dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction Paleomagnetism provides one of the principal tools for the quantitative reconstruction of Earth's paleogeography. Paleomagnetic data are used to construct apparent polar wander paths (APWPs) that describe the apparent motion of the paleomagnetic pole relative to a fixed continent or tectonic plate through time (e. g. ,  Creer et al. , 1954). Assuming that the time-averaged geomagnetic pole coincides with the Earth's spin axis allows the translation of an APWP into the motion of a continent or plate relative to the geographic pole. By rotating paleomagnetic data from all major plates to a common reference plate using independent constraints on relative plate motions, a global APWP may be constructed that places a global model of relative plate motions into an 'absolute' reference frame (e.
First, the paleomagnetic poles (or paleopoles) that are used as input for APWP construction are commonly assigned equal weight, regardless of the uncertainties in the position of the paleopole or in the age of the rocks from which they were derived. Second, such paleopoles are calculated from widely different, and essentially arbitrary numbers of paleomagnetic sites  (Vaes et al. , 2022) , whereby each site is interpreted to represent a 'spot reading' of the past geomagnetic field (e. g. ,  McElhinny and McFadden, 2000). In previous APWPs, each input paleopole was assumed to have averaged 'out' the paleosecular variation (PSV) of the geomagnetic field, but  Vaes et al. (2022)  showed that the dispersion of input paleopoles around the most recent global APWP becomes larger with a smaller number of sites, creating a bias towards poles based on smaller datasets with larger uncertainty.
Thus, the classical approach allows the calculation of non-unique APWPs with different uncertainties using the same underlying data depending on the subjective choice of how to distribute data over paleopoles  (Vaes et al. , 2022). To overcome these problems, APWPs may instead be computed from site-level paleomagnetic data, that is, from virtual geomagnetic poles (VGPs) (e. g. ,  McElhinny et al. , 1974; Hansma and Tohver, 2020; van Hinsbergen et al. , 2017; Vaes et al. , 2022; Gallo et al. , 2023) , or by weighting paleopoles against the number of sites  (McFadden and McElhinny, 1995). In these approaches, equal weight is assigned to each 'spot reading' of the past geomagnetic field (that is, a site) rather than to each paleopole based on some collection of site-level data (Fig. 1 ). However, building a database with site-level data for the many hundreds of studies that reported relevant input data is not straightforward as paleomagnetic data is not always reported at the site-level, particularly in older publications, and it would require an enormous effort to compile those that are only listed in the original publication and not in databases such as MagIC  (Jarboe et al.
, 2012). While an ultimate goal would be to use actual site-level data,  Vaes et al. (2022)  recently introduced an alternative approach: they showed that when site-level data are parametrically re-sampled from a collection of reported paleopoles and their statistical parameters, a distribution of simulated VGPs may be obtained that provides an accurate approximation of the original data. This approach thus provides a promising avenue to use published paleomagnetic poles to compute APWPs from site-level data, allowing the incorporation of key uncertainties in the construction of APWPs as well as the weighting of datasets against the number of sites. Although recent studies have incorporated key sources of uncertainty, such as spatial and age uncertainties, in the computation of an APWP (e.
g. ,  Swanson-Hysell et al. , 2019; Hansma and Tohver, 2020; Gallo et al. , 2021; Wu et al. , 2021; Gallo et al. , 2023), this  has not yet been applied to the computation of a global APWP. In this study, we compute the first global apparent polar wander from site-level paleomagnetic data, for the last 320 Ma, in which the key uncertainties in the underlying paleomagnetic datasets, in position and age, are incorporated and weighted. To transfer paleomagnetic data to a common reference plate, we use an updated global plate circuit that includes the most recent marine geophysics-based ocean basin reconstructions. We also provide an updated paleomagnetic database that updates the compilation of  Torsvik et al. (2012). We have filtered that Fig. 1. a) Example of an apparent polar wander path for the last 60 Ma (blue squares, with 95% confidence regions).
This way, both the number of sites behind each paleopole and its spatial and temporal uncertainties are taken into account in the computation of the reference poles of an APWP. In the VGP-based approach used in this study, the mean age of the (re-sampled) VGPs is used for the reference pole, rather than the center age of the time window. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. ) database using stringent, statistics-based, quantitative quality criteria and have extended the database with new, high-quality paleomagnetic datasets from stable plate interiors that have been published in the last decade. We also compiled data from regions that were previously not incorporated, such as the China Blocks, Iberia, and the Antarctic Peninsula, for the time period during which their motions relative to major tectonic plates are determined independently of paleomagnetism.
g. , the site-mean direction from a lava flow, or a thin dyke) (see e. g. ,  McElhinny and McFadden, 2000). Although it is often difficult to estimate the amount of geological time contained in a single sedimentary bed, individual samples obtained from sedimentary rocks may also provide independent readings of the past geomagnetic field  (Tauxe and Kent, 2004; Bilardello and Kodama, 2010b). Demonstrating this may be challenging for small sediment-based datasets, but  Vaes et al. (2021)  recently formulated a stringent set of criteria to determine whether large paleomagnetic datasets (n > 80 directions) derived from sediments represent collections of paleomagnetic spot readings. Site-level data referred to hereafter in this manuscript thus includes site-mean directions from lavas flows or thin dykes, as well as individual directions obtained from a single sedimentary horizon or bed.
Methods We developed an approach to compute a global APWP for the last 320 Ma from simulated site-level paleomagnetic data. To obtain a paleomagnetic dataset at the site-level, we use an iterative, parametric re-sampling approach (Fig. 2 ). Although it would be possible to calculate a global APWP directly from published site-level data, compiling these from the many hundreds of studies with relevant input data would require a major effort and is complicated by the fact that not all these studies have reported their data at the site-level. Recent analysis, however, showed that parametric re-sampling of VGPs from a set of reported paleopoles and their statistical parameters provides an accurate approximation of the original distribution of VGPs, albeit with a slightly larger dispersion  (Vaes et al.
, 2022). To generate a simulated site-level dataset, we first compiled a database of 'classical' paleomagnetic poles as reported in literature, with statistical properties that describe the number of underlying paleomagnetic sites and their dispersion, the sampling location, uncertainties associated with inclination shallowing correction, and age (see section 5). Using this database, we generate simulated site-level paleomagnetic data from each paleopole included in our compilation and repeat this procedure 2000 times (Fig. 2 ). This large number of iterations allows the propagation of both spatial and temporal uncertainties in the confidence bounds of the APWP. For each iteration, we parametrically re-sample a set of pseudo-VGPs from a  Fisher (1953)  distribution that is centered around the paleopole and defined by its precision parameter K.
We generate the same number of VGPs as the number of sites that was included in the calculation of the paleopole (or grand mean paleomagnetic direction) reported in the original publication. In our approach, equal weight is thus assigned to each (pseudo-) VGP rather than to each paleopole, and the weight of each paleomagnetic dataset directly depends on its number of sites. In our workflow, we also address the important source of uncertainty in the computation of APWPs that is known as 'inclination shallowing', which affects paleomagnetic datasets derived from sedimentary rocks. A 'blanket' correction factor (of f = 0. 6 in  Torsvik et al. , 2012)  has often been used in the computation of APWPs (e. g. ,  Torsvik et al. , 2012; Wu et al. , 2021; Kulakov et al. , 2021)  but this underestimates the natural variation in the magnitude of inclination shallowing and assumes that all sediments are affected by shallowing which is not always the case (e.
g. ,  Bilardello and Kodama, 2010a; Bilardello et al. , 2011; Kodama, 2012; Gallo et al. , 2017; Kent and Muttoni, 2020; Vaes et al. , 2021; Pierce et al. , 2022). In the computation of our global APWP, we only include datasets from sedimentary rocks to which an inclination shallowing correction has been applied and whereby the uncertainty in the correction is quantified. Except for two datasets that were corrected using an anisotropy-based correction technique  (Kodama, 2009; Brandt et al. , 2019) , all sedimentary datasets were corrected for inclination shallowing using the elongation-inclination (E/I) method of  Tauxe and Kent (2004). To incorporate the uncertainty in the shallowing correction in our workflow, we build upon the recent work of  Pierce et al. (2022). These authors developed a way to express the uncertainty of the E/I correction as an uncertainty in paleomagnetic pole position along the great-circle between the paleopole and the sampling locality, i.
e. , in the colatitude direction. Using the ensemble of flattening factor obtained from the bootstrapped ensemble of paleomagnetic directions, they computed the ensemble of possible paleomagnetic pole positions, each with a different paleomagnetic paleo-and co-latitude. Pierce et al. (2022)  noted that the distribution of estimated paleolatitudes approximates that of a normal distribution. Here, we assume that the distribution of paleolatitudes, and thus the co-latitudes, approximates a normal distribution, and use this to incorporate the extra uncertainty in the colatitude direction resulting from inclination shallowing. To this end, we compute the standard deviation of the colatitude distribution for every inclination shallowing corrected dataset in our compilation. We obtain this value either by applying the E/I correction to the individual paleomagnetic directions that were published in the original paper or provided to us by the authors.
If we were unable to obtain the directional dataset, we derived the standard deviation from the reported 95% confidence regions on the inclination or paleolatitude by taking these confidence regions as two standard deviations. For the two datasets corrected by an anisotropy-based approach, we use the reported confidence regions on the correction to obtain this value. For each iteration in our workflow, we first re-sample the paleomagnetic co-latitude from a normal distribution with a mean corresponding to the co-latitude of the shallowing-corrected pole and the listed standard deviation. We then compute a new position of the paleopolealong the great-circle between the sampling location and the reported shallowing-corrected paleopoleusing this re-sampled co-latitude and the paleomagnetic declination computed from the original shallowing-corrected pole.
This procedure yields a new position of each sediment-derived paleopole, thereby incorporating the additional uncertainty in the co-latitude direction resulting from inclination shallowing. Next, pseudo-VGPs are generated from this new paleopole position, following the workflow outlined above (Fig. 2a ). The second step in our workflow is to propagate the uncertainties in the age of the sampled rocks. To this end, we randomly draw an age for each pseudo-VGP from a uniform distribution that corresponds to the age uncertainty range listed for each paleopole in the database. Quantifying the age uncertainty by a uniform distribution is intuitive for sedimentderived datasets, whose age uncertainty range is often determined by bio-and/or magnetostratigraphy, and a uniform distribution may straightforwardly be defined by the upper and lower age limit of the geological time period or interpreted magnetozones.
The age of igneous rocks, on the other hand, is often based on radiometric dating, for which the uncertainty on individual age determinations is often reported as one or two standard deviation(s), and a Gaussian distribution could thus be used to quantify the uncertainty in age (see e. g. ,  Swanson-Hysell et al. , 2019; Wu et al. , 2021; Gallo et al. , 2021; Rose et al. , 2022; Gallo et al. , 2023). However, because the age of sampled igneous rocks is typically determined by multiple radiometric ages, either from multiple dated samples or determined for the regional magmatic activity (e. g. , for a large igneous province (LIP)), it is difficult to use a Gaussian distribution for the age uncertainty for all igneous datasets. We therefore choose a slightly more conservative approach and also use a uniform distribution between the upper and lower limit of the age range determined for the paleomagnetic datasets that were derived from igneous rocks.
The contribution of each paleomagnetic dataset to a given reference pole of the APWP is thus weighted against the overlap between the age range of the dataset and the time window of the reference pole. Because in each iteration, the pseudo-VGPs are redrawn and are assigned a new random age, the number of VGPs that falls within the chosen time window will differ between iterations. So, although the total number of pseudo-VGPs that are generated for the entire APWP is equal for each iteration, the exact number of pseudo-VGPs that is used to compute each reference pole will vary due to the re-sampling of ages. We compute each reference pole by taking the Fisher mean of the pseudo-VGPs that fall within the time window, yielding a reference pseudo-pole that provides an estimate of the time-averaged paleomagnetic pole positionand thus the rotation axisin a South African coordinate frame.
We empirically calculate the 95% confidence region of the reference poles of the global APWP as the circle that includes 95% of the 2000 reference pseudo-poles, which we refer to as the P 95. In this approach to calculating global apparent polar wander and its confidence, we thus incorporate a number of key uncertainties, including spatial and temporal uncertainties in the paleomagnetic datasets, the uncertainty associated with the E/I correction for inclination shallowing of sedimentary rocks, as well as uncertainties in the rotation of the VGPs to the reference coordinate system that results from uncertainties in age. All these uncertainties are reflected in the dispersion of the simulated VGPs, which is largely controlled by the betweenpole dispersion of the coeval paleopoles and their K values that are used to parametrically re-sample the VGPs.
Other incidental errors in the dataset, such as incorrect age assignments, unrecognized regional vertical-axis rotations, or unrecognized magnetic overprints, cannot be explicitly taken into account or corrected for, but such errors would likely lead to increased dispersion in the simulated VGPs per time window. We will compare the average scatter, elongation, and Fisher precision parameter of the simulated VGPs with values expected from PSV to assess whether and which reference poles may suffer from such errors.
Updated global reference database We present here an updated database of paleomagnetic datasets for the tectonic plates and continental blocks described in the previous section (see Fig. 4 , Table  2 ). Our compilation builds upon the efforts of the many paleomagnetists that collected, evaluated, and tabulated paleomagnetic results from hundreds of paleomagnetic studies of the last ~60 years, overviews of which have been published in a series of seminal papers (e. g. ,  Irving, 1964 Irving, , 1977;; Irving and Irving, 1982; Van der Voo, 1990b; Lock and McElhinny, 1991; Torsvik et al. , 2008 Torsvik et al. , , 2012) )  and compiled in the global paleomagnetic database. In this study, we used the data compilation presented in  Torsvik et al. (2012)  as a starting point. We have expanded this database by adding high-quality paleomagnetic results from undeformed or mildly folded regions that may be considered part of the stable plate interior, and that were published from 2012 to 2022, i.
e. , after the database of  Torsvik et al. (2012)  was compiled, as well as newly compiled datasets from the additional regions. We have also included datasets that were published prior to 2012 that were not incorporated by  Torsvik et al. (2012) , but that were included in recent compilations of 'cratonic' paleopoles (e. g. ,  Gallo et al. , 2021; Kulakov et al. , 2021; González et al. , 2022). For transparency, we have included all paleomagnetic data that were published from stable plate interiors and that fit the basic criteria for inclusion (primary magnetization, modern demagnetization techniques, principal component analysis). When these data were subsequently excluded based on the selection criteria outlined in section 5. 2, this is indicated in the database (Table  S2 ). For the last 10 Ma, we have limited our data compilation to the paleomagnetic datasets that were included in the PSV10 database  (Cromwell et al.
, 2018). This database consists of 83 paleomagnetic datasets that are obtained from volcanic rocks that formed in the last 10 Ma. Not all of these datasets were used for the calculation of the global APWP, however, as some do not satisfy the selection criteria described in the next section. We note that not all of these datasets are obtained from regions that would be considered as 'stable' plate interiors. Following  Cromwell et al. (2018) , we assume that regional deformation has not significantly influenced the paleomagnetic results from these young rocks (predominantly <3 Ma) and assign each dataset to the most appropriate tectonic plate that is included in the global plate circuit as described in section 4 (e. g. , a PSV10 dataset from Alaska is considered to be derived from North America).
The paleomagnetic data in the PSV10 database is compiled on the site-level and contains 2401 VGPs. Instead of using the published site-level data, we have calculated the paleomagnetic poles from each dataset and generate simulated VGPs from those poles, to ensure consistency in our parametric re-sampling approach. We note that the application of this approach to the PSV10 database yields a distribution of simulated VGPs that mimics that of the published VGPs, as recently shown by  Vaes et al. (2022). We have compiled metadata and statistical parameters for each paleomagnetic dataset (Table  2 ), based on the information provided in the original publications. For the application of our selection criteria, we have classified the lithology of the sampled rocks as either igneous or sedimentary.
g. ,  Butler, 1992 ) -we use the analytical formula of  Cox (1970)  to convert the k (and associated a95) to K (and A95), after estimating the paleolatitude using the reported mean paleomagnetic inclination (see  Deenen et al. (2011)  for more details). For each paleomagnetic dataset, we have listed an age range that describes the uncertainty of the age determination of the sampled rocks, whereby we mostly follow the age assignment of the original authors. This may correspond to the uncertainty of an individual radiometric age, to the mean computed from multiple radiometric age determinations, or to a certain age interval from which the rocks are derived. For biostratigraphically or magnetostratigraphically dated sediments, we have updated the numerical ages using the most recent geological timescale, of  Gradstein et al.
(2020) , which was also used for the plate model. When new age constraints were available, we have updated the ages of individual database entries, e. g. , for data from LIPs. We emphasize here that not all age determinations are without controversy and that there are likely revised age determinations that we were not aware of during the compilation of our database. Finally, we note that additional details on the age determination, statistical parameters and the dominant lithology of the sampled rocks are provided in the extended database in Table  S2.
Selection criteria We applied a number of selection criteria during the compilation of the paleomagnetic datasets that were used for construction of the global APWP. First, we re-compiled the data that were included in the compilation of  Torsvik et al. (2012)  from the original publications. We excluded data for which evidence was reported that it does not represent a reliable estimate of the time-averaged field at the time of formation of the sampled rocks, as concluded by the original authors or by others in more recent work that evaluated that particular dataset. We also rejected datasets for which no modern demagnetization techniques were used, as is common procedure (Van der Voo, 1990a;  Meert et al. , 2020). In addition, we removed duplicates: in some cases, the paleomagnetic data used to compute a paleopole that was included in the  Torsvik et al.
(2012)  database were also used (and combined with other or newer data) to compute more recently published paleopoles. Reasons for exclusion are provided in Table  S2  and include, for instance, evidence for remagnetization or unremoved magnetic overprints, local or regional vertical-axis rotations, erroneous structural corrections, or poor age control. We note that paleomagnetic datasets that were not originally compiled by  Torsvik et al. (2012)  and that did not satisfy the above criteria, were immediately rejected, and are not included in Table  2. We then applied the following criteria to all paleomagnetic datasets: 1) We exclude datasets derived from <5 sites that are interpreted as independent spot readings of the past geomagnetic field. This number is essentially arbitrary but establishing whether such small datasets accurately represent PSV is difficult, and in our site-level computation of the APWP, the impact of such small datasets is negligible.
We do not require that sites are based on averages of multiple samples, as this was shown to have minor effects on paleopole position or precision  this study  (Gerritsen et al. , 2022). 2) We exclude paleomagnetic datasets from igneous rocks if their A 95 values fall outside of the N-dependent reliability envelope of  Deenen et al. (2011). This criterion evaluates whether the dispersion of VGPs is consistent with what may be expected from secular variation. If the reported A 95 cone of confidence of the paleopole falls outside of the A 95, min-max reliability envelope, this suggests that the dataset is likely affected by one or more sources of additional scatter that are unrelated to PSV (if A 95 > A 95, max ), or that PSV was insufficiently sampled by the dataset (if A 95 < A 95, min ), for instance, due to the limited temporal coverage of the sampled sites (see  Deenen et al.