RESEARCH LETTER Observational Test of the Global Moving Hot Spot 10.1029/2019GL083663 Reference Frame Key Points: Chengzu Wang1 , Richard G. Gordon1 , Tuo Zhang1 , and Lin Zheng1 • The fit of the Global Moving Hotspot Reference Frame (GMHRF) to 1Department of Earth, Environmental, and Planetary Sciences, William Marsh Rice University, Houston, TX, USA observed geologically young trends of hot spot tracks is evaluated • The data are fit significantly worse (p = 0.005) by the GMHRF than by Abstract The Global Moving Hotspot Reference Frame (GMHRF) has been claimed to fit hot spot tracks fixed hot spots better than the fixed hot spot approximation mainly because the GMHRF predicts ≈1,000 km southward • Either plume conduits do not advect motion through the mantle of the Hawaiian mantle plume over the past 80 Ma. As the GMHRF is passively with mantle flow or the GMHRF mantle velocity field is determined by starting at present and calculating backward in time, it should be most accurate and incorrect reliable for the recent geologic past. Here we compare the fit of the GMHRF and of fixed hot spots to the observed trends of young tracks of hot spots. Surprisingly, we find that the GMHRF fits the data significantly Supporting Information: worse (p = 0.005) than does the fixed hot spot approximation. Thus, either plume conduits are not passively • Supporting Information S1 advected with the mantle flow calculated for the GMHRF or Earth's actual mantle velocity field differs substantially from that calculated for the GMHRF. Correspondence to: Hot spots are the surface manifestations of plumes of hot rock that R. G. Gordon, Plain Language Summary [email protected] rise from deep in the mantle. The tracks of hot spots, such as the Hawaiian island and seamount chain, have been used in two very different ways to estimate the motion of tectonic plates relative to the deep mantle. Originally, it was assumed that the hot spots are “fixed” and do not move relative to each other or Citation: Wang, C., Gordon, R. G., Zhang, T., & relative to the deep mantle. In a later approach, termed the “Global Moving Hotspot Reference Frame” Zheng, L. (2019). Observational test of (GMHRF), the motion of each hot spot relative to the deep mantle was predicted from a calculation of the the global moving hot spot reference global flow of mantle rocks. The latter approach assumes that hot spot motion can be reliably calculated over frame. Geophysical Research Letters, 46, 8031–8038. https://doi.org/10.1029/ the past 130 million years, but does not test its predictions using data from the trends of young hot spot 2019GL083663 chains. We compare the statistical fit of the GMHRF and fixed hot spots using data from the observed trends of young hot spot tracks. Surprisingly, we find that the GMHRF fits the data significantly worse than Received 14 MAY 2019 does the fixed hot spot approximation. Thus, simple fixed hot spots provide the more useful reference frame Accepted 20 JUN 2019 Accepted article online 3 JUL 2019 and some assumptions made to construct the GMHRF are incorrect. Published online 29 JUL 2019

1. Introduction Nearly 50 years ago, Morgan (1971, 1972) proposed that hot spots, sites of intraplate volcanism or excessive volcanism along a plate boundary, are approximately fixed in location and provide a reference frame for determining plate motion relative to the deep mantle. He further proposed that plumes of hot rock rise up from deep in the mantle and are the cause of hot spots at the surface, which had been proposed by Wilson (1963) to explain the origin of chains of seamounts and islands, such as the Hawaiian island chain. Since Morgan's (1971, 1972) work, hot spot tracks have been widely used to estimate plate motion relative to the deep mantle, especially for geologically current plate motions (e.g., Chase, 1978; Gripp & Gordon, 1990, 2002; Minster et al., 1974; Minster & Jordan, 1978; Morgan & Morgan, 2007; Wang et al., 2017, 2018, 2019). How fast individual hot spots move relative to each other and relative to the lower mantle has long been debated. If relative velocities of individual hot spots are low, it would provide support for the usefulness of the fixed hot spot approximation, while high individual hot spot velocities would indicate the need for alternative methods, possibly including a moving hot spot reference frame with its attendant complexity and additional adjustable parameters. Prior studies resulted in inconsistent opinions concerning hot spot velocities. For example, Morgan (1981, 1983) and Duncan (1981) found that individual hot spots move rela- tive to a mean hot spot reference frame at ≈3 to 5 mm/a. Recent work is consistent with these early results and find that nominal relative velocities between Pacific hot spots and Indo‐Atlantic hot spots over the past 50 Ma are only 2−6 mm/a over the past 48 Ma (Andrews et al., 2006; Koivisto et al., 2014). In contrast, to ≈ – fi ©2019. American Geophysical Union. explain the track of the Emperor chain ( 50 80 Ma) on the Paci c plate, several studies found that the velo- All Rights Reserved. city of the Hawaiian hot spot was as high as 40 to 80 mm/a in early Cenozoic and Late Cretaceous time

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(Konrad et al., 2018; Norton, 1995; Raymond et al., 2000; Tarduno et al., 2003). Morgan (1981), Duncan (1981), and Koivisto et al. (2014) have argued, however, that the high apparent velocity of the Hawaiian hot spot during the formation of the Emperor chain is an artifact of missing motion in the global plate motion circuit, most likely due to unmodeled motion between East and West Antarctica, as seems required by paleomagnetic data (Gordon & Cox, 1980; Acton & Gordon, 1994; but see a differing opinion in Doubrovine & Tarduno, 2008). Acting in part on the belief that the Hawaiian hot spot moved southward relative to the mantle during the formation of the Emperor chain, a belief that we do not share (Petronotis et al., 1994; Petronotis & Gordon, 1989; Woodworth & Gordon, 2018b), Doubrovine et al. (2012) asserted that the fixed hot spot reference frame should be abandoned and replaced by a so‐called Global Moving Hotspot Reference Frame (GMHRF) for which hot spot velocities are predicted from a velocity field calculated for the mantle over the past ≈130 Ma. If indeed the motion of hot spots could be reliably calculated (or predicted) over the past ≈130 Ma from models of flow in the mantle, it would advance global geophysics. How far can one rely, however, on these predicted velocities between hot spots? After all, the mantle‐plume system is complex and any estimate of mantle flow must be based on many simplifying assumptions. Our understanding of many key variables in a mantle flow model, such as mantle viscosity structure, may not be sufficiently well constrained for reliable calculations. Given these potential sources of uncertainty, it would be useful to be able to test the predictions of any such model with observations not used in the construction of the model. Fortunately, Morgan and Morgan (2007) developed a data set of the trends of young hot spot chains. This rich data set was evidently not used by Doubrovine et al. (2012) in developing the GMHRF and thus could be used to test its predictions. Because errors accumulate with age and the calculations for the GMHRF proceed from the present Earth backward in time, the predictions from the GMHRF should be at their most reliable and accurate for the recent geologic past. Here we investigate the following question: is the improvement in fit to trends of young hot spot tracks realized by the GMHRF large enough to justify the considerable complexity and its additional adjustable parameters relative to the simple fixed hot spot approximation? Surprisingly, we find that the GMHRF fits the observed trends of young hot spot tracks much worse than the assumption of fixed hot spots.

2. Data: Hot Spot Trends and Uncertainties Morgan and Morgan (2007) estimated the trends of 57 young tracks of hot spots produced by 54 hot spots (their Table 1). Following Wang et al. (2017, 2019), we omit the Comores track, leaving 56 hot spot tracks. Doubrovine et al. (2012) estimate the locations as a function of time of 44 hot spots (their Table S6). Thirty eight of the hot spots modeled by Doubrovine et al. (2012) correspond to 41 of the 56 trends of hot spot tracks adopted by Wang et al. (2019). Thus, we use the observed trends of these 41 tracks (Figure 1 and Table S1 in the supporting information) to test the predictions of the GMHRF. We adopt the current hot spot locations and current trends from Morgan and Morgan (2007). The uncertainties in trends are calculated objectively using hot spot track length and width (Gripp & Gordon, 2002; Wang et al., 2019).

3. Methods 3.1. Predicted Velocities of Hot Spots Steinberger and O'Connell (1998) proposed a method to estimate plume and hot spot velocity through numerical modeling of mantle convection and advection of plume conduits in the mantle flow field. Following Steinberger and O'Connell (1998), Doubrovine et al. (2012) computed a large‐scale mantle flow field from global plate motions, a radial mantle viscosity structure, and a mantle density structure inferred from seismic tomography. A plume conduit is inserted into the flow field under the assumption that plume conduits do not influence larger‐scale mantle flow. Plume velocity is determined by a sum of the mantle flow velocity and plume vertical buoyant rising velocity. The hot spot velocities adopted herein are determined from the hot spot locations at present and at 5 Ma given by Doubrovine et al. (2012). For those hot spots without locations specified precisely at 5 Ma, we linearly interpolate from the specified locations having ages immediately less than, and immediate greater

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Figure 1. Observed and calculated hot spot trends. Black = observed trend from data set of 41 hot spot trends. Blue = calculated hot spot trend in the fixed hot spot reference frame. Red = calculated hot spot trend in the GMHRF (equal to the direction of plate motion relative to the hot spot at that location).

than, 5 Ma. We determine each hot spot velocity for the past 5 Ma, assuming that motion is along a great circle defined by endpoint locations at present and at 5 Ma. The hot spot speeds thus determined range from 0.4 mm/a for Cobb to 29.9 mm/a for Society, with mean of 11.4 mm/a and median of 10.9 mm/a (Figure 2, Table S1). 3.2. Finding the Best Fit to Hot Spot Trends

We use the term “hot spot‐mantle velocity” (Vhotspot − mantle) to refer to the velocity of an individual hot spot relative to the mean mantle reference frame. We use the term “plate‐mantle velocity” (Vplate − mantle) to refer to the velocity of a plate relative to the mean mantle reference frame, which is calculated using

V plate−mantle ¼ ωplate−mantle×r; (1)

where ωplate‐mantle is the angular velocity of a given plate relative to the mean mantle reference frame and r is the vector from the center of the Earth to the point of interest on Earth's surface. We use the term “plate‐ hot

spot velocity” (Vplate − hotspot) to refer to the velocity of the lithosphere relative to an individual hot spot at a given location and is defined by

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Figure 2. Hot spot‐mantle velocity, plate‐mantle velocity, and plate‐hot spot velocity in the GMHRF. Red = hot spot velocity relative to the mean mantle reference frame (Doubrovine et al., 2012). Blue = plate velocity relative to mean mantle reference frame determined herein by minimizing the sum‐square normalized misfit assuming that hot spots move relative to the mean mantle reference frame as proposed by Doubrovine et al. (2012) and shown in red. Black = Plate velocity relative to each individual hot spot. The line length corresponding to 20 mm/a is shown in the inset.

V plate−hotspot ¼ V plate−mantle−V hotspot−mantle ; (2)

In the special case of assumed‐fixed hot spots, the hot spot‐mantle velocity is zero for each hot spot, and therefore in that special case the plate‐mantle velocity and the plate‐hot spot velocity are identical for every hot spot. The fitting function we use is similar to those used by Gripp and Gordon (2002) and Wang et al. (2019). We take the sum‐square normalized misfittoN hot spot trends to be  ðÞα = 2 ¼ ∑N 2 sin i 2 ; r i¼1 (3) σi

where αi is the difference in angle between the ith observed and ith calculated trend and σi is the 1‐sigma uncertainty of the ith observed trend (Wang et al., 2019).

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Figure 3. Magnitudes of angular misfit and normalized angular misfit for fixed hot spots and for the GMHRF. Angular misfit equals the difference between observed and calculated trend. Normalized misfit = 2 sin (αi/2)/σi, where αi is the angular misfit and σi is the 1‐sigma uncertainty of the ith trend.

We solve for a set of plate angular velocities relative to a mantle reference frame that minimize r while constraining the relative plate angular velocities to consistency with the MORVEL set of relative plate angular velocities (DeMets et al., 2010). The calculated hot spot trend is the direction of plate‐hot spot velocity at the location of a given hot spot (Figure 2). In the special case of assumed‐fixed hot spots, the calculated hot spot trend equals the direction of plate‐mantle velocity. For equal time‐averaging intervals, trends of hot spot tracks on fast‐moving lithosphere tend to have smaller uncertainties (Wang et al., 2019), and thus tend to be given more weight in our inversion procedure (cf. equation (3)). On the other hand, longer time averaging intervals tend to be used for trends of hot spot tracks on slow‐moving lithosphere (Morgan & Morgan, 2007), which partly offsets the effect of lithosphere

speed on σi (Wang et al., 2019).

4. Results 4.1. Fixed Hot Spot Reference Frame The magnitudes of the angular misfits range from 0.3° for the Galapagos track on the Cocos plate to 116° for the Iceland track on the Eurasia plate with a median misfit magnitude of 10° (Figures 1 and 3). The magni- tudes of the normalized misfits (i.e., misfit divided by its 1σ uncertainty) range from 0.01 for the Balleny track on the Antarctica plate to 3.08 for the Marquesas track on the Pacific plate with a median of 0.64 (Table S2 and Figure 3). The sum‐square normalized misfit is 44.7 with 3 adjustable parameters while fitting 41 trends of hot spot tracks. The probability of obtaining a value of chi square greater than or equal to 44.7 with 38 degrees of freedom if the hot spots are fixed is p = 0.21; therefore, from this test we do not reject the null hypothesis that the hot spots are fixed.

4.2. Global Moving Hot Spot Reference Frame The magnitudes of the angular misfits range from 0.1° for the Fernando track on the South America plate to 112° for the Eifel track on the Eurasia plate with a median of 11° (Figures 1 and 3). The magnitudes of the normalized misfits range from 0.002 for the Fernando track on the South America plate to 5.42 for the Hoggar track on the Nubia plate with a median magnitude of 0.72 (Table S2 and Figure 3).

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The sum‐square normalized misfit is 105.6 with 3 adjustable parameters while fitting 41 observed trends of hot spot tracks. The probability of obtaining a value of chi‐square of 105.6 or greater with 38 degrees of free- − dom if the hot spot velocities from the GMHRF are correct is p = 2.50 × 10 8. Therefore, from this test we reject the validity of the predicted hot spot velocities of the GMHRF at a high level of confidence.

4.3. Comparisons for Individual Plates For any hot spot track, incorporating the hot spot velocity from the GMHRF instead of assuming a fixed hot spot can affect the fit between the observed and calculated trend of the hot spot in one of three ways: (1) the predicted hot spot velocity could be in a direction that causes the misfit to increase irrespective of its magni- tude; (2) the predicted hot spot velocity could have a direction and magnitude that decreases the misfit; and (3) the predicted hot spot velocity could be in a direction that could cause the misfit to decrease for small magnitudes, but the magnitude is large enough that it instead increases the misfit. These possibilities are considered in detail in Text S1, Table S3, and Figures S1–S10. In total, 21 hot spots are predicted by the GMHRF to move in a direction that increases angular misfits irrespective of speed. Eighteen hot spots are predicted to move in a direction with a magnitude that decreases angular misfits. Two hot spots are predicted to move in a direction that could improve the fit, but the predicted speeds are high enough that they instead increase angular misfits (Table S3).

4.4. Further Comparison of the Fit to the Fixed Hot Spot Reference Frame With the Fit to the GMHRF Overall, the trends of 23 hot spot tracks fit better in the fixed hot spot reference frame and the trends of 18 hot spot tracks fit better in the GMHRF. Six plates (Antarctica, Australia, Cocos, Nubia, Nazca, and Pacific) have more hot spot tracks that fit better in the fixed hot spot reference frame than in the GMHRF. Three plates (Eurasia, South America, and Somalia) have more hot spot tracks that fit better in the GMHRF than in the fixed hot spot reference frame. One plate (North America) has an equal number of hot spot tracks that fit better in the fixed hot spot reference frame and the GMHRF (Table S3). The ratio of the sum‐square normalized misfit for the fit to the GMHRF (106 with 38 degrees of freedom) to that of the fit assuming fixed hot spots (45 also with 38 degrees of freedom) is 2.36. If this ratio is F‐distributed, the probability of obtaining a value this large or larger with 38 versus 38 degrees of freedom if the parent populations have identical variances is 0.005, which indicates that the GMHRF fits the trend data significantly worse than does assumed‐fixed hot spots.

5. Hot Spot Speed if the Fit of the GMHRF to Observed Trends of Young Hot Spot Tracks Is Optimized Above we showed that the overall fit to the GMHRF is significantly worse (p = 0.005) than the fittofixed hot spots, and that more than half the directions of hot spot motion predicted by the GMHRF make the fit worse irrespective of the predicted speed of the hot spot. For two hot spots, however, the predicted directions would have improved the fit if only the predicted speeds had been lower. Might the directions and relative speeds of hot spots predicted by the GMHRF be correct, but the mean speed be wrong? To answer this question, we conducted a further test by constructing many sets of hot spot velocities. Each set of hot spot velocities has the same direction and relative speeds as those in the GMHRF, but all speeds are multiplied by a uniform factor, γ. For the special case of γ = 1, the predicted velocities are identical to those of the GMHRF. For the special case of γ = 0, the predicted velocities are equivalent to the fixed hot spot hypoth- esis. For completeness, we consider not just values of γ between 0 and 1, but in a range from −1.5 to 1.5 in increments of 0.01 where negative values of γ correspond to directions of motion precisely opposite to that predicted by the GMHRF. We find that γ = 0.03 gives the minimum sum‐square normalized misfit and has 95% confidence limits ranging from −0.57 to 0.22, which unsurprisingly excludes γ = 1 (i.e., the GMHRF) while including γ =0 (i.e., fixed hot spots; Figure 4). The mean hot spot speed corresponding to γ = 0.03 is 0.3 mm/a. The mean hot spot speeds corresponding to γ = −0.57 and γ = 0.22, respectively, are −6.3 and +2.4 mm/a where negative speeds indicate velocities opposite in direction to those predicted by the GMHRF.

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6. Discussion Our results show that the global fits to the observed trends of young hot spot tracks are significantly worse (p = 0.005) if the hot spot velocities pre- dicted by the GMHRF are used instead of the assumption of fixed hot spots. It follows that either the plume conduits are not passively advected by the mantle as assumed in constructing the GMHRF or the actual man- tle convection velocity field differs substantially from that calculated by Doubrovine et al. (2012). In a convecting mantle, plumes and their surface manifestation, hot spots, cannot be truly stationary. It has been proven difficult, however, to resolve their relative velocities (Andrews et al., 2006; Koivisto et al., 2014; Wang et al., 2017, 2019). The results above demonstrate that the hot spots and plumes do not move as predicted by the GMHRF. The present results, along with those of Acton and Gordon (1994), Petronotis et al. (1994), Andrews et al. (2006), Koivisto et al. (2014), Wang et al. (2017, 2019), and Woodworth and Gordon (2018a), indicate that motion between hot spots is slow, nominally several millimeters per year. Our results stand in stark contrast with the claim of Doubrovine et al. (2012) that “Fits of absolute kinematic solutions that incorporate esti- mates of hot spot motion were always superior compared to those in ‐ fi Figure 4. Sum square normalized mis t to trends of young tracks of hot which hot spots were assumed fixed … .” Evidently, their statement spots as a function of γ, which is a scale factor by which we multiply the depends strongly on the putative southward motion of the Hawaiian hot spot velocities predicted by the GMHRF (Doubrovine et al., 2012). γ =0 (red vertical line) corresponds to fixed hot spots. γ = 1 (blue vertical line) hot spot through the mantle and relative to other hot spots from 80 to corresponds to the set of velocities of hot spots predicted from the GMHRF. 60 Ma, an inference with which we disagree (e.g., Petronotis et al., The best fit (black‐filled circle) is obtained for γ = 0.03. The horizontal 1994; Petronotis & Gordon, 1989; Woodworth & Gordon, 2018b). Given fi γ dashed line indicates the range of the 95% con dence interval for , which that the predictions of the GMHRF fail to improve the fits to the young varies from −0.57 to 0.22. Negative values of γ indicate plate velocities in the tracks of hot spots, for which the relative plate motions are orders of direction opposite to that predicted by the GMHRF. magnitude more reliable than for those in early Cenozoic and Late Cretaceous time, there is no reason to give credence to its predictions for hot spot motions in the geologic past. Therefore, geoscientists should reject the GMHRF. While it would be useful to be able to correct for motion between hot spots from an estimate of the current and past velocity field in the mantle, the GMHRF fails to do so accurately. Until a more successful model is available with predictions that explain the observations better than the simple fixed hot spot approxima- tion, the latter remains the best approach for estimating absolute plate motion over Cenozoic and late Mesozoic time.

7. Conclusions 1. The GMHRF does no better than flipping a coin in correctly predicting the direction of hot spot motion that could potentially improve the fit to observed trends of hot spot tracks. 2. The hot spot velocities predicted by the GMHRF fit the observed trends of young hot spot chains signifi- cantly worse (p = 0.005) than fits obtained by assuming fixed hot spots. 3. If the predicted directions of motion and relative speeds of hot spots in the GMHRF are correct, but wrong by a uniform multiplicate scale factor, the mean hot spot speed that best fits the observed trends of young hot spot tracks is 0.3 mm/a with a lower bound (95% confidence limits) of −6.3 mm/a (a nega- tive value means hot spot motions opposite in direction predicted by the GMHRF) and an upper bound of +2.4 mm/a. Thus, fixed hot spots are an excellent approximation. 4. Either plume conduits do not advect with mantle flow as assumed in the GMHRF or Earth's actual man- tle velocity field differs substantially from that assumed in constructing the GMHRF. 5. It would be useful if it were possible to reliably predict past and present motions between hot spots from models of the flow in the mantle. The state of the art, however, is evidently insufficient to be useful at present. Until that day arrives, the simple fixed hot spot assumption appears to be the best option available.

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Acknowledgments References This work was supported by National Acton, G. D., & Gordon, R. G. (1994). Paleomagnetic tests of Pacific plate reconstructions and implications for motion between hotspots. Science Foundation grant OCE‐ Science, 263(5151), 1246–1254. https://doi.org/10.1126/science.263.5151.1246 1559316. Some figures were made with Andrews, D. L., Gordon, R. G., & Horner‐Johnson, B. C. (2006). Uncertainties in plate reconstructions relative to the hotspots; Pacific‐ the Generic Mapping Tools software hotspot rotations and uncertainties for the past 68 million years. Geophysical Journal International, 166(2), 939–951. https://doi.org/ (Wessel & Smith, 1991). The data 10.1111/j.1365‐246X.2006.03029.x supporting the conclusions can be Chase, C. G. (1978). Plate kinematics: The Americas, East Africa, and the rest of the world. Earth and Planetary Science Letters, 37(3), obtained in the references, tables, and 355–368. https://doi.org/10.1016/0012‐821X(78)90051‐1 supporting information. DeMets, C., Gordon, R. G., & Argus, D. F. (2010). Geologically current plate motions. Geophysical Journal International, 181(1), 1–80. https://doi.org/10.1111/j.1365‐246X.2009.04491.x Doubrovine, P. V., Steinberger, B., & Torsvik, T. H. (2012). Absolute plate motions in a reference frame defined by moving hot spots in the Pacific, Atlantic, and Indian Oceans. Journal of Geophysical Research, 117, B09101. https://doi.org/10.1029/2011JB009072 Doubrovine, P. V., & Tarduno, J. A. (2008). Linking the Late Cretaceous to Paleogene Pacific plate and the Atlantic bordering continents using plate circuits and paleomagnetic data. Journal of Geophysical Research, 113, B07104. https://doi.org/10.1029/2008JB005584 Duncan, R. A. (1981). Hotspots in the southern oceans—An absolute frame of reference for motion of the Gondwana continents. Tectonophysics, 74(1‐2), 29–42. https://doi.org/10.1016/0040‐1951(81)90126‐8 Gordon, R. G., & Cox, A. (1980). Paleomagnetic test of the early Tertiary plate circuit between the Pacific basin plates and the Indian plate. Journal of Geophysical Research, 85(B11), 6534–6546. https://doi.org/10.1029/JB085iB11p06534 Gripp, A. E., & Gordon, R. G. (1990). Current plate velocities relative to the hotspots incorporating the NUVEL‐1 global plate motion model. Geophysical Research Letters, 17(8), 1109–1112. https://doi.org/10.1029/GL017i008p01109 Gripp, A. E., & Gordon, R. G. (2002). Young tracks of hotspots and current plate velocities. Geophysical Journal International, 150(2), 321–361. https://doi.org/10.1046/j.1365‐246X.2002.01627.x Koivisto, E. A., Andrews, D. L., & Gordon, R. G. (2014). Tests of fixity of the Indo‐Atlantic hot spots relative to Pacific hot spots. Journal of Geophysical Research: Solid Earth, 119, 661–675. https://doi.org/10.1002/2013JB010413 Konrad, K., Koppers, A. A. P., Steinberger, B., Finlayson, V. A., Konter, J. G., & Jackson, M. G. (2018). On the relative motions of long‐lived Pacific mantle plumes. Nature Communications, 9(1), 854. https://doi.org/10.1038/s41467‐018‐03277‐x Minster, J. B., & Jordan, T. H. (1978). Present‐day plate motions. Journal of Geophysical Research, 83(B11), 5331–5354. https://doi.org/ 10.1029/JB083iB11p05331 Minster, J. B., Jordan, T. H., Molnar, P., & Haines, E. (1974). Numerical modelling of instantaneous plate tectonics. Geophysical Journal of the Royal Astronomical Society, 36(3), 541–576. https://doi.org/10.1111/j.1365‐246X.1974.tb00613.x Morgan, W. J. (1971). Convection plumes in the lower mantle. Nature, 230(5288), 42–43. https://doi.org/10.1038/230042a0 Morgan, W. J. (1972). Deep mantle convection plumes and plate motions. AAPG bulletin, 56(2), 203–213. Morgan, W. J. (1981). In C. Emiliani (Ed.), 13. Hotspot tracks and the opening of the Atlantic and Indian Oceans. The oceanic lithosphere, (Vol. 7, pp. 443–487). New York: Wiley. Morgan, W. J. (1983). Hotspot tracks and the early rifting of the Atlantic. In Developments in Geotectonics, (Vol. 19, pp. 123–139). Elsevier. Morgan, W. J., & Morgan, J. P. (2007). In G. R. Foulger, & D. M. Jurdy (Eds.), Plate Velocities in the Hotspot Reference frame. Special papers‐ Geological Society of America, Geological Society of America Bulletin, (Vol. 430, pp. 65–78). Boulder, Colorado. https://doi.org/10.1130/ 2007.2430(04) Norton, I. O. (1995). Plate motions in the North Pacific: The 43 Ma nonevent. Tectonics, 14(5), 1080–1094. https://doi.org/10.1029/ 95TC01256 Petronotis, K. E., & Gordon, R. G. (1989). Age dependence of skewness of magnetic anomalies above seafloor formed at the Pacific‐Kula spreading center. Geophysical Research Letters, 16(4), 315–318. https://doi.org/10.1029/GL016i004p00315 Petronotis, K. E., Gordon, R. G., & Acton, G. D. (1994). A 57 Ma Pacific plate palaeomagnetic pole determined from a skewness analysis of crossings of marine magnetic anomaly 25r. Geophysical Journal International, 118(3), 529–554. https://doi.org/10.1111/j.1365‐ 246X.1994.tb03983.x Raymond, C. A., Stock, J. M., & Cande, S. C. (2000). In M. A. Richards, R. G. Gordon, & R. D. van der Hilst (Eds.), The history and dynamics of global plate motions, Geophysical Monograph Series, (Vol. 121, pp. 359–375). Washington, D. C: American Geophysical Union. Steinberger, B., & O'Connell, R. J. (1998). Advection of plumes in mantle flow: Implications for hotspot motion, mantle viscosity and plume distribution. Geophysical Journal International, 132(2), 412–434. https://doi.org/10.1046/j.1365‐246x.1998.00447.x Tarduno, J. A., Duncan, R. A., Scholl, D. W., Cottrell, R. D., Steinberger, B., Thordarson, T., et al. (2003). The Emperor Seamounts: Southward motion of the Hawaiian hotspot plume in Earth's mantle. Science, 301(5636), 1064–1069. https://doi.org/10.1126/ science.1086442 Wang, C., Gordon, R. G., & Zhang, T. (2017). Bounds on geologically current rates of motion of groups of hot spots. Geophysical Research Letters, 44, 6048–6056. https://doi.org/10.1002/2017GL073430 Wang, C., Gordon, R. G., Zhang, T., & Zheng, L. (2019). Uncertainties in Trends of Young Hotspot Tracks. Geophysical Research Letters. https://doi.org/10.1029/2019GL082580 Wang, S., Yu, H., Zhang, Q., & Zhao, Y. (2018). Absolute plate motions relative to deep mantle plumes. Earth and Planetary Science Letters, 490,88–99. https://doi.org/10.1016/j.epsl.2018.03.021 Wessel, P., & Smith, W. H. (1991). Free software helps map and display data. Eos, Transactions American Geophysical Union, 72(41), 441–446. https://doi.org/10.1029/90EO00319 Wilson, J. T. (1963). A possible origin of the Hawaiian Islands. Canadian Journal of Physics, 41(6), 863–870. https://doi.org/10.1139/p63‐ 094 Woodworth, D., & Gordon, R. G. (2018a). Paleolatitude of the Hawaiian hot spot since 48 Ma: Evidence for a mid‐Cenozoic true polar stillstand followed by late Cenozoic true polar wander coincident with northern hemisphere glaciation. Geophysical Research Letters, 45(21), 11–632. Woodworth, D., & Gordon, R. G., (2018b). Further evidence for a stationary Hawaiian hotspot during formation of the Emperor Seamount chain: Skewness analysis of Pacific plate magnetic anomaly 24r. Abstract GP31A‐0709 presented at 2018 Fall Meeting, AGU, Washington, D.C., Dec. 10–14

WANG ET AL. 8038

Geophysical Research Letters

Supporting Information for

Observational Test of the Global Moving Hotspot Reference Frame

Chengzu Wang, Richard G. Gordon, Tuo Zhang, and Lin Zheng

Department of Earth, Environmental, and Planetary Sciences

Rice University, Houston, Texas, USA

Contents of this file

Introduction

Text S1

Tables S1 – S3

Figure S1 – S10

Introduction

This supporting information provides text, tables, and figures to support and document the main article.

Hotspot trends and velocities of plate-mantle, hotspot-mantle, plate-hotspot are shown for each hotspot on each plate in Figures S1 to Figure S10.

Text S1: Comparisom of the Fit of Observed Trends of Young Hotspot Tracks to the Fixed

Hotspot Reference Frame and to the GMHRF

For any hotspot track, incorporating the hotspot velocity from the GMHRF instead of assuming a fixed hotspot can affect the fit between the observed and calculated trend of the hotspot in one of three ways: (1) The predicted hotspot velocity could be in a direction that causes the misfit to increase irrespective of its magnitude. (2) The predicted hotspot velocity could have a direction and magnitude that decreases the misfit. (3) The predicted hotspot velocity could be in a direction that could cause the misfit to decrease for small magnitudes, but the magnitude is large enough that it instead increases the misfit.

These possibilities can be examined visually in Figures S1 to S10, which show observed and calculated trends for each of the ten plates having hotspot tracks.

For the Antarctica plate, the hotspot velocities predicted for all three hotspots (Balleny,

Kerguelen, and Marion) are in directions that cause the trend misfit to increase relative to the fixed hotspot fit. Fixed hotspots fit better than the GMHRF (Figure S1).

For the Australia plate, velocities predicted for the East Australia and Lord Howe hotspots are in directions that increase the misfits. The velocity predicted for the Tasmantid hotspot decreases the misfit. Overall, fixed hotspots fit better than the GMHRF (Figure S2).

For the Cocos plate, the velocity predicted for the Galapagos hotspot is in a direction that increases the angular misfit. Fixed hotspots fit better than the GMHRF (Figure S3).

For the Eurasia plate, the velocity predicted for the Eifel hotspot is in a direction that increases the angular misfit. The velocities for the Azores and Iceland hotspots decrease the misfits. Overall, the GMHRF fits better than fixed hotspots (Figure S4). For the North America plate, the velocities predicted for the Azores and Iceland hotspots are in directions that increase the misfits. The velocities predicted for the Raton and Yellowstone hotspots decrease the misfits. Overall, fixed hotspots and the GMHRF fit equally well (Figure

S5).

For the Nubia plate, the velocities predicted for the Cameroon, Cape Verde, Hoggar, and

Shona hotspots are in directions that increase the misfits. The velocity predicted for the Jebel

Marra hotspot is in a direction that could decrease the misfit, but is so large that it increases the misfit. The velocities predicted for the Canary, Great Meteor, St. Helena, and Tibesti hotspots decrease the misfits. Overall, fixed hotspots fit better than the GMHRF (Figure S6).

For the Nazca plate, the velocities predicted for the Galapagos and San Felix hotspots are in directions that increase the misfits. The velocity predicted for the Juan Fernandez hotspot is in a direction that could decrease the misfit, but is so large that it increases the misfit. The velocity predicted for the Easter hotspot decreases the misfit. Overall, fixed hotspots fit better than the

GMHRF (Figure S7).

For the Pacific plate, the velocities predicted for the Hawaii, Macdonald, Marquesas,

Pitcairn, Samoa, and Society hotspots are in directions that increase the misfits. The velocities predicted for the Bowie, Caroline, Cobb, Guadelupe, and Louisville hotspots decrease the misfit.

Overall, fixed hotspots fit better than the GMHRF (Figure S8).

For the South America plate, the velocities predicted for the Fernando and Trindade/Martin

Vaz hotspots decrease the misfits. The GMHRF fits better than fixed hotspots (Figure S9).

For the Somalia plate, the velocity predicted for the Réunion hotspot decreases the misfit.

The GMHRF fits better than fixed hotspots (Figure S10). In total, 21 hotspots were predicted to move in the wrong direction and increase angular misfits; 18 hotspots are in the right direction and decrease angular misfits; and 2 hotspots are in the right direction but overshoot and increase angular misfits.

Table S1: Location, Trend, Uncertainty, and Predicted Hotspot Veolocity for each Hotspot Track Hotspot velocity in the GMHRF Hotspot Plate Lat. (° N) Lon. (° E) ζ (°) σ (°) Trend (°) Rate (mm/a) Balleny AN -67.6 164.8 325 46 114.9 18.4 Kerguelen AN -49.6 69.0 50 9 241.5 11.0 Marion AN -46.9 37.6 80 24 207.7 15.5 East Australia AU -40.8 146.0 0 3 295.8 2.5 Lord Howe AU -34.7 159.8 351 6 203.3 15.8 Tasmanid AU -40.4 155.5 7 6 185.8 8.9 Galapagos CO -0.4 -91.6 45 5 255.5 22.5 Azores EU 37.9 -26.0 110 52 207.0 2.6 Eifel EU 50.2 6.7 82 61 109.2 9.6 Iceland EU 64.4 -17.3 75 88 223.3 7.7 Azores NA 37.9 -26.0 280 20 207.0 2.6 Iceland NA 64.4 -17.3 287 20 223.3 7.7 Raton NA 36.8 -104.1 240 20 129.1 10.3 Yellowstone NA 44.5 -110.4 235 20 108.5 15.2 Cameroon NU -2.0 5.1 32 21 10.9 11.9 Canary NU 28.2 -18.0 94 53 157.5 3.3 Cape Verde NU 16.0 -24.0 60 13 245.7 12.6 Great Meteor NU 29.4 -29.2 40 51 192.6 3.2 Hoggar NU 23.3 5.6 46 12 59.6 14.4 Jebel Marra NU 13.0 24.2 45 21 21.6 23.8 Shona NU -51.4 1.0 74 16 110.1 4.2 St Helena NU -16.5 -9.5 78 18 274.7 5.4 Tibesti NU 20.8 17.5 30 6 33.7 17.7 Easter NZ -26.4 -106.5 87 13 250.0 15.9 Galapagos NZ -0.4 -91.6 96 16 255.5 22.5 Juan Fernandez NZ -33.9 -81.8 84 12 153.2 10.9 San Felix NZ -26.4 -80.1 83 13 78.7 12.9 Bowie PA 53.0 -134.8 306 18 108.6 8.3 Caroline PA 4.8 164.4 289 9 61.6 17.3 Cobb PA 46.0 -130.1 321 17 26.1 0.4 Guadalupe PA 27.7 -114.5 292 14 123.5 12.0 Hawaii PA 19.0 -155.2 304 10 102.4 4.7 Louisville PA -53.6 -140.6 316 10 185.6 7.2 Macdonald PA -29.0 -140.3 289 9 142.7 5.2 Marquesas PA -10.5 -139.0 319 9 43.8 17.3 Pitcairn PA -25.4 -129.3 293 9 80.2 21.0 Samoa PA -14.5 -169.1 285 9 134.1 18.2 Society PA -18.2 -148.4 295 9 301.7 29.9 Fernando SA -3.8 -32.4 266 24 248.9 9.4 Martin Vaz SA -20.5 -28.8 264 27 224.2 3.0

Hotspot locations and trends are from Morgan and Phipps Morgan (2007). Uncertainties in trend are from Wang et al., (2019). Hotspot velocities are calculated from hotspot locations as a function of time specified in the supplementary material of Doubrovine et al., (2012). ζ is hotspot trend clockwise of north. Plate name abbreviations: AN, Antarctica; AU, Australia; CO, Cocos; EU, Eurasia; NA, North America; NU, Nubia; NZ, Nazca; PA, Pacific; SA, South America; SO, Somalia. Other abbreviations: Lat., Latitude; Lon., Longitude; N, North; E, East.

Table S2. Calculated Trends and Misfits in the Fixed Hotspot Reference Frame and in the GMHRF. ζcal (°) | ζobs - ζcal | (°) Normalized Misfit Hotspot Name Plate ζobs (°) σ (°) Fixed GMHRF Fixed GMHRF Fixed GMHRF

Balleny AN 325 46 325 295 0 30 0.01 0.64

Kerguelen AN 50 9 59 60 9 10 0.99 1.06

Marion AN 80 24 69 51 11 29 0.45 1.20

East Australia AU 0 3 6 10 6 10 2.10 3.23

Lord Howe AU 351 6 2 8 11 17 1.89 2.86

Tasmanid AU 7 6 1 3 6 4 1.06 0.72

Galapagos CO 45 5 45 54 0 9 0.05 1.87

Azores EU 110 52 27 45 83 65 1.46 1.18

Eifel EU 82 61 9 330 73 112 1.12 1.56

Iceland EU 75 88 319 7 116 68 1.10 0.73

Azores NA 280 20 286 293 6 13 0.30 0.66

Iceland NA 287 20 292 310 5 23 0.26 1.16

Raton NA 240 20 218 233 22 7 1.08 0.33

Yellowstone NA 235 20 214 235 21 0 1.03 0.01

Cameroon NU 32 21 49 82 17 50 0.81 2.31

Canary NU 94 53 26 27 68 67 1.21 1.19

Cape_Verde NU 60 13 71 72 11 12 0.86 0.95

Great_Meteor NU 40 51 69 59 29 19 0.57 0.38

Hoggar NU 46 12 25 337 21 69 1.75 5.42

Jebel Marra NU 45 21 31 107 14 62 0.64 2.79

Shona NU 74 16 64 61 10 13 0.64 0.82

St Helena NU 78 18 68 75 10 3 0.57 0.14

Tibesti NU 30 6 26 29 4 1 0.62 0.10

Easter NZ 87 13 103 98 16 11 1.24 0.83

Galapagos NZ 96 16 94 90 2 6 0.16 0.40

Juan Fernandez NZ 84 12 86 79 2 5 0.15 0.43

San Felix NZ 83 13 84 89 1 6 0.11 0.43

Bowie PA 306 18 319 315 13 9 0.73 0.52

Caroline PA 289 9 296 288 7 1 0.75 0.09

Cobb PA 321 17 309 310 12 11 0.69 0.64

Guadalupe PA 292 14 289 291 3 1 0.22 0.06

Hawaii PA 304 10 298 298 6 6 0.58 0.59

Louisville PA 316 10 296 301 20 15 2.00 1.53

Macdonald PA 289 9 292 293 3 4 0.29 0.47

Marquesas PA 319 9 291 280 28 39 3.08 4.23

Pitcairn PA 293 9 288 282 5 11 0.59 1.27

Samoa PA 285 9 297 301 12 16 1.34 1.76

Society PA 295 9 293 289 2 6 0.17 0.71

Fernando SA 266 24 259 266 7 0 0.28 0.00

Martin Vaz SA 264 27 259 260 5 4 0.19 0.16 Reunion SO 47 46 39 40 8 7 0.49 0.44

Table S3: Comparison of Misfits to the Fixed Hotspot Reference Frame (FHRF) and to the GMHRF Number of FHRF GMHRF Plate Name Which is Better? Hotspots Fits Better Fits Better Antarctica 3 3 0 F Australia 3 2 1 F Cocos 1 1 0 F Eurasia 3 1 2 G North America 4 2 2 - Nubia 9 5 4 F Nazca 4 3 1 F Pacific 11 6 5 F South America 2 0 2 G Somalia 1 0 1 G TOTAL 41 23 18 G=3, F=6

The second column gives the number of trends of hotspot tracks investigated on each plate. The third column is the number of trends on that plate that are fit better by the fixed hotspot approximation. The fourth column is the number of trends on that plate that are fit better by the Global Moving Hotspot Reference Frame. The fifth column lists which assumption fits the trends on that plate better, “F” (fixed hotspot approximation) or “G” (Global Moving Hotspot Reference Frame).

Figure S1a: Hotspot trends for Antarctica. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S1b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Antarctica. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S2a: Hotspot trends for Australia. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S2b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Australia. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S3a: Hotspot trends for Cocos. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S3b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Cocos. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S4a: Hotspot trends for Eurasia. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S4b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Eurasia. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S5a: Hotspot trends for North America. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S5b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for North America. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S6a: Hotspot trends for Nubia. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S6b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Nubia. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S7a: Hotspot trends for Nazca. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S7b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Nazca. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S8a: Hotspot trends for Pacific. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S8b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Pacific. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S9a: Hotspot trends for South America. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S9b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for South America. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.

Figure S10a: Hotspot trends for Somalia. Black solid, observed trend; Blue, calculated trend in the fixed hotspot reference frame (equals the direction of plate velocity relative to the mantle); Red, calculated trend in the GMHRF (equals to the direction of plate velocity relative to individual hotspot); Black dash, direction of hotspot velocity relative to mantle. Lengths have no information.

Figure S10b: Hotspot-mantle velocity, plate-mantle velocity, and plate-hotspot velocity for Somalia. Black, hotspot-mantle velocity; Blue, plate-mantle velocity; Red, plate-hotspot velocity. Lengths are proportional to speed.