hence may lack the resolution necessary to define the PSV on a ^ values seems shorter timescale. Thus, the use of observed K to be a more natural and conservative choice. [60] Denoting the values of ^q corresponding to q ± 1 standard error as q+ and q, respectively,

ð17Þ

9 of 24

S qþ ¼ q þ pffiffiffiffi dðqþ Þ N

ð22Þ


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Table 4. Results of the Consistency Test for Synthetic Reference Poles Transferred Through the East-West Antarctica Plate Circuita Site Koko Nintoku Suiko Suikob Detroit-y Detroit-o

^ o (deg) S*o (deg) l ^ p (deg) S*p (deg) Age (Ma) l 49.9 55.0 60.7 60.7 75.4 79.1

Poles of Besse 22.0 27.1 27.0 26.8 34.4 36.6

and Courtillot [2002] 2.3 27.1 1.6 2.9 33.6 1.6 1.7 36.2 1.7 3.2 36.2 1.7 2.4 32.3 2.7 2.7 31.9 2.5

t0

P (%)

1.822 1.948 3.828 2.589 0.578 1.268

7.9 6.0 0.032 1.5 56.9 22.2

Poles of Torsvik et al. [2001a] 22.0 2.3 28.4 1.2 2.459 2.1 27.1 2.9 33.3 1.1 2.017 5.4 27.0 1.7 34.6 1.1 3.735 0.041 26.8 3.2 34.6 1.1 2.305 3.0 34.4 2.4 36.4 2.3 0.609 54.8 36.6 2.7 33.4 2.0 0.938 36.1 a ^ o and l ^ p are the observed and predicted Parameters are as follows: l latitudes (see text for definitions), S*o and S*p are their standard errors; t0 is the test statistics (equation (25)); P is the probability of observing the value as large as t0 or larger provided the null hypothesis is true. b ^ o and S*o are from Cox and Gordon [1984]. The values of l Koko Nintoku Suiko Suikob Detroit-y Detroit-o

50.0 55.0 60.0 60.0 75.0 80.0

S q ¼ q pffiffiffiffi d ðq Þ N

ð23Þ

the standard error of the corrected mean can be approximated by [Cox and Gordon, 1984] S* ¼

qþ q S dðq Þ dðqþ Þ ¼ pffiffiffiffi þ 2 2 N

ð24Þ

[61] Assuming that the distribution of ^q is approximately normal with mean q0 and variance s*2 (estimated by S*2) and by analogy with normal samples, the statistics ^q1 ^q2 t 0 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S1*2 þ S2*2

ð25Þ

is expected to be approximately distributed as Student’s t with 2 2 S1* þ S2*2 df ¼ 4 4 S* 1 þ S *2 N1 1

ð26Þ

uncertainty ellipse and the great circle connecting the pole and the site. [63] On a cautionary note, it must be remembered that the t0 test described above is approximate and the rejection of the null hypothesis should be deferred in cases of marginal significance. To be on the conservative side, we arbitrary defined cases of ‘‘marginal consistency’’ as those for which the probability of the observed t0 is within the 3% to 7% range. When the probability fell below the 3% level, the null hypothesis was rejected; otherwise, it was retained at the nominal 5% significance level. 3.2.5. Results ô = [64] The observed bias-corrected mean latitudes (l ^ 90° qo) and their standard errors (S*o ) were calculated using VGL data from the Pacific seamounts as described in ^ o for Koko, section 3.1 (Tables 4 and 5). The values of l Suiko and Detroit seamounts are exactly the same as the maximum likelihood estimates of paleolatitude obtained using the McFadden and Reid [1982] method (Table 2). ^ o estimates for the The difference between the lMLE and l Nintoku data set is 0.1°, which is negligibly small compared to the uncertainties of the two estimates. The estimates of ^ calculated using the Gaussian Fisher precision parameter (K) approximation (equation (16)) and the McFadden and Reid [1982] method were also very close, the difference never exceeding 0.2 radians squared or 0.1° for the angular dispersion of underlying VGP distribution (equation (5)). Thus, both the method of McFadden and Reid [1982] and the correction of equatorial bias in the ordinary latitude mean [Cox and Gordon, 1984] produce essentially the same estimates of the observed latitudes and their variances for the four Pacific sections. ^ p) were calculated from the [65] The predicted latitudes (l angular distances between the Pacific sites and the reference poles transferred to the Pacific plate; their standard errors were estimated from the total pole uncertainties. The values of t0 and the corresponding probabilities of observing the test statistics as large as t0 under the hypothesis that the true values of observed and predicted latitudes are equal (H0:lo = lp) are given in Tables 4 and 5. Because the positions of the transferred reference poles are not very sensitive to the choice of plate circuit (Figure 2), essentially the same Table 5. Results of the Consistency Test for Synthetic Reference Poles Transferred Through the Australia-Lord Howe Rise Plate Circuit

N2 1

Site

degrees of freedom. The null hypothesis of a common q0 (H0:q01 = q02) can be rejected at an a significance level if jt0j > ta/2[df]. [62] For colatitudes predicted by reference poles, a Fisherian mean pole is an unbiased estimate of the paleogeographic pole. Hence, the unbiased estimate of colatitude (^q) is simply the angular distance between the pole and the site. If the pole is far from the site (e.g., ^q > 3A95), the variance ^ For a reconof ^q can be approximated by S*2 = 1/(KN). structed pole, the variance also includes the reconstruction ^ + n 1 cos2 8 + n 2 sin2 8, uncertainty, so that S*2 = 1/(KN) where n 1 and n 2 are the nonzero eigenvalues of the covariance matrix of the reconstructed pole (see section 3.2.2) and 8 is the angle between the major axis of the

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^ o (deg) S*o (deg) l ^ p (deg) S*p (deg) Age (Ma) l

Koko Nintoku Suiko Suikoa Detroit-y Detroit-o

49.9 55.0 60.7 60.7 75.4 79.1

Koko Nintoku Suiko Suikoa Detroit-y Detroit-o

50.0 55.0 60.0 60.0 75.0 80.0

and Courtillot [2002] 2.3 28.0 1.6 2.9 34.4 1.7 1.7 36.8 1.7 3.2 36.8 1.7 2.4 32.5 2.7 2.7 30.9 2.5

Poles of Torsvik et al. [2001a] 22.0 2.3 29.3 27.1 2.9 34.3 27.0 1.7 35.4 26.8 3.2 35.4 34.4 2.4 36.6 36.6 2.7 34.2

1.2 1.1 1.2 1.2 2.3 2.1

P (%)

2.119 2.198 4.063 2.759 0.529 1.547

4.3 3.5 0.015 0.99 60.2 14.0

2.793 2.311 4.092 2.536 0.675 0.704

0.98 2.9 0.012 1.8 50.7 49.1

^ o and S*o are from Cox and Gordon [1984]. The values of l

a

10 of 24

Poles of Besse 22.0 27.1 27.0 26.8 34.4 36.6

t0

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results were obtained for the two alternative reconstructions, and the following discussion will apply to the both. [ 66 ] The Late Cretaceous poles (75 and 80 Ma, Figures 2e and 2f) agree well with the paleolatitude estimates from the Detroit Seamount basalts. For all Late Cretaceous comparisons, the reference poles are within the 95% confidence bands of colatitude (Figure 2) and the statistical test (Tables 4 and 5) confirms a low significance of the observed discrepancies. If the only reason for disagreement between the observed and predicted latitudes was unrecognized inaccuracies in the plate circuit reconstructions, it would be natural to expect similar or better agreement of all subsequently younger data. In contrast, the Paleocene and early Eocene data show more significant discrepancies than the older (Late Cretaceous) pole comparisons. [67] The observed and predicted latitudes of Koko and Nintoku seamounts (50 and 55 Ma) are marginally consistent, except for the comparisons of the Koko data with the 50 Ma pole of Torsvik et al. [2001a] where the discrepancy appears significant. However, it should be stressed that the consistency is marginal in all remaining cases. For the majority of these comparisons, the failure to reject the null hypothesis at the nominal 5% level is due to approximations used to derive the distribution of the test statistics and the nominal probability P(jtj t0) is less than 5%. [68] Comparison of the Paleocene (60 Ma) reference poles and the data from the Suiko seamount basalts yield a relatively large discrepancy. In all comparisons for Suiko seamount, an 8° to 10° difference between the mean predicted and observed latitudes is significant at a high confidence level attested by high t0 values and low probabilities (P(jtj t0) < 0.05%) in Tables 4 and 5. [69] The observed latitude of Suiko seamount was calculated from the VGLs of the 40 inclination groups originally defined by Kono [1980], who assigned adjacent lava flow units to a single inclination group if the flow-mean inclinations were statistically indistinguishable. Cox and Gordon [1984] used a different approach in which flows or groups with significantly different mean inclinations were considered time-independent only if the successive inclinations did not form a smooth trend, i.e., when they were not serially correlated. They identified 20 independent inclination units in the succession of 65 lava flows and estimated the mean (bias-corrected) paleolatitude to be ^ o = 26.8° with the standard error due to random errors l SR = 2.5°. (Note that this estimate does not significantly ^ o = 27.0° ± 1.7°, one standard differ from our value (l pffiffiffi error uncertainty quoted), and that SR = 2.5° 1.7° 2, exactly as expected from the twice smaller number of independent units.) [70] Allowing a generous 2.0° systematic error due to the possible borehole tilt (which is probably an overestimate), Cox and Gordon [1984] calculated the total standard error of the bias-corrected mean to be 3.2°. Using this conserva^ o = 26.8°), the test statistics becomes tive value as S*o (and l smaller, but the calculated probability P(jtj t0) does not increase above 3% (Tables 4 and 5), suggesting that the difference between the observed and predicted latitudes of Suiko seamount is significant at the 5% level.

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[71] However, we note that the Cox and Gordon [1984] method is based on an older idea of Cox [1968] that the secular variation is nearly sinusoidal, an idea that subsequent data have failed to support. Moreover, Tarduno et al. [2003] introduced a more conservative approach of first grouping lavas in the ‘‘lava units’’ on the basis of petrology and geochemistry. Using such a method on the Suiko drill section would likely result in a lower N (and perhaps a slightly different mean), but such an analysis is beyond the scope of this work. 3.3. Comparisons With the Most Reliable Individual Poles [72] Synthetic APWPs have been criticized in some studies [e.g., Riisager et al., 2002, 2003], where it was pointed out that the inclusion of a large number of mutually inconsistent poles with questionable reliability (e.g., those from sedimentary sequences, which are prone to the inclination shallowing, or those from the early studies which did not use adequate demagnetization techniques) may have caused a systematic bias of the synthetic poles that is not adequately represented in their nominal confidence limits. The marginal agreement of the Pacific paleolatitudes with the predictions from synthetic poles in the early Paleogene provides motivation to examine the most reliable poles from paleomagnetic case studies for individual plates, to check whether the discrepancies are due to unrecognized biases in the synthetic poles. 3.3.1. Selection Criteria [73] The most reliable paleomagnetic poles were extracted from the Global Paleomagnetic Database (GPMDB version 4.6 updated in 2005) [McElhinny and Lock, 1996] using the following criteria. [74] 1. Poles from sedimentary formations, from the locations which have not remained tectonically coherent with the stable plate interior, and from the intrusive rocks lacking clear stratigraphic control for the potential postemplacement tilt are excluded. [75] 2. The age of a particular igneous formation should be reliably constrained by radiometric dates, stratigraphic evidence and/or magnetostratigraphy to an interval no longer than 10 Ma. [76] 3. The nominal (median) age assigned to the pole should be within 3 Ma of the age of one of the Pacific basalt sections (Table 2). [77] 4. Demagnetization procedures and the directional data analysis should be adequate to define characteristic remanence (ChRM) directions, and include the evidence that the isolated ChRM is a primary magnetization (e.g., field tests or rock magnetic experiments). [78] 5. The time interval sampled by a particular formation and the number of sites or time-independent directional units should be sufficient to average secular variation (e.g., Dt 104 yr, N 10); the number of samples defining a single directional unit should be 3. [79] 6. If more than one nearly coeval poles from the same plate satisfy conditions 1– 5, the pole with the overall highest reliability is preferred. [80] These criteria (apart from the constraint tying the reference poles to the ages of the Pacific seamounts) are more restrictive than those used for the synthetic APWP

11 of 24


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Table 6. North American, Eurasian, and Greenland Reference Poles Rock unit

Age (Ma)a

fp lp (°N) (°E)

A95 N (deg)

North America Eocene Intrusives, MT 51.5 ± 3.5 82.0 170.2 94 Paleocene Intrusives, MT 63 ± 4 81.8 181.4 36

^ K

Ref

3.5 5.4

18.6 20.2

1 1

Faroe Islands Lavas Faroe Islands Lavasb

Eurasia 56.5 ± 2.5 71.4 154.7 43 69.7 159.6

6.0

14.3

2

West Greenland Lavas West Greenland Lavasb

Greenland 58 ± 4 73.6 160.5 44 76.0 166.0

6.2

13.1

3

a

The nominal age assigned to the pole on the basis of reported radiometric dates and magnetostratigraphy (rounded to 0.5 Ma). b Poles transferred to North America using the following rotations: Eurasia to North America, pole: 63.02°N, 141.55°E, angle: 14.02° (interpolated to 56.5 Ma using the rotations of Srivastava and Roest [1989]); Greenland to North America, pole: 21.97°N, 215.35°E, angle: 3.21° (interpolated to 58 Ma using the rotations of Roest and Srivastava [1989]). References: 1, Diehl et al. [1983]; 2, Riisager et al. [2002]; 3, Riisager et al. [2003].

calculations (section 3.2.1). Surprisingly, only four Paleogene poles satisfy all selection criteria: two poles from North America, one from Eurasia (the Faroe Islands), and one from West Greenland (Table 6). 3.3.2. Selected Poles [81] The two North American poles which pass our reliability criteria are from the intrusive and extrusive rocks of Montana exposed in the area east of the leading edge of the Rocky Mountains deformation front. The poles from the Eocene (48– 55 Ma) and Paleocene (59 –67 Ma) intrusives of northern and central Montana [Diehl et al., 1983] have been considered as two of the best defined and most reliable reference poles for the North American craton, both in terms of the age constraints and the quality of paleomagnetic data [e.g., Butler, 1992]. [82] The Faroe Islands and West Greenland poles of Riisager et al. [2002, 2003] are the two most recent poles from the North Atlantic Igneous Province (NAIP). Although the European part of the NAIP (the British Tertiary Igneous Province, BTIP) has been extensively studied, and the GPMDB lists fifteen additional poles which satisfy the minimum reliability criteria of Torsvik et al. [2001a] (11 of them were also included in the compilation of Besse and Courtillot [2002]), most of them are from early paleomagnetic studies which routinely used blanket demagnetization for the bulk sample collections and the outdated minimum dispersion method to calculate unit-mean directions. Riisager et al. [2002] discussed these limitations and suggested that many of these data may have been contaminated by unremoved viscous overprints, resulting in a systematic bias in the estimated pole positions. [83] Most of the BTIP was emplaced during a short time interval between 58– 61 Ma, with the most voluminous igneous activity concentrated within chron 26r [e.g., Bell and Williamson, 2002, and references therein]. The high eruption rates and the emplacement of numerous intrusive bodies during a short time interval led to the currently exposed sequences that, taken as a known, may not be time-

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independent. This is important because early studies (or a compilation of results from early studies) may comprise ‘‘oversampling,’’ in which separate igneous units (e.g., lava flows, dikes, intrusions) were treated as independent cooling units, without consideration of their possible temporal correlation. [84] The formation of the BTIP started shortly before and continued during the breakup between Greenland and Eurasia. The BTIP rocks were emplaced into already stretched and thermally uplifted continental crust, which later underwent further extension and subsidence of the passive continental margin. This tectonic regime have resulted in the local block faulting and postemplacement tilting on many sites on the British and Faroe Islands where the BTIP rocks were sampled. Good stratigraphic control on the attitude of the lava flows, and host rocks for the intrusive bodies, is thus a necessary condition for correcting the tectonic tilt and defining paleomagnetic poles. Yet, in many cases (e.g., when dikes intruded much older and already folded strata), the tectonic corrections were not available, and in situ directions were used to calculate the poles. It is also possible that small tilts may result in inclination differences that mimic secular variation (again, adding to the danger of oversampling). [85] The pole of Riisager et al. [2002] from the Faroe Islands flood basalts is based on detailed stepwise demagnetization experiments; the principal component analysis [Kirschvink, 1980] was used to accurately define the ChRM directions; all data were structurally corrected; the indistinguishable site-mean directions of the consecutive and stratigraphically correlated flows were combined into the directional groups; and none of the 43 directional groups defined in the basalt sequence recorded transitional (or excursional) field directions. The age of the sequence was constrained by radiometric dates and magnetostratigraphic correlation to the interval spanning chrons 24r – 25n– 25r – 26n (54– 59 Ma). Hence, this pole appears to be the most reliable among the available BTIP poles. The 56.5 Ma nominal age assigned to the pole (Table 6) is in perfect agreement with the reported radiometric dates. [86] The West Greenland pole of Riisager et al. [2003] is of remarkably high quality and is clearly superior to the poles from the earlier studies of the NAIP rocks outcropping at the western and eastern coasts of Greenland. The pole is based on 44 independent paleomagnetic directional groups (excluding those which recorded transitional field directions) from two well-exposed formations of the West Greenland flood basalts. The quality of tectonic corrections based on a detailed stereo photogrammetry analysis is exceptional, and the nonexcursional data pass the fold test. The age is well constrained by the Ar-Ar radiometric dates [e.g., Storey et al., 1998] and magnetostratigraphy to chron 24r for the younger Kanisut formation (54– 57 Ma) and chrons 26r – 27n for the older Vaigat formation (59– 62 Ma). Geologic evidence for time sampled by the West Greenland lavas, and a favorable comparison with the global PSV data [McFadden et al., 1991] lend further credibility to the result. [87] The GPMDB lists ten poles from the earlier studies of the Greenland part of the NAIP, which can be assigned a quality factor Q 3 [e.g., Torsvik et al., 2001a]. All these studies were published in the 1970s and the early 1980s, and hence are prone to the limitations discussed above for

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Figure 3. North American, European, and Greenland reference poles rotated to the Pacific plate. The Pacific colatitude circles are the same as in Figure 2. Black and white symbols show the poles rotated through the East-West Antarctica and Australia-Lord Howe Rise plate circuits, respectively. the early studies of the BTIP (e.g., inadequate demagnetization techniques, oversampling of PSV). Because of the poor consistency with the North American and European data, Torsvik et al. [2001a] considered these poles ‘‘anomalous,’’ suggesting that the anomaly may be related to a persistent octupole component of the time-averaged geomagnetic field (see discussion in section 4); therefore they did not include them into their synthetic APWP. [88] In contrast, when the new pole of Riisager et al. [2003] is transferred to North America using the kinematic model of Roest and Srivastava [1989] and compared to the Paleocene reference pole of Diehl et al. [1983] (Table 6), the two poles pass the Watson F test for a common mean [Watson, 1956] at the 95% confidence level (F = 1.830 < F0.05[2, 156] = 3.054). The West Greenland pole cannot be distinguished from the Faroe Islands pole of Riisager et al. [2002] at the 95% confidence level when the latter is transferred to Greenland [Riisager et al., 2003], or when the two poles are rotated to North America (F = 1.848 < F0.05[2, 170] = 3.049). Nevertheless, at the resolution of the tests needed here, there are important differences which will become clear when the poles are viewed in Pacific coordinates. 3.3.3. Results [89] The Faroe Islands and West Greenland reference poles were rotated to North America using the rotation parameters estimated from the kinematic models of Srivastava and Roest [1989] and Roest and Srivastava [1989], respectively (Table 6). These, and the North American reference poles, were then transferred to the Pacific plate using the rotations in auxiliary Tables A11 and A12. The

reconstructed poles are plotted in Figure 3; their coordinates and reconstruction uncertainties are presented in auxiliary Table A15. [90] The comparisons of the Pacific paleolatitude data with the predictions from individual reference poles are detailed in Table 7. The Eocene and Paleocene North American poles of Diehl et al. [1983] agree remarkably

Table 7. Results of the Consistency Test for Individual Reference Poles Site Poles Koko Nintoku Nintoku Suiko Suiko Suikob Suikob

Polea

ô l (deg)

Transferred Through the EIM 51.5 22.0 FIL 56.5 27.1 WGL 58.0 27.1 WGL 58.0 27.0 PIM 63.0 27.0 WGL 58.0 26.8 PIM 63.0 26.8

Poles Transferred Koko EIM Nintoku FIL Nintoku WGL Suiko WGL Suiko PIM b WGL Suiko b PIM Suiko a

Age (Ma)

S*o (deg)

^p l (deg)

S*p (deg)

t0

P (%)

East-West Antarctica Plate Circuit 2.3 24.1 1.4 0.791 43.5 2.9 36.0 2.4 2.364 2.2 2.9 31.3 2.4 1.116 27.0 1.7 34.7 2.4 2.600 1.1 1.7 27.4 2.2 0.162 87.2 3.2 34.7 2.4 1.968 5.6 3.2 27.4 2.2 0.167 86.8

Through the Australia-Lord Howe Rise 51.5 22.0 2.3 25.2 1.4 56.5 27.1 2.9 37.2 2.4 58.0 27.1 2.9 32.2 2.4 58.0 27.0 1.7 35.5 2.4 63.0 27.0 1.7 28.3 2.2 58.0 26.8 3.2 35.5 2.4 63.0 26.8 3.2 28.3 2.2

Plate Circuit 1.184 24.5 2.694 0.97 1.334 18.8 2.871 0.53 0.448 62.7 2.172 3.6 0.400 69.2

Abbreviations are as follows: EIM, Eocene Intrusives, MT; FIL, Faroe Islands Lavas; WGL, West Greenland Lavas; PIM, Paleocene Intrusives, MT. b ^ o and S*o are from Cox and Gordon [1984]. The values of l

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well with the paleolatitudes of Koko and Suiko seamounts, respectively, the predicted latitudes being within 1 – 3° from the observed values. [91] The West Greenland pole [Riisager et al., 2003] also yields results consistent with the Pacific data. The West Greenland pole spans the ages of Suiko and Nintoku Seamounts; it yields predictions that agree with the paleolatitude of Nintoku Seamount, and are marginally consistent with the Suiko paleolatitude (using the confidence intervals based on N = 20). This suggests that the mean age of the West Greenland pole is closer in age to Nintoku Seamount than Suiko Seamount. [92] The Faroe pole [Riisager et al., 2002], however, yields incongruous results. It has an age similar to Nintoku Seamount, but yields predictions that are clearly discordant with the observed paleolatitude (predicting a significantly higher latitude). But when we view the Faroe and West Greenland poles in Pacific coordinates, we see that the Faroe prediction is also of higher latitude than the West Greenland prediction, yet they are derived from poles that do not differ at the 95% confidence level (Figure 3b). [93] Clearly, at the level of importance of resolution of interest here, the differences between the West Greenland and Faroe mean pole positions are important, even though they technically cannot be distinguished at the 95% confidence level. They nevertheless represent a latitude disparity that is comparable to any of those we have tentatively identified between Pacific data and non-Pacific data as linked by the plate circuits. [94] In summary, the Early Eocene and Paleocene individual paleomagnetic poles from North America and Greenland agree with the Pacific data better than the synthetic APWP values. The reasons of this, and the one anomalous result from an apparently high quality pole (Faroes), however, require further investigation.

4. Discussion 4.1. Discrepancies in Paleogene Data 4.1.1. Assumptions Underlying the Consistency Tests [95] The paleomagnetic consistency test described in section 3 uses two implicit assumptions. First, it is assumed that both the Pacific paleolatitude data and the non-Pacific reference paleomagnetic poles accurately represent timeaveraged geomagnetic field, i.e., that there are no significant systematic biases in the paleolatitude data and reference pole positions. Second, the time-averaged geomagnetic field is assumed to have the morphology of the geocentric axial dipole (GAD) field, with no significant contribution from higher-order terms (e.g., zonal quadrupole or octupole components). [96] Because of the discrepancies between the different sets of the non-Pacific reference poles (resulting in diverse paleolatitude predictions, sections 3.2.5 and 3.3.3), the validity of the first assumption seems to be of the most critical importance. To illustrate this point, let us consider the Paleocene (60 Ma) closure of the two North America to Pacific plate circuits. A researcher who places absolute confidence in the 60 Ma synthetic pole of Besse and Courtillot [2002] would reach a conclusion that both plate circuits underestimate the total amount of extension between East Antarctica and the Pacific since the Paleocene

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by an amount from at least 500 km up to 1000 – 1500 km (Tables 4 and 5). Because the synthetic pole was rotated from East Antarctica, and the amount of extension is not consistent with the history of deformation in Antarctica and New Zealand, this would send him on the search for a missing plate boundary somewhere between the Campbell Plateau and the northern part of the Pacific plate [e.g., Acton and Gordon, 1994]. In contrast, one who believes that the Paleocene North American pole of Diehl et al. [1983] is a more reliable marker of the spin axis at about 60 Ma than the synthetic poles (i.e., because of the inclusion of poor quality data in the synthetic APWPs, the use of long averaging windows, etc.) would find no need for invoking an extra plate boundary within the Pacific Ocean, because the excellent agreement of the Suiko paleolatitude with the reconstructed pole positions suggests that both plate circuits provide fairly accurate reconstructions. [97] The presence of persistent nondipole components may also be in part responsible for the discrepancies between the synthetic and individual reference poles. Since a synthetic pole is usually based on data from widely separated locations, the effect of the nondipole field is expected to be averaged out to a certain degree. If the studies contributing to a synthetic pole (reconstructed to account for the past plate motion) were distributed evenly over the globe, the synthetic mean is expected to coincide (within the uncertainties) with the spin axis. This is usually not the case. The global paleomagnetic data for the Late Mesozoic and Cenozoic come almost entirely from the continents in the Indo-Atlantic hemisphere, with little or no coverage of the antipodal Pacific hemisphere. Nevertheless, some averaging of the nondipole field bias in the synthetic poles should be anticipated. [98] In contrast, individual paleomagnetic poles record the time-averaged field ‘‘as it is’’ (i.e., was) at the sampling location. If a significant nondipole component was present, and this was neglected in the pole calculation using the GAD assumption, the pole may be significantly biased from the position of the spin axis. The same is applicable to paleolatitudes estimated from azimuthally unoriented directional data. [99] Thus, it is critical to access the causes of discrepancies between the synthetic and ‘‘individual’’ reference poles and the possible effects of the nondipole field before attempting to make any plate tectonic inference based on the results of the paleomagnetic consistency tests. 4.1.2. Possible Biases in the 50– 60 Ma Poles [100] In the discussion of synthetic APWP models, Riisager et al. [2002] pointed out that 15 out of 16 Eurasian poles included in the compilation of Torsvik et al. [2001a] for the 40– 70 Ma interval are from the early paleomagnetic studies of the British Tertiary Igneous Province. The BTIP poles make 50% of data in the 40– 60, 45– 65, and 50– 70 Ma averaging windows and the resulting 50, 55, and 60 Ma poles of the synthetic APWP (Table 3) fall approximately halfway between the Paleocene-Eocene reference poles of Diehl et al. [1983] and the mean BTIP pole (74°N, 178°E, when transferred in North American coordinates). Ten early BTIP poles were used by Besse and Courtillot [2002]; these make 30% of data in the 50– 60 and 55– 65 Ma averaging windows where the differences between the observed and predicted latitudes are the most significant (Tables 4 and 5).

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The 50– 60 Ma poles of the two synthetic APWPs are not statistically distinct. Hence, the influence of the BTIP data on the 50– 60 Ma poles of Besse and Courtillot [2002] appears substantial. [101] Riisager et al. [2002, 2003] questioned the reliability of the BTIP data, pointing out the inconsistencies within the data set and between their new pole from the Faroe Islands lavas (FIL) and the earlier results from the BTIP. They suggested that the main reason for these discrepancies may be the use of blanket demagnetization and outdated methods of the data analysis, which failed to uncover true directions of the primary magnetization uncontaminated by the later overprints, and that the inclusion of this data set may have resulted in a systematic bias in the synthetic 50– 60 Ma poles. [102] To test this hypothesis, we reanalyzed the BTIP paleomagnetic data. A database consisting of 1032 VGPs from the 13 studies with quality factor Q 3 [Van der Voo, 1993] was compiled from the literature, including the data from Scotland (Ardnamurchan, Arran, Mull, Skye, Muck, Eigg, Rhum and Canna), Northern Ireland (Antrim), Lundy Island in Bristol Channel, and Faroe Islands (the data of Riisager et al. [2002]). The references for these studies can be found in the Global Paleomagnetic Database [McElhinny and Lock, 1996] under reference numbers 83, 85, 86, 340, 654, 755, 1040, 1055, 1169, 1204, 1377, 3433 and 3494. The unit-mean directions were not published in the four additional studies quoted by Riisager et al. [2002] (reference numbers 419, 650, 1041 and 1174); these data were not included. [103] Each VGP corresponds either to the mean direction from a single sampling site (e.g., a dike, a flow) or to the mean from a group of nearby sites with indistinguishable site-mean directions (e.g., consecutive lava flows, closely spaced dikes), if such directional groups were defined in the original studies. The strategy was to compile all available site-mean and/or group-mean directions (including those earmarked as transitional or excursional), to convert them into VGPs, and then to analyze the entire VGP data set from the BTIP rocks. Data from the units which have not remained in situ since their emplacement (e.g., collapsed calderas) were excluded. Structurally corrected data were used wherever it was possible; the uncorrected data retained in the data set are mostly from the Scottish dikes for which the postemplacement tilt is generally not significant. [104] Sixty nine VGPs were rejected on the basis that they were calculated from less than 3 samples per site, or for which the within-site a95 was greater than 15°. This left us with the 963 VGPs of acceptable quality, which are shown in Figure 4. [105] The orientation matrix T of the accepted VGP set was calculated using 0 XN

x2 i¼1 i

B XN T ¼B @ Xi¼1 xi yi N xz i¼1 i i

XN

xi yi Xi¼1 N yi 2 XNi¼1 yz i¼1 i i

XN

1 x z i i Xi¼1 C N yi zi C A i¼1 XN 2 z i¼1 i

ð27Þ

where N = 963 is the number of VGPs, and xi, yi and zi are the direction cosines of the unit vector corresponding to the ith VGP. The eigenvectors and eigenvalues of this matrix

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(t 1, t 1 and t 3, in the descending order) were calculated using the Jacobi method [e.g., Press et al., 1992] and each VGP was assigned to normal or reverse polarity, depending on whether it was ‘‘to the north’’ or ‘‘to the south’’ of the great circle perpendicular to the eigenvector corresponding to the maximum eigenvalue (t 1). The southern VGPs (from reversely magnetized rocks) were then flipped into the northern hemisphere, and 71 outliers in the VGP distribution, corresponding to the transitional or excursional directions, were trimmed with a 41.1° cutoff angle, which was defined using the iterative procedure of Vandamme [1994]. [106] The Fisherian statistics of the nontransitional VGP data set is given in Table 8. Figure 4 shows that the VGPs from the reversely magnetized rocks are generally far-sided (shallower inclinations than that of the recent time-averaged field), while the normal polarity VGPs are not. The mean pole for the reversed polarity is 14° away from the normal polarity mean; this distance is much larger that the respective values of A95 (Table 8). Thus, the entire nontransitional VGP data set fails the reversal test at high significance level (note the probability of obtaining the Watson F test statistics under the null hypothesis that the two VGP subsets are drawn from the same Fisherian distribution, Table 8). [107] The situation when reversely magnetized rocks show shallower inclinations than those recording normal magnetic polarity is typical when the isolated ChRMs are contaminated by viscous overprints of normal polarity acquired during the Brunhes epoch ( 0, the inclinations in both hemispheres are shallower than that of the GAD, and the time-averaged directions with the opposite polarity are expected to be antiparallel at any site. Thus, the mean poles (or paleolatitudes) based on mixed polarity data and calculated under the GAD assumption can be easily corrected for octupole contributions, while the G2 correction requires taking the opposite polarity data apart, correcting them independently, and then recombining them to produce a quadrupole-adjusted pole. However, if it is assumed that the quadrupole component does not change the sign during field reversals (i.e., the sign of G2 switches back and forth), the quadrupole correction becomes qualitatively similar (though not identical) to the adjustment for an octupole contribution, and it becomes possible to work with the ‘‘mixed polarity’’ mean poles rather than with the separate polarity data.

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[119] Recognizing that any ad hoc solution for the timeaveraged nondipole components (e.g., those designed to bring reconstructed paleomagnetic poles, or different reference frames, into better consistency [e.g., Torsvik et al., 2001b]) is not unique and that essentially the same result can be obtained using the octupole (G3) and quadrupole (G2) components, or a combination of the two [e.g., Van der Voo and Torsvik, 2001], we will analyze the effect of the octupole field only. However, we would like to stress that the G3 value, which will be suggested below, should not be considered as an estimate of the time-averaged octupole component, but rather as a qualitative indication of the presence (or absence) of the long-term nondipole field. [120] The forward problem of adjusting a paleomagnetic pole for a known octupole contribution is relatively simple. If the apparent paleolatitude corresponding to the GAD field is l0 (equation (4)), then the ‘‘corrected’’ latitude l (corresponding to the GAD + G3 field) can be related to l0 using the following expression [e.g., Merrill et al., 1996] "

# 2 þ 2G3 5 sin2 l 3 tan l0 ¼ tan l 2 þ 3G3 5 sin2 l 1

ð28Þ

which implicitly defines l as a function of l0. (Note that G3 is assumed to be small, so there is one-to-one correspondence between l0 and l. The cases when equation (28) has multiple roots require G3 values on the order of few tens of percent and will not be considered.) Equation (28) is solved numerically using the ‘‘observed’’ value of l0 as input to obtain l. The pole is then shifted along the great circle connecting the sampling site and the pole by the amount d = l l0, toward or away from the initial (GAD) pole depending on the sign of d. For synthetic APWPs, this procedure is applied to each individual pole within the selected time window and the corrected poles are then averaged to produce an adjusted synthetic mean. [121] Because G3 is not known a priori, some independent criteria should be used to select the G3 value, which is believed to be the ‘‘best estimate’’ of the time-averaged octupole contribution. Van der Voo and Torsvik [2001] used global paleomagnetic data and the regression analysis of the observed versus predicted latitude in the three 80 to 100 Ma long windows to suggest a G3 0.1 contribution in the Late Paleozoic and Mesozoic, which considerably improves the reconstructions of Pangea in Late Carboniferous to Early Triassic times. [122] Torsvik and Van der Voo [2002] and Torsvik et al. [2001b] selected variable G3 values ranging from zero to 0.2, which minimize the great circle distances between the Laurussia and Gondwana poles in the Mesozoic-Paleozoic reconstructions, and also minimize the motion of the paleomagnetic axis relative to the Indo-Atlantic hot spots for the last 95 Ma. Using these values, they proposed a global nondipole field-corrected APWP, which Torsvik and Van der Voo [2002, p. 790] considered ‘‘better than any GADbased APW paths.’’ This synthetic APWP incorporates the data of Torsvik et al. [2001a] (section 3.2.1) and the Gondwana paleomagnetic database of Van der Voo [1993]. A flat G3 = 0.08 correction was used for Paleogene and Late Cretaceous time.

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[123] To test how this octupole-corrected synthetic APWP will perform in the plate circuit test (section 3), the 50, 60, 70 and 80 Ma synthetic poles were rotated from North America to the Pacific plate (using the kinematic parameters given in auxiliary Tables A11 and A12) and compared with the Pacific data (Figure 5). The Pacific paleolatitudes and their upper and lower 95% confidence limits (Table 2) were corrected for the G3 = 0.08 octupole contribution using equation (28). [124] Figure 5 shows a noticeably improved agreement between the 50 and 60 Ma octupole-corrected data compared to the tests, which used uncorrected synthetic poles of Besse and Courtillot [2002] and Torsvik et al. [2001a]. The 50 Ma pole rotated through the two alternative circuits is within the 95% uncertainty band of the Koko paleolatitude (Figure 5a), and hence predicts a latitude indistinguishable from the observed value. Both the 50 Ma and 60 Ma poles fall into the uncertainty band for Nintoku Seamount (Figure 5b). The two poles are within their respective 95% ellipses suggesting that the APWP prediction for the age of the Nintoku section (56 Ma) is indistinguishable from the direct paleomagnetic estimate. [125] The 60 Ma pole is located 6° from the Suiko colatitude circle and its 95% confidence region overlaps that of the colatitude circle (Figure 5c). When the estimate based on the 40 inclination groups or VGLs (Table 2) is used for comparison, the pole is outside the 95% uncertainty band of colatitude in both reconstructions, and the discrepancy appears to be significant. However, when the estimate of Cox and Gordon [1984] for the Suiko colatitude is used, the pole is within the colatitude uncertainty region and the latitude difference is not significant at the 5% level. [126] The Late Cretaceous (70 and 80 Ma) reference poles are both within the younger (76 Ma) colatitude band of Detroit Seamount. Assuming smooth poleward motion during this time interval, the 76 Ma pole is expected to lie between the 70 and 80 Ma poles, which would result in a latitude prediction consistent with the observed value. The 80 Ma pole plots on the very edge of the colatitude band for the older (80 Ma) basalt group irrespective of the plate circuit used, suggesting lower paleolatitude. Although the 80 Ma paleolatitude and reference octupole-corrected data are marginally consistent, the observed-predicted latitude difference is larger by 3 –6° compared to results obtained using uncorrected data (section 3.2.5). [127] Thus, it may be concluded that the octupole correction with G3 = 0.08 markedly improves the agreement between the Pacific paleolatitudes and the non-Pacific global reference data for the Paleogene (50, 55 and 60 Ma). On the other hand, the incorporation of an 8% octupole term degrades the consistency for the Late Cretaceous poles and paleolatitudes, although not to the level where the discrepancies become significant. [128] As an independent test, we can analyze how the nondipole contribution will affect the positions of the individual reference poles deemed to be the most reliable (section 3.3.2). The Early Eocene and Paleocene reference poles of Diehl et al. [1983] (EIM and PIM, respectively) suggest little or no motion of North America in the paleomagnetic reference frame between 65 and 50 Ma (Figure 6a). When the 58 Ma pole from the West Greenland lavas (WGL) [Riisager et al., 2003] is reconstructed to

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Figure 5. Synthetic, octupole-corrected poles of Torsvik and Van der Voo [2002] rotated to the Pacific plate. Bold solid lines show the Pacific colatitudes adjusted by the same value of the octupole contribution as reference poles (G3 = 0.08). Solid ellipses and dashed lines show the 95% uncertainties. Black and white symbols show the poles rotated through the East-West Antarctica and Australia-Lord Howe Rise plate circuits, respectively. North America, it is not distinguishable from the two North American poles, supporting this suggestion. However, the WGL pole is 6.5° away from the North American poles, and the nearly coeval Faroe Islands pole [Riisager et al., 2002] is distinct from both North American poles (Figure 6a). If these differences are at least in part due to a neglected nondipole field component, it may be expected that the grouping of the four poles will improve when the nondipole field bias is corrected. [129] To estimate the optimal value of the octupole correction which would minimize the scatter between the four reference poles, the G3 value was varied from 0.3 to 0.3 at 0.005 increments, and the Fisher precision parameter and the angular dispersion of the G3-corrected poles were calculated at each step. Figure 6b shows the variation of these parameters with the increasing G3. The maximum value of K and minimum angular dispersion correspond to G3 = 0.07, which

is close to the 0.08 value proposed by Torsvik et al. [2001b] and within the 0.05 – 0.1 Paleogene range of Torsvik and Van der Voo [2002]. Although some may consider a 40% increase in the precision parameter insignificant, it should be remembered that the uncorrected and corrected poles are not the two independent random samples. [130] Visually the poles adjusted with G3 = 0.07 do not show markedly better grouping (Figure 6a), and the FIL pole is still distinct from the American poles, although the distance between them decreased and the EIM and PIM poles are now within the A95 circle of the WGL pole. However, when the corrected Eocene-Paleocene poles are transferred to the Pacific plate, all of them are in excellent agreement with the Koko, Nintoku and Suiko paleolatitudes similarly corrected for the 7% octupole contribution (Figure 7). [131] The octupole correction does not degrade the originally good fits between the EIM and PIM poles and the

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Figure 6. (a) Individual reference poles in the North American coordinates (top) before and (bottom) after the correction for the octupole component G3 = 0.07. Abbreviations are the same as in Figure 3. (b) Variation of the Fisher precision parameter and angular dispersion for the four reference poles as a function of the applied octupole correction. The gray line shows the optimal G3 value (see text).

Figure 7. Individual reference poles corrected for the G3 = 0.07 octupole contribution and rotated to the Pacific plate. Abbreviations are the same as in Figure 3. Bold solid lines show the Pacific colatitudes adjusted by the same value of the octupole contribution as reference poles. Solid ellipses and dashed lines show the 95% uncertainties. 20 of 24

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paleolatitudes of Koko and Suiko seamounts, respectively (Figures 7a and 7c). The WGL pole shows excellent agreement with the paleolatitudes of Nintoku and Suiko seamounts (Figures 7b and 7c). Most remarkably, the FIL pole, which was clearly discordant with the Nintoku paleolatitude is now within its 95% confidence band and close to the mean colatitude circle (Figure 7b). The controversy about which of the two NAIP poles is a better choice of the reference pole becomes irrelevant for the comparison with the Nintoku data because both of them predict paleolatitudes indistinguishable from each other and from the observed value. Thus, a correction for the 7% octupole contribution eliminates the discrepancies between the observed and predicted paleolatitudes for all comparisons with individual Eocene-Paleocene reference poles (section 3.2.5). [132] It is well known that any bias leading to anomalously shallow inclinations (e.g., the inclination shallowing in the sedimentary rocks or incomplete removal of normal polarity recent overprints in reversely magnetized rocks) can closely mimic the effect produced by the axial octupole contribution to the paleomagnetic field. The values of G3 invoked to minimize the discrepancies between paleomagnetic poles [e.g., Torsvik and Van der Voo, 2002] or poles and colatitudes are likely to be overestimated if the shallow inclination bias was not recognized in the data. However, both the individual paleomagnetic poles based on highquality data from igneous rocks and synthetic reference poles consistently suggest that when a several percent octupole contribution is added to the GAD field, the agreement between the Paleocene and Early Eocene poles and the Pacific paleolatitudes considerably improves. In contrast, better agreement is achieved for the Late Cretaceous data when a purely GAD field is assumed. [133] Thus, a small but significantly nonzero G3 component cannot be dismissed as a possible explanation for the paleolatitude discrepancies, although we highlight that the inclusion of these terms is ultimately ad hoc in the sense that we do not have independent sources to support the presence of these components. In fact, some other tests of the morphology of the Paleocene geomagnetic field have failed to detect significant nondipole fields [e.g., Schneider and Kent, 1990]. 4.2. Consistency of Late Cretaceous Data [134] Good agreement between the Pacific paleolatitude data and the synthetic reference poles for Late Cretaceous time (Figure 2) suggests that the possible errors of the plate circuit reconstructions are below the resolution of the Pacific and the reference paleomagnetic data. The observed consistency also supports the reliability of paleolatitude data from the Detroit Seamount basalts (irrespective of the reference data) and the GAD morphology of the paleomagnetic field in the Late Cretaceous. However, the recognition that lower-quality poles could affect the reliability of the Paleogene apparent polar wander paths naturally raises questions about the Late Cretaceous synthetic poles. [135] Because of the general paucity of paleomagnetic data for the Late Cretaceous, the number of individual poles included in the 75 and 80 Ma averages in both synthetic paths is at least twice smaller than those for the Paleocene and early Eocene (Table 3), and none of the included individual poles meet our strict reliability criteria

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(section 3.3.1). The majority of Late Cretaceous data in the both synthetic APWP compilations come from the tectonically disturbed igneous rocks of the western United States, which have not remained tectonically coherent with the North American craton. The remaining data are several poles from sedimentary sequences and few poorly defined poles from African and South American extrusive complexes. [136] Unlike the case of the Paleogene synthetic poles, there is not a single dominant data set that, if contaminated by the recent field, could exert a very large influence on the mean pole positions. In fact, because of the sliding time window methodology used in the construction of the mean synthetic poles, a time window that is less densely represented by data will be influenced by slightly younger and older data from adjacent time slices. This is essentially equivalent to composing an apparent polar wander path that is smooth, representing continuous plate motion. [137] We can further examine whether this is the case by examining the Late Cretaceous apparent polar wander path for North America. Here we see that the 75.4 Ma pole of Besse and Courtillot [2002] falls reasonably well between the well-established mid-Cretaceous standstill poles [e.g., Globerman and Irving, 1988; Tarduno and Smirnov, 2001] and the previously discussed high-quality Paleocene pole (Figure 8). The Late Cretaceous poles of Torsvik et al. [2001a] (75 and 80 Ma) cannot be distinguished from the mid-Cretaceous standstill poles. The only pole that appears anomalous is the 79.1 Ma pole of Besse and Courtillot [2002], but as mentioned previously, this pole does not lead to a noticeably better consistency with the Pacific data. So, while the Late Cretaceous poles from all the continents need improvement, detailed examinations of the North American poles seem to support the accuracy of the existing estimates contained in the synthetic apparent polar wander paths. 4.3. Implications for the Plate Circuit Models [138] Although two different chains of relative plate motion were used to transfer the non-Pacific reference poles to the Pacific plate, the final positions of the same pole rotated using the alternative plate circuits do not differ by more than 3° and 2° for the Late Cretaceous and PaleoceneEocene poles, respectively (Figures 2 and 3). These differences are significantly smaller than the 95% uncertainties for all reference poles. Much higher resolution of reference paleomagnetic data (e.g., A95 1° to 2°) is required to discriminate between the two alternative kinematic models. [139] The East-West Antarctica plate circuit reconstructions put the reconstructed Paleogene poles slightly closer to the Pacific colatitude circles than those using the Lord Howe Rise-Australia circuit. A similar relationship is not seen in the Late Cretaceous comparisons. In all cases, however, the differences in predicted latitudes (Tables 4, 5, and 7) are minuscule compared to their uncertainties and to the uncertainties of the Pacific paleolatitudes, and the results of the consistency test are insensitive to which of the two plate circuits was used to transfer the non-Pacific poles.

5. Conclusions [140] There is overall agreement between the Late Cretaceous paleomagnetic data from the Pacific plate, available

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ment of Paleogene Pacific data with the prediction based on poles from synthetic apparent polar wander paths. But there is no independent evidence supporting a significant nondipole term in the time-averaged Paleocene geomagnetic field. However, Paleogene Pacific data are in excellent agreement with the highest-quality North American poles, suggesting that a small bias in the synthetic poles is a more likely explanation of the discrepancies observed. Specifically, synthetic APWPs for Paleogene time are heavily weighted by data from the North Atlantic Igneous Province, and it is clear that many of these data are internally inconsistent. Only a renewed effort of resampling to constrain and date independent units, coupled with extensive rock magnetic and paleomagnetic analysis (employing exhaustive demagnetizations) can resolve the resolution issues posed by the existing North Atlantic Igneous Province data. [142] The uncertainties of the Pacific paleolatitude data and the non-Pacific reference poles are larger than the differences related to the use of the two alternative plate circuits (through East to West Antarctica and through Australia to the Lord Howe Rise) that link the Atlantic and Pacific hemispheres. While no preference can thus be given to either plate circuit, their overall consistency with paleomagnetic data suggests that they can be used to investigate long-term motion of the Pacific plate since Late Cretaceous times. [143] Acknowledgments. We thank Steven Cande, who provided his unpublished uncertainties for the Pacific-West Antarctica reconstructions; Dennis Kent for helpful discussions; and Joann Stock for constructive comments on the manuscript.

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Figure 8. Comparison of mid-Cretaceous (MK, 88– 100 Ma) and Paleocene (PIM, 59– 67 Ma) North American reference poles (open circles) of Globerman and Irving [1988] and Diehl et al. [1983], respectively, with synthetic Late Cretaceous (75 – 80 Ma) poles of Besse and Courtillot [2002] and Torsvik et al. [2001a]. North American reference frame. from lavas of the Emperor Seamounts, and global paleomagnetic data summarized in synthetic apparent polar wander paths when these data sets are compared using plate circuit reconstructions. This agreement supports both the veracity of the plate circuits and the accuracy of the paleomagnetic estimates. [141] For the Paleogene data sets, minor disagreements are seen. A small octupole component improves the agree-

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P. V. Doubrovine and J. A. Tarduno, Department of Earth and Environmental Sciences, University of Rochester, Rochester, NY 14627, USA. ([email protected]; [email protected])

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