True polar wander since 32 Ma B.P.: A paleomagnetic investigation of the skewness of magnetic anomaly 12r on the Pacific plate

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi:10.1029/2009jb006862, 2010 True polar wander since 32 Ma B.P.: A paleomagnetic investigation of the skewness of magnetic anomaly 12r on the Pacific plate Benjamin C. Horner Johnson 1 and Richard G. Gordon 1 Received 7 August 2009; revised 2 February 2010; accepted 4 March 2010; published 4 September 2010. [1] We test the fixed hot spot and fixed spin axis hypotheses through a paleomagnetic investigation of the skewness of crossings of magnetic anomaly 12r (32 Ma B.P.) between the Galapagos and Clarion fracture zones on the Pacific plate. We focus on this region for three reasons. First, numerical experiments show that these crossings, of all those available from the Pacific plate, should contain the most information about the location of the 32 Ma B.P. paleomagnetic pole for the Pacific plate. Second, many of the available crossings are from vector aeromagnetic profiles, which have superior signal to noise ratios. Third, the rate of seafloor spreading recorded in these crossings exceeds the threshold (half rate of 50 mm a 1 ) above which anomalous skewness is negligible. The new pole (83.5 N, 44.6 E) has compact 95% confidence limits (ellipse with major semiaxis length of 3.1 toward 84 clockwise from north and minor semiaxis length of 1.2 ) and is not subject to the biases inherent in other methods for estimating Pacific plate paleomagnetic poles. The pole differs significantly by 5 from the pole predicted if the Pacific hot spots have been fixed with respect to the spin axis, thus demonstrating, for the first time from paleomagnetic data, that Pacific hot spots have moved relative to the spin axis since the formation of the elbow in the Hawaiian Emperor chain. The pole is consistent, however, with previously published paleomagnetic poles in a reference frame fixed relative to Indo Atlantic hot spots. Thus, the new results require no motion between Pacific and Indo Atlantic hot spots since 32 Ma B.P. Instead, superimposed on whatever motion occurs between hot spots, as expected for true polar wander. Citation: Horner Johnson, B. C., and R. G. Gordon (2010), True polar wander since 32 Ma B.P.: A paleomagnetic investigation of the skewness of magnetic anomaly 12r on the Pacific plate, J. Geophys. Res., 115,, doi:10.1029/2009jb006862. 1. Introduction [2] Prior studies have shown that Pacific hot spots and Indo Atlantic hot spots have moved in approximate unison relative to the spin axis since 65 Ma B.P. [Morgan, 1981; Gordon and Cape, 1981; Gordon, 1982] and since 56 Ma B.P. [Petronotis et al., 1994], which is most simply interpreted as true polar wander. In contrast, Pacific hot spots and Indo Atlantic hot spots give conflicting results for 72 and 81 Ma B.P., which may indicate motion between Pacific hot spots and Indo Atlantic hot spots [Tarduno and Cottrell, 1997; Petronotis and Gordon, 1999; Besse and Courtillot, 2002; Tarduno et al., 2003]. Thus, it is important to estimate Pacific plate apparent polar wander (APW) for more time intervals. From this, the APW of Pacific hot spots can be inferred and compared with that of Indo Atlantic hot spots. [3] The estimation of paleomagnetic poles for oceanic plates poses problems different from those for continents. The sparseness of subaerial outcrop from which fully oriented 1 Department of Earth Science, Rice University, Houston, Texas, USA. Copyright 2010 by the American Geophysical Union. 0148 0227/10/2009JB006862 samples can be obtained requires the use of alternative methods for estimating the pole. These alternative methods include the determination of paleocolatitudes from vertical, azimuthally unoriented core samples, estimation of poles from the magnetic anomaly over seamounts, and poles estimated from skewness analysis of magnetic anomalies due to seafloor spreading. Each approach has its challenges. Core data come mainly from sediments, which in many cases give shallowly biased remanent magnetic inclinations [Gordon, 1990; Kodama, 1997; Kent and Tauxe, 2005]. Core data from basalts are expensive to obtain and may have many fewer independent estimates of the paleomagnetic field than the number of flows sampled [Cox and Gordon, 1984]. Even if all other problems with azimuthally unoriented cores are solved, there remains the limitation that it only resolves one of two components of the location of a pole. Poles from seamount magnetic anomalies are reliable only if a seamount formed during a single magnetic polarity and are unbiased only if later overprints, including those from the Brunhes and present magnetic field, as well as its induced magnetization, can be neglected. [4] Skewness analysis also has had its challenges, the largest of which is the presence of so called anomalous 1of16

Figure 1. Magnetic anomaly profiles analyzed in this paper are plotted along track on top of gridded topography [Smith and Sandwell, 1997]. Depths are in meters. The magnetic profiles have been reduced to the best fitting paleomagnetic pole obtained herein. White shaded profiles are those used to obtain estimates of the effective remanent inclination. The two gray shaded profiles are used to refine our estimate of the strikes of the magnetic lineations for anomalies 12 and 13. Inset shows location on the Pacific plate. skewness [Cande, 1976]. Nonetheless, we believe that skewness analysis is the most promising approach to estimating paleomagnetic poles for the Pacific plate for several reasons. First, many widely distributed magnetic profiles are already available for analysis. Magnetic overprints, which are an issue for seamount poles because they can bias the results, presumably do not bias the results for skewness analysis. A uniform overprint in a planar body, such as the oceanic crust and uppermost mantle, produces no observable magnetic field. Although overprints may locally contribute to error, when measured over many sites they are not expected to bias the resulting paleomagnetic poles. Third, when low paleolatitude sites are available, the estimated pole positions are insensitive to anomalous skewness and strongly constrain the location of the paleomagnetic pole [Acton and Gordon, 1991]. Fourth, if widely distributed sites are available, anomalous skewness can be estimated from the skewness estimates themselves [Petronotis et al., 1992]. Fifth, the spreading rate dependence of anomalous skewness has been estimated from cross ridge comparisons for several key anomalies (20r, 25r, and 33r) [Roest et al., 1992] and the dependence on spreading rate of anomalies corresponding to seafloor with ages from 40 to 80 Ma B.P. has also been established from cross ridge comparisons [Dyment et al., 1994]. The cause of anomalous skewness is reasonably well understood, and models for the magnetization of the seafloor can reproduce the observed spreading rate dependence of anomalous skewness [Dyment and Arkani Hamed, 1995]. Thus, if spreading rates are known, anomalous skewness can be modeled and subtracted from observed skewness of anomalies. Sixth, if spreading rates exceed 50 mm a 1, anomalous skewness is negligible [Roest et al., 1992; Dyment et al., 1994], as is the case for the anomalies investigated in this paper. [5] Here we present a study of the skewness of anomaly 12r between the Galapagos and Clipperton and between the Clipperton and Clarion fracture zones. We chose this region for several reasons: First, numerical experiments [Acton and Gordon, 1991] show that these crossings, of all those available from the Pacific plate, should contain the most information about the location of the chron C12r (32 Ma B.P.) paleomagnetic pole for the Pacific plate. As will be shown 2of16

Figure 2a. Useful magnetic profiles (as observed, but after removal of a reference geomagnetic field) with crossings of anomaly 12r between the Galapagos and Clipperton fracture zones are plotted perpendicular to anomaly strike. Gaps shorter than 10 km have been linearly interpolated. Vertical gray shading shows the locations of anomalies 13 and 12. Latitudes of the crossing of anomaly 12r and the profile identification are given to the left of each observed profile. Gray observed profiles were not used to estimate the paleomagnetic pole. Vd and Ed indicate vertical and east components, respectively, of an aeromagnetic profile. Profiles at the top and the bottom of the diagram are synthetic magnetic anomaly profiles appropriate for the elevation of a ship and of an airplane, respectively. below, these crossings span the 32 Ma B.P. paleoequator. Second, in these two spreading rate corridors, spreading half rates range from 72 to 86 mm a 1 and, therefore, have negligible anomalous skewness, given that they exceed 50 mm a 1. Third, one of the challenges to interpreting magnetic anomalies in low latitudes where the anomalies strike nearly north south is the very low amplitude of the signal relative to the noise, the latter of which can be especially intense near the present magnetic equator due to the amplification of diurnal variation by the equatorial electrojet. In a prior paper [Horner Johnson and Gordon, 2003], we showed that vector aeromagnetic profiles record lowlatitude Pacific plate magnetic anomalies due to seafloor spreading with much greater clarity than do shipboard profiles in the same region. Advantages of the available aeromagnetic data include the following: (1) Aeromagnetic data are collected at a speed of 630 km h 1, 35 times faster than a typical ship survey ( 18 km h 1 or 430 km d 1 ). The transit speed of shipboard magnetic acquisition can map time variations, including diurnal variation, into wavelengths similar to those of the anomalies due to seafloor spreading. For example, as shown below, it takes a ship about 12 h to fully cross anomalies 12, 12r, and 13, but only about 20 min for the airplane to do so. Thus, the diurnal variation recorded on an airplane transit maps into wavelengths much longer than the wavelengths of anomalies due to seafloor spreading. (2) The higher elevation of data acquisition leads to more averaging across topographic variations, which can be a source of geologic noise in shipboard data. (3) The data are vector instead of total intensity data, and hence, the amplitude of the crustal magnetic signature for low latitude magnetic lineations 3of16

Figure 2b. Same crossings as Figure 2a, after each individual profile has been deskewed to best fit anomaly 12r. The phase shift used to deskew each profile is given after each profile name. subparallel to north is 2 to 3 times greater than that for total intensity data collected at the same elevation. Thus, in some places, the signal in vector aeromagnetic data collected at an altitude of 7 km is of higher amplitude than is that of total intensity data collected at sea level, while the noise in the aeromagnetic data is at least an order of magnitude lower than in the total intensity shipboard magnetic data. [6] The pole that we obtain has compact 95% confidence limits. We reduce the profiles to this pole and show that the appearance of the reduced to the pole profiles is sensitive to the assumed pole position. The new pole shows that Pacific hot spots have moved significantly relative to the spin axis and is consistent with Pacific hot spots having moved in unison with Indo Atlantic hot spots relative to the spin axis since 32 Ma B.P. 2. Paleomagnetic Methods 2.1. Overview [7] The analysis comprised several steps. First, potentially useful magnetic profiles between the Galapagos and Clipperton fracture zones and between the Clipperton and Clarion fracture zones were identified by searching the archives of the National Geophysical Data Center. Second, the profiles were projected perpendicular to magnetic anomaly strike. (This step was usually iterated after profiles are initially deskewed and a preliminary pole was estimated as the anomaly strikes can be estimated more accurately after the profiles have been reduced to the pole.) Third, the profiles were phase shifted to estimate the shift that best deskews these profiles; that is, we found the shift that causes the profile to most resemble a synthetic magnetic anomaly profile constructed assuming vertical magnetization, vertical ambient magnetic field, and vertical reversal boundaries. Fourth, time plots were used to investigate the time of day that ships crossed anomaly 12r and to assess how much the anomaly may be influenced by diurnal variation or other effects of time varying currents in the ionosphere. Fifth, the estimated skewnesses were used to determine a paleomagnetic pole. Sixth, the profiles were reduced to the best fitting pole, which permitted a direct look at how well the best fitting pole fits the observations. Seventh, the best fitting pole was used to predict the relative amplitudes of the profiles, which were compared with the observed amplitudes. 4of16

Figure 2c. Same crossings as Figures 2a and 2b, after reduction to the best fitting paleomagnetic pole determined herein. The phase shift used to reduce each profile to the pole is given after each profile name. 2.2. Preprocessing, Time Plots, and Deskewing of Anomaly Profiles [8] After the magnetic anomaly profiles were extracted, a reference magnetic field was removed from each of them using the Definitive Geomagnetic Reference Field. The resulting residual anomalies are mainly produced by the magnetization of the crust and uppermost mantle. For each profile, magnetic intensity was plotted against local time to assess the possible influence of time varying magnetic fields, in particular diurnal variation. On a magnetically quiet day, the geomagnetic field increases smoothly from night values beginning at about sunrise ( 6 A.M.) to a maximum between 10 A.M. and 2 P.M. and then smoothly decreases to night values at sunset ( 6 P.M.). [9] The profiles were plotted on maps of gridded gravity or topography or both. Profiles for further analysis were identified and projected perpendicular to strike. The skewness of anomaly 12r was visually estimated for each profile by trial and error, a procedure that we and others have used successfully many times before [e.g., Larson and Chase, 1972; Cande, 1976; Petronotis and Gordon, 1989, 1999; Acton and Gordon, 1991; Petronotis et al., 1994; Dyment et al., 1994]. 2.3. Estimating Lineation Azimuth [10] For each region between fracture zones, profiles reduced to the pole were overlaid on a background of satellite derived gravity [Sandwell and Smith, 1997] or bathymetry [Smith and Sandwell, 1997] or both. The lines that best fit the points along the young and old edges of anomaly 12r were determined and plotted on top of the profiles and bathymetry using a Mercator projection (e.g., Figure 1). The uncertainty in the azimuths of the magnetic lineations was estimated visually by plotting lines oriented at various azimuths and centered near the middle of each magnetic anomaly between a pair of fracture zones. 2.4. Determining Paleomagnetic Poles and Confidence Limits [11] Paleomagnetic poles were determined using methods described by Gordon and Cox [1980], Gordon [1982], and 5of16

Figure 3a. Useful magnetic profiles (as observed, but after removal of a reference geomagnetic field) with crossings of anomaly 12r between the Clipperton and Clarion fracture zones are plotted perpendicular to anomaly strike. Gaps shorter than 10 km have been linearly interpolated. Vertical gray shading shows the locations of anomalies 13 and 12. Latitudes of the crossing of anomaly 12r and the profile identification are given to the left of each profile. Vd and Ed indicate vertical and east components, respectively, of an aeromagnetic profile. Profiles at the top and the bottom of the diagram are synthetic magnetic anomaly profiles appropriate for the elevation of a ship and of an airplane, respectively. Petronotis et al. [1992]. The estimated phase shifts and corresponding effective remanent inclinations are each assumed to have equal uncertainty estimated from the standard deviation of the effective remanent inclinations about the best fitting model. The 95% confidence limits for the pole are determined in two ways: (1) by linear propagation of errors [Gordon and Cox, 1980] and (2) by constant c 2 boundaries [Petronotis et al., 1992]. The two methods generally give similar 95% confidence regions but can differ substantially when a linear approximation is not accurate [Petronotis et al., 1992]. In the latter case, constant c 2 boundaries are preferred. Because the spreading half rates for all the profiles exceed 50 mm a 1, there is no need to correct for, or to solve for, the value of anomalous skewness [Roest et al., 1992; Dyment et al., 1994]. 2.5. Uncertainty in the Poles due to the Uncertainties in the Lineation Azimuths [12] In prior work, the uncertainty in the pole position due to the uncertainty in the azimuths of the magnetic lineations was neglected, but cannot be neglected herein. Thus, we incorporate it as follows. We separately estimate the effect of uncertainties in the strike of the lineations in the Clipperton Clarion corridor and in the Galapagos Clipperton corridor. For example, we determined the pole found from an extreme (i.e., at the 95% confidence limit) clockwise value of strike of the Clipperton Clarion lineations. Similarly, we determined the pole found from an extreme counterclockwise value of strike of the Clipperton Clarion lineations. In each case, we found the distance and azimuth of the extreme pole from the original pole. The distance is divided by a factor of 1.96 to convert a one dimensional 95% confidence interval to a one dimensional standard 6of16

Figure 3b. Same crossings as Figure 3a, after each individual profile has been deskewed to best fit anomaly 12r. The phase shift used to deskew each profile is given after each profile name. error. After rotating one of the azimuths by 180, we averaged the two estimates to obtain a symmetrical confidence limit, which we expressed by an appropriate two by two covariance matrix. The procedure was repeated for the Galapagos Clipperton lineation. The final covariance matrix was the sum of these two covariance matrices plus the covariance matrix found from the dispersion of the effective remanent inclinations about the best fitting model [Gordon and Cox, 1980]. Thus, the final covariance matrix incorporates not only the uncertainty due to the dispersion of the estimated effective remanent inclinations but also the uncertainty due to the uncertainty in the lineation azimuths. 2.6. Relative Amplitudes of the Anomalies [13] The best fitting paleomagnetic pole was used to predict the relative amplitudes of observed magnetic anomalies. Relative amplitude factors are given by M = C (sini r /sini r )(1+3g 2 ) 1 = 2 where C is an unknown constant of proportionality, herein assigned a nominal value of one, I r is the inclination of the remanent magnetization, I r is the inclination of the effective remanent magnetization, and g is the cosine of the paleocolatitude [Schouten and Cande, 1976; Gordon, 1982]. Relative amplitude factors correspond to actual relative anomaly amplitudes only if anomalies are observed at the same elevation. Thus, the factors for and amplitudes of shipboard profiles are compared only with those for other shipboard profiles, while the factors for and amplitudes of airplane profiles are compared only with those for other airplane profiles. 3. Magnetic Profiles [14] Phase shifts were estimated for crossings of anomaly 12r on 11 shipboard magnetic profiles (seven between the Clipperton and Clarion fracture zones and four between the Galapagos and Clipperton fracture zones) and seven vector aeromagnetic profiles (three between the Clipperton and Clarion fracture zones and four between the Galapagos and Clipperton fracture zones). Each vector profile contains both a vertical and a horizontal component of the magnetic field, and thus, these two components are analyzed independently to obtain two estimates of skewness from each vector 7of16

Figure 3c. Same crossings as Figures 3a and 3b, after reduction to the best fitting paleomagnetic pole determined herein. The phase shift used to reduce each profile to the pole is given after each profile name. magnetic profile, resulting in a total of 25 estimates of skewness, 11 from the shipboard profiles and 14 from the aeromagnetic profiles (Figures 1 3). In addition, the undeskewed, deskewed, and reduced to the pole results are plotted for two shipboard profiles (C2011 and SWAN 1AR) near the paleoequator. These profiles were not used to estimate the pole because they could not be completely deskewed by any phase shift (Figures 2a 2c). We note that they are recorded over a bathymetric gradient in the ocean floor, which we suspect is responsible for the downward tilt to the right when they are reduced to the pole (Figures 1 and 2c). 4. Paleomagnetic Results 4.1. Time Plots and Diurnal Variation [15] All the shipboard profiles record some effect of time varying magnetic field; in some cases, it is evident in the time plots, and in others, it is not. Figure 4 shows some examples. Profile 80012103 records diurnal variations in which the field amplitude is 100 nt larger at noon than at midnight (Figure 4). Because anomaly 12r was recorded during a 12 h interval roughly centered on midnight, we do not think it meaningfully biases our estimate of the skewness of this anomaly. There are subtle indications of diurnal variation in profiles ALCY01MV and VLCN09MV (Figure 4). Their respective crossings of anomaly 12r are not only offset in time of day by several hours but in opposite directions (i.e., VLCN09MV traverses anomaly 12r from west to east, whereas ALCY01MV traverses anomaly 12r from east to west). The observed and reduced to the pole crossings of anomaly 12r on ALCY01MV strongly resemble their counterparts on VLCN09MV (Figures 3a, 3c, and 4) suggesting that diurnal variation has little effect on their shapes and thus on our analysis. [16] Figure 1 of Horner Johnson and Gordon [2003] shows an anomaly profile from cruise DOLP02HO, which we rejected for the present study because of the enhanced diurnal variation near the present magnetic equator. 8of16

of our paleomagnetic analysis. The standard deviation of the observed effective remanent inclinations about the best fitting model is 9.9. The magnetic profiles (after the main geomagnetic field is subtracted) are shown reduced to the pole along their tracks in Figure 1 where they are plotted on top of topography. [18] The observed profiles (after the reference model for the main geomagnetic field is subtracted) are projected perpendicular to the strike of anomaly 12r and aligned in Figures 2a (profiles between the Galapagos and Clipperton fracture zones) and 3a (profiles between the Clipperton and Clarion fracture zones). The same profiles are displayed in the same manner after being deskewed (Figures 2b and 3b) and after reduction to the pole (Figures 2c and 3c). Profiles were reduced to the pole using the best fitting pole of 83.5 N, 44.6 E. They resemble the synthetic profile for anomaly 12r in having a roughly symmetrical appearance with an approximately flat base along the main part of anomaly 12r (Figures 2c and 3c). The biggest departures from this appear to be the two equatorial aeromagnetic profiles (0480 084 and 0550 047). When reduced to the pole, anomaly 12r in both components of 0550 047 and the vertical component of 0480 084 slope up to the right. We are not overly concerned about this inconsistency, however, for two reasons. First, on the same three component profiles, anomaly 13r slopes down to the right, in the opposite direction from the up to the right slope of anomaly 12r. Moreover, both profiles record a course change in the flight that occurred while the plane traversed anomaly 13 (Figure 1). [19] Figure 5 shows the observed and calculated values of effective remanent inclination (e a ) plotted versus latitude. Figure 4. Time plots for three shipboard profiles: ALCY01MV (recorded in 1985), VLCN09MV (recorded in 1981), and 80012103 (recorded in 1980). Magnetic anomalies are shown after subtraction of a reference geomagnetic field but with no other processing. Time increases from left to right for VLCN09MV but decreases for the other two profiles. Diurnal variation of the geomagnetic field is expected to cause magnetic intensity highs each day centered on local noon ( 12 ) and lows from 6 P.M. ( 18 ) to6a.m.( 06 ) local time. This pattern is clear on 80012103 but subtle on ALCY01MV and VLCN09MV. Notes on time records of other profiles (profile, direction of travel, start and finish times to traverse anomaly 12r): UM6503 B, E W, 9 A.M. to 3 P.M.; ARIA01WT, E W, 7 P.M. to 2 A.M.; ODP137JR, W E, 9 P.M. to 6 A.M.; DSDP16GC, E W, 3 P.M. to 11 P.M.; 80012103, E W, 7 P.M. to 3 A.M.; V2003, E W, 8 A.M. to 10 P.M.; C2011, W E, 2 P.M. to 4 A.M.; SWAN 1AR, W E, 5 P.M. to 2 A.M.; C1005, E W, 9 P.M. to noon; V3210, E W, 10 A.M. to 7 P.M.; AMPH01ar.c3, E W, 5 P.M. to 9 A.M.; PLDS03MV, E W,6A.M.to3A.M.(27hduration). 4.2. Main Paleomagnetic Results [17] The results are illustrated in Figures 1 11. Table 1 gives our estimates of the phase shift (D) that deskews each crossing of anomaly 12r such that it best resembles a synthetic magnetic anomaly created from a model with vertical magnetization, vertical ambient field, and vertical reversal boundaries. Table 1 also gives the other parameters Figure 5. Latitude versus effective remanent inclination inferred from skewness. Solid black circles, observed effective remanent inclination for each profile component. Gray curve, effective remanent inclination calculated from the best fitting paleomagnetic pole. 9of16

Figure 6. Best fitting paleomagnetic poles and great semicircles. Solid white star, best fitting pole from airplane and shipboard data combined; its 95% confidence region determined from constant c 2 boundaries is shaded blue; Solid white hexagon, best fitting pole from airplane data only; its 95% confidence region is shaded goldenrod. Each great semicircle is the locus of paleomagnetic poles exactly consistent with a single estimate of effective remanent inclination inferred from skewness (solid if from airplane data; dashed if from shipboard data). Solid white circles, hypothetical pole positions used in constructing Figure 7. The observed values range from a low of about 50 to a high of nearly 90 with the calculated values spanning nearly the same range. This wide range of values is expected for sites straddling the paleoequator when the anomaly strikes nearly north south [Acton and Gordon, 1991]. Zero effective remanent inclination, which occurs only at the paleoequator if the paleomagnetic field is dipolar, is calculated to occur just south of the Clipperton fracture zone (Figure 5). [20] Figure 6 shows each of the great semicircles along which a paleomagnetic pole is required to lie to be precisely consistent with skewness estimated from a single component of a single crossing of anomaly 12r. Great semicircles for profiles between the Galapagos and Clipperton fracture zones lie in one group, and great semicircles for profiles between the Clipperton and Clarion fracture zones lie in another. The best fitting paleomagnetic pole lies in the region of overlap between the two groups (Figure 6). Although all the skewness estimates are given equal weight in our pole estimation procedure, this does not mean that they contribute equal information to the pole. The information contribution of each datum is quantified in Table 1 as a datum importance [Minster et al., 1974; Gordon and Cox, 1980]. These results show that the greatest information is contributed by the southern crossings between the Clipperton and Clarion fracture zones. Figure 6 shows that the best fitting pole is closer to the tips of the great semicircles for these crossings than for any other crossings. Because of this, small changes in the assumed pole position lead to large changes in predicted skewness [Acton and Gordon, 1991]. [21] Figure 6 also shows the paleomagnetic pole determined from the skewness of only the aeromagnetic profiles (83.1 N, 34.1 E, 95% confidence ellipse with major semiaxis length of 2.4 oriented 84.0 clockwise of north and minor semiaxis length of 0.8 ; the standard deviation of effective inclinations is 7.7 ). With all the shipboard data omitted, the confidence limits remain compact. 4.3. Sensitivity of the Magnetic Profiles to the Assumed Location of the Paleomagnetic Pole [22] Figure 7 examines the sensitivity of three reduced tothe pole profiles to changes in the assumed paleomagnetic pole. Four alternative hypothetical paleomagnetic poles are considered (shown by open circles on Figure 6). (1) The best fitting pole is shifted 5 closer to the anomaly crossing sites in the Pacific, which we label 5 C in Figures 6 and 7. (2) The best fitting pole is shifted 5 farther from the 10 of 16

Figure 7. Sensitivity of three crossings of anomaly 12r to the reducing pole. For each of the three profiles, the best fitting paleomagnetic pole is used as the reducing pole in the middle profile and the other two profiles are reduced by alternative poles, shown in Figure 6, and each lying five great circle degrees from the best fitting paleomagnetic pole. For the profile between the Clipperton and Clarion fracture zones, the reducing poles are the ones labeled 5 L and 5 R. For the two profiles between the Galapagos and Clipperton fracture zones, the reducing poles are the ones labeled 5 C and 5 F. The alternative reducing poles produce phase shifts that are discernible by eye in the profiles, thus illustrating the sensitivity of the data to the assumed pole position. Red line segments illustrate the change in slope of anomaly 12r in the various profiles. Vertical gray bars show the locations of anomalies 12 and 13. anomaly crossing sites in the Pacific, which we label 5 F. (3 and 4) The best fitting pole is shifted 5 perpendicular to shifts 1 and 2 above, which we label 5 L (left, a shift to the left if viewed from the magnetic anomaly crossings) and 5 R (right; Figures 6 and 7), respectively. [23] The geometry of great semicircles in Figure 6 indicates that data between the Clipperton and Clarion fracture zones are mainly sensitive to left and right shifts in the assumed paleomagnetic pole. One profile (80012103) illustrates how shifts of the hypothetical pole five great circle degrees to the left or right cause visible shifts in the shapes of anomalies reduced to that pole. Anomaly 12r tilts up to the right for the hypothetical pole 5 left of the best fitting pole. Accordingly, anomaly 12r tilts down to the right for the hypothetical pole 5 right of the best fitting pole (Figure 7). [24] The geometry of great semicircles in Figure 6 indicates that data between the Galapagos and Clipperton fracture zones are mainly sensitive to closer and farther shifts in the assumed paleomagnetic pole. Two profiles (0480 268 vertical and C1005) illustrate how shifts of the hypothetical pole 5 closer or farther cause visible shifts in the shapes of anomalies reduced to that pole. Anomaly 12r on both of these profiles tilts up to the right for the hypothetical pole 5 closer to the location of the crossings. Accordingly, anomaly 12r on both of these profiles tilts down to the right for the hypothetical pole 5 farther from the crossings (Figure 7). 4.4. Comparison of Predicted and Observed Relative Amplitudes of the Magnetic Anomalies [25] No information from the amplitudes of the magnetic profiles was used in estimating the paleomagnetic pole, but they also contain information about the pole [Vine, 1968; Schouten and Cande, 1976; Gordon, 1982]. Figure 8 shows the relative amplitudes predicted by the best fitting paleomagnetic pole (pluses and circles for shipboard magnetic profiles; triangles for aeromagnetic profiles). These relative amplitudes are for observations made at the same distance from the seafloor and thus do not account for the disparity in distance from the seafloor of ships ( 5 km above the seafloor) versus airplanes ( 12 km above the seafloor), which leads to a wave number dependent decrease in amplitude with distance. [26] The lowest amplitudes are predicted to occur in the southernmost profiles north of the Clipperton fracture zone, as is observed. For the aeromagnetic data, the equatorial 11 of 16

4.5. Uncertainty in the Paleomagnetic Pole due to Uncertainty in the Azimuths of the Magnetic Lineations [29] The range of azimuths that acceptably fit the edges of anomaly 12r is 165 ± 3 (95% confidence limits) between the Galapagos and Clipperton zones and 174.5 ± 2 (95% confidence limits) between the Clipperton and Clarion fracture zones. The 1s uncertainty in the paleomagnetic pole due to the uncertainty in the azimuths of the Galapagos Clipperton lineations is 0.4 oriented 116 clockwise of north. The 1s uncertainty in the paleomagnetic pole due to the uncertainty in the azimuths of the Clipperton Clarion lineations is 0.9 oriented 72 clockwise of north. When we combine these with the uncertainty due to the dispersion of the effective remanent inclinations, we find that the 95% confidence limits of the paleomagnetic pole are described by a major semiaxis of 3.1 oriented 84 clockwise of north and a minor semiaxis of 1.2 (Figure 10), substantially larger than the 1.9 by 0.9 95% confidence ellipse determined if the uncertainty in the azimuths is neglected (Table 1). Figure 8. Latitude versus relative amplitude factors [Gordon, 1982] predicted from the best fitting 32 Ma B.P. paleomagnetic pole. Open circles and pluses, factors for shipboard data; triangles, factors for aeromagnetic data. profiles (0480 084 and 0550 047) are predicted to have the highest amplitudes, the profiles near 4 N (0480 268 and 0550 055) are predicted to have the second highest amplitudes, the profile near 13 N (0480 069) is predicted to have the third highest amplitude, and the profiles near 10 N (0480 055 and 0550 045) are predicted to have the lowest amplitude, as is observed (Figures 2c and 3c). For the shipboard data, the northernmost shipboard profiles (UM6503 B, ALCY01MV, and VLCN09MV) are predicted to have the highest amplitudes, the profiles near 13 N (ARIA01WT, ODP137JR) and all those south of the Clipperton fracture zone (C1005, V3210, AMPH01AR, and PLDS03MV) are predicted to have the second highest amplitudes, and the profiles between 11 N and 12 N (DSDP16GC and 80012103) are predicted to have the lowest amplitude, which is consistent with what is observed (Figures 2c and 3c). [27] Thus, the comparison of the predicted and observed relative amplitudes of the anomalies provides further support for the accuracy of the paleomagnetic pole. [28] We were initially surprised that the lowest amplitudes occur not near the present equator but near 10 N. One cause of this is illustrated in Figure 9, which shows the azimuths (or declinations) of the anomaly 12r lineation, the remanent magnetization, and the present geomagnetic field. North of the Clipperton fracture zone, the lineation azimuth is clockwise of that south of the Clipperton fracture zone and closer to the paleomagnetic and present magnetic declinations. Thus, the effective magnetization (i.e., the component of magnetization perpendicular to the lineation) is lower north of the Clipperton fracture zone than south of it. Moreover, the lineation is also closer to the orientation of the present field, which further reduces the magnitude of the shipboard magnetic anomalies. 5. Motion Between the Spin Axis, Pacific Hot Spots, and Indo Atlantic Hot Spots [30] Figure 10 shows the predicted location of the spin axis in the Pacific plate reference frame if the Pacific hot spots have been fixed with respect to the spin axis (found by Figure 9. Comparison of the azimuths (declinations) of magnetic anomaly 12r (thick solid line), the 32 Ma B.P. paleomagnetic field (dashed line), and present magnetic field (thin solid line) between the Galapagos and Clarion fracture zones on the Pacific plate. Triangles show the center points of crossings of anomaly 12r. 12 of 16

Figure 10. Comparison of new 32 Ma B.P. Pacific plate paleomagnetic pole (blue 95% confidence ellipse, which incorporates uncertainties in lineation azimuth) with other poles: Solid violet circle with violet 95% confidence ellipse, estimated from equatorial sediment facies (83 N, 22 E, major semiaxis of 5.7 toward 94 clockwise of north and minor semiaxis of 2.5 ) [Parés and Moore, 2005]; solid white circle with green 95% confidence ellipse; paleomagnetism of azimuthally unoriented samples (mainly sediments) from vertical cores (80.0 N, 24.7 E) [Beaman et al., 2007]; solid black hexagon with yellow 95% confidence ellipse, north pole predicted if the hot spots have been fixed with respect to the spin axis (rotations of Andrews et al. [2006]); small black outlined hexagon, north pole predicted if hot spots have been fixed with respect to the spin axis (rotations of Wessel and Kroenke [2008]). Four additional poles shown inside the blue ellipse and connected by line segments to the main pole: solid green circle, pole if Galapagos Clipperton azimuth is shifted to 162 ; solid blue circle, pole if Galapagos Clipperton azimuth is shifted to 168 ; solid red circle, pole if Clipperton Clarion azimuth is shifted to 172.5 ; solid orange circle, pole if Clipperton Clarion azimuth shifted to 176.5. That the yellow and blue ellipses overlap only slightly shows that motion of the Pacific hot spots relative to the spin axis since 32 Ma B.P. has been statistically significant. linearly interpolating the angle of the relevant stage pole from the Pacific hot spot rotations of Andrews et al. [2006], which resulted in a rotation of 24.93 about a pole located at 68.4 N, 70.6 E). The uncertainties in the Pacific hot spot rotation (also found by interpolation from those of Andrews et al. [2006]) induce an uncertainty in the predicted position of the spin axis in the Pacific plate reference frame; the corresponding 95% confidence limits are shown as a yellowfilled ellipse. The location of the ellipse for the predicted position of the spin axis and that for the observed position (i.e., the paleomagnetic pole) differ significantly, consistent with the small amount of overlap between the confidence ellipses and demonstrating that Pacific hot spots have moved relative to the spin axis since 32 Ma B.P. [31] Also shown in Figure 10 are two other estimates of the location of the ancient spin axis in the Pacific plate reference frame. The first pole is determined from the location and orientation of the 32 Ma B.P. paleoequator on the Pacific plate as inferred from analysis of equatorial sediment facies [Parés and Moore, 2005]. We determined the 95% confidence ellipse from the geometry and uncertainty of the paleoequator described by Parés and Moore [2005]. We assumed a one dimensional 95% confidence limit of ±2 in the middle of the paleo equatorial band of sediments and ±3 for the endpoints of the band. The new skewness pole does not differ significantly from, but has more compact confidence limits than, the pole inferred from equatorial sediment facies. [32] The second pole is a 30 Ma B.P. pole determined from paleomagnetic measurements of samples from azimuthally unoriented vertical cores, mainly of sediment, but also including a few cores of basalt [Beaman et al., 2007]. The pole from core data differs significantly from both the skewness pole and the pole from equatorial sediment facies. 13 of 16

Figure 11. Comparison of the apparent polar wander of Pacific hot spots with that of Indo Atlantic hot spots. Solid blue circle (84.5 N, 165.8 E) with blue 95% confidence ellipse, 32 Ma B.P. paleomagnetic pole for Pacific hot spots found by reconstructing the 32 Ma B.P. Pacific plate paleomagnetic pole along with the Pacific plate relative to the Pacific hot spots. Yellow 95% confidence ellipse shows the uncertainty in the location of the north pole of the Pacific hot spot reference frame at 32 Ma B.P. Solid gray diamonds with orange 95% confidence circles, 30 and 40 Ma B.P. paleomagnetic poles for Indo Atlantic hot spots found by reconstructing paleomagnetic poles from various continents along with their home plates relative to the Indo Atlantic hot spots [Besse and Courtillot, 2002]. The agreement of paleomagnetic poles for Indo Atlantic hot spot poles with paleomagnetic poles for Pacific hot spots is consistent with the hypothesis that Pacific hot spots have been fixed with respect to Indo Atlantic hot spots. That both differ from the north pole of the coordinate system attached to the hot spots shows that they have moved approximately in unison relative to the spin axis, which is most simply interpreted as true polar wander. Prior comparisons of paleomagnetic results from Pacific plate sediments with results from other Pacific plate data indicate that the inclinations from the sediments tend to be shallowly biased [Gordon, 1990]. A large body of work shows that paleomagnetic inclinations from sediments from many widespread locations elsewhere also tend to be shallowly biased [e.g., Kodama, 1997; Kent and Tauxe, 2005]. The bias can be substantial: Kent and Tauxe [2005] apply corrections ranging from 2 to 14 in paleolatitude. Within uncertainties, 9 of the 10 paleomagnetic sites in sediments incorporated by Beaman et al. [2007] could have been deposited in the Northern Hemisphere and a shallow bias would explain the difference between the pole from core data and the poles from skewness and equatorial sediment facies. The entire difference could be explained by an overall bias of merely 3 in paleolatitude or 6 in inclination, near the low end of the range of estimates of bias found in prior work. The smallness of the postulated bias is consistent with what would be expected for the low paleolatitudes of nearly all the sites [Beaman et al., 2007]. [33] In Figure 11, the 32 Ma B.P. Pacific plate paleomagnetic pole from skewness and the 32 Ma B.P. north pole of the Pacific hot spots reference frame, along with their 95% confidence regions, have been rotated along with the Pacific plate to their locations relative to the Pacific hot spots at 32 Ma B.P. The Pacific plate skewness paleomagnetic pole in the Pacific hot spot reference frame is located at 84.5 N, 165.8 E; its 95% confidence ellipse has its major axis oriented 2 clockwise of north. That the confidence region of the skewness pole only slightly overlaps the confidence region of the north pole of the coordinate system attached to the hot spot reference frame indicates that the Pacific hot spots have shifted significantly relative to the spin axis since 32 Ma B.P. This does not necessarily mean that Pacific hot spots have moved relative to Indo Atlantic hot spots, however. 14 of 16

Table 1. Summary of Data and Results a Profile Lat. ( N) Lon. ( E) D ( ) Azimuth CW of N e a ( ) e m ( ) Resid. ( ) Importance um6503 b 16.76 232.31 31.0 174.5 79.0 73.0 6.0 0.033 alcy01mv 14.77 232.57 38.0 174.5 73.1 69.1 4.0 0.044 vlcn09mv 14.76 232.55 38.0 174.5 73.1 69.1 4.0 0.045 aria01wt 13.21 232.51 31.0 174.5 81.6 64.8 16.8 0.060 odp137jr 12.97 232.75 65.0 174.5 48.2 63.9 15.7 0.062 0480 069.Vd 12.95 232.61 35.0 174.5 55.0 63.9 8.9 0.062 0480 069.Ed 12.95 232.61 130.0 174.5 50.0 63.9 13.9 0.062 dsdp16gc 11.91 232.68 33.0 174.5 81.5 59.7 21.8 0.078 80012103 11.11 232.77 54.0 174.5 61.0 55.5 5.5 0.094 0550 045.c2.Vd 10.25 232.79 46.0 174.5 44.0 49.9 5.9 0.118 0550 045.c2.Ed 10.25 232.79 132.0 174.5 48.0 49.9 1.9 0.118 0480 055.Vd 9.90 232.86 42.0 174.5 48.0 47.1 0.9 0.131 0480 055.Ed 9.90 232.86 139.0 174.5 41.0 47.1 6.1 0.131 0550 055.Vd 3.93 230.02 122.0 165.0 32.0 18.4 13.6 0.091 0550 055.Ed 3.93 230.02 198.0 165.0 18.0 18.4 0.4 0.091 0480 268.Vd 3.85 230.01 98.0 165.0 8.0 18.9 10.9 0.091 0480 268.Ed 3.85 230.01 210.0 165.0 30.0 18.9 11.1 0.091 c1005 3.34 230.08 165.0 165.0 16.0 22.2 6.1 0.089 v3210 2.61 230.30 162.0 165.0 10.7 26.6 16.0 0.086 amph01ar.c3 1.91 230.51 191.0 165.0 36.4 30.6 5.7 0.082 plds03mv 0.98 230.66 204.0 165.0 46.2 35.5 10.8 0.075 0550 047.c2.Vd 0.00 230.94 122.0 165.0 32.0 39.9 7.9 0.067 0550 047.c2.Ed 0.00 230.94 212.0 165.0 32.0 39.9 7.9 0.067 0480 084.c4.Vd 0.00 230.93 134.0 165.0 44.0 39.9 4.1 0.067 0480 084.c4.Ed 0.00 230.93 218.0 165.0 38.0 39.9 1.9 0.067 a Main paleomagnetic results are Chron 12r paleomagnetic pole: 83.5 N, 44.6 E. 95% confidence ellipse: major semiaxis length = 1.9 oriented 98 clockwise of north, minor semiaxis length = 0.9 before incorporation of lineation azimuth uncertainty; major semiaxis length = 3.1 oriented 84 clockwise of north, minor semiaxis length = 1.2 after incorporation of lineation azimuth uncertainty. Abbreviations: Lat., site latitude; Lon., site longitude; D, experimentally determined phase shift that best deskews the crossing of anomaly 12r; Azimuth, azimuth of 12r magnetic lineation; e a, apparent effective remanent inclination (observed); e m, modeled effective remanent inclination (calculated from best fitting pole); Resid., residual (e a e m ); Importance, data importance, which measured the information contribution of a datum. Data importances sum to two. s = 9.9. [34] Figure 11 compares the inferred 32 Ma B.P. paleomagnetic pole position of the Pacific hot spots with the 30 and 40 Ma B.P. poles for the Indo Atlantic hot spots estimated by Besse and Courtillot [2002], which are similar to the poles of the same age in the dipolar global apparent polar wander path of Torsvik et al. [2002] plotted in the North American hotspot reference frame. That their confidence regions do not overlap the north pole of the coordinate system attached to the hot spot reference frame suggests that the Indo Atlantic hot spots have shifted relative to the spin axis since 30 and 40 Ma B.P. The consistency, however, between the pole inferred for Pacific hot spots and the coeval poles inferred for Indo Atlantic hot spots is in turn consistent with Pacific hot spots having been fixed relative to Indo Atlantic hot spots for the past 32 Ma. The consistency also supports the assumption of a dipolar paleomagnetic field and obviates the need for a 10% octupole field proposed by Torsvik et al. [2002]. Within uncertainties, there could have been some motion between Pacific and Indo Atlantic hot spots, but the results indicate that the Pacific hot spots have moved approximately in unison with the Indo Atlantic hot spots relative to the spin axis. This element of common motion is most simply interpreted as true polar wander [Hargraves and Duncan, 1973; Morgan, 1981; Gordon and Cape, 1981; Besse and Courtillot, 2002]. The direction and magnitude of true polar wander observed here is roughly consistent with that predicted from mantle convection models that advect density anomalies backward in time [Steinberger and O Connell, 1997] or calculate density anomalies from the evolving geometry of subducted slabs [Richards et al., 1997]. [35] Pacific plate paleomagnetic results now show consistency with the hypothesis of fixed hot spots moving in unison relative to the spin axis for three distinct ages: 65 Ma [Morgan, 1981; Gordon and Cape, 1981; Gordon, 1982; Acton and Gordon, 1991], 56 Ma [Petronotis et al., 1994; Petronotis and Gordon, 1999], and 32 Ma (this paper). Thus, the evidence for approximately fixed hot spots and for true polar wander is strong for the past 65 Ma. In contrast, results for 81 Ma [Tarduno and Cottrell, 1997; Tarduno et al., 2003] and for 72 Ma [Petronotis and Gordon, 1999] appear to be inconsistent with the Pacific hot spots being fixed with respect to Indo Atlantic hot spots. Perhaps this is due to motion of the Hawaiian hot spot (and possibly other Pacific hot spots) relative to Indo Atlantic hot spots [Molnar and Stock, 1987; Tarduno and Cottrell, 1997; Petronotis and Gordon, 1999]. Alternatively, there may be a bias in Indo Atlantic paleomagnetic data or plate reconstructions for 72 to 81 Ma [Acton and Gordon, 1994; Petronotis and Gordon, 1999]. Both alternatives merit further investigation. 6. Conclusions [36] Paleomagnetic poles with compact confidence limits can be found from skewness data with a limited geographic distribution. Vector aeromagnetic data collected near the present equator and paleoequator have the potential to dramatically improve our knowledge of the paleomagnetic apparent polar wander path of the Pacific plate. 15 of 16

[37] The results demonstrate significant motion of Pacific hot spots relative to the spin axis since 32 Ma B.P. Moreover, when the 32 Ma B.P. Pacific plate paleomagnetic pole is reconstructed into the Pacific hot spot reference frame, it is consistent with the paleomagnetic pole of the Indo Atlantic hot spots. Thus, the global set of hot spots has (within uncertainties) moved in unison relative to the spin axis since 32 Ma B.P., which is most simply interpreted as true polar wander. Taken together with prior results for 65 Ma B.P. [Morgan, 1981; Gordon and Cape, 1981; Gordon, 1982] and 56 Ma B.P. [Petronotis et al., 1994], we conclude that the hot spots have been approximately fixed relative to one another but have moved in approximate unison relative to the spin axis over the past 65 Ma. [38] Acknowledgments. This work was partly supported by NSF grant OCE 0527375. Many of the working plots and final figures were produced using Generic Mapping Tools [Wessel and Smith, 1998]. 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Horner Johnson, Department of Earth Science, Rice University, MS 126, 6100 S. Main St., Houston, TX 77005 1892, USA. (rgg@rice.edu) 16 of 16