Analyzing Triassic and Permian Geomagnetic Paleosecular Variation and the Implications for Ancient Field Morphology

Studying paleosecular variation (PSV) can provide unique insights into the average morphology of the geomagnetic field and the operation of the geodynamo. Although recent studies have expanded our knowledge of paleomagnetic field behavior through the late Mesozoic, relatively little is known regarding the Triassic period (ca. 251.9–201.3 Ma). This study compiles the first Triassic virtual geomagnetic pole (VGP) database for the analysis of PSV, as part of a longer Post‐Permo‐Carboniferous Reversed Superchron (PCRS) time interval (265‐198 Ma). VGP angular dispersion and its dependence on apparent paleolatitude are compared against a new PCRS compilation and published PSV compilations for intervals across the last ∼320 Ma. We find that the Post‐PCRS displays near latitudinal invariance of VGP dispersion while the PCRS displays very strong latitudinal dependence. PSV behavior during the Post‐PCRS appears indistinguishable to that previously reported for the interval preceding the Cretaceous Normal Superchron (Pre‐CNS; 126–198 Ma). The near‐constant behavior between time intervals with significantly different apparent average polarity reversal frequencies does not support a suggested relationship between VGP dispersion and reversal frequency. The dispersion observed for the PCRS is consistent with the results of previous studies and represents behavior that is potentially unique over the last ∼320 Ma. A recently published approach to obtain a description of field morphology from equatorial VGP dispersion shows the PCRS geomagnetic field to have been more strongly axial dipole dominated than any interval since. This observation may be causally linked to the PCRS being the longest known superchron in the Phanerozoic geomagnetic polarity timescale.

requires complete and ideally well-dated magnetostratigraphic sections which are not available for most of Earth's history (Ogg, 2012). This is particularly the case for the Precambrian as biostratigraphy cannot be used and radiometric dating comes with large uncertainties (Bleeker, 2004). There is also the potential to obtain a greater understanding of geodynamo evolution. Periodic variations in the reversal record have been observed on similar time-scales to those of mantle processes; this constitutes support for the hypothesis that core-mantle boundary (CMB) heat flux variations influence geomagnetic field behavior (Biggin et al., 2012;Tarduno & Cottrell, 2005).
Earth's polarity reversal record is largely well-defined since the latest Carboniferous (∼320 Ma; Hounslow et al., 2018) and demonstrates extreme long-term variations. During superchrons, reversals are essentially absent and the Earth's magnetic field exhibits a stable polarity for tens of millions of years. Two such events have been identified in the last 350 Ma, the Permo-Carboniferous Reversed Superchron (PCRS; ∼318-265 Ma; Haldan et al., 2009;Opdyke & Channell, 1996), and the Cretaceous Normal Superchron (CNS;126-84 Ma;Ogg, 2012). In contrast, an apparent average reversal rate of ∼11 per Myr (Myr −1 ; Ogg, 2012) is assigned to a time interval referred to as the Jurassic hyperactivity period (∼171-155 Ma; Ogg, 2012). The Triassic (ca. 251.9-201.3 Ma;Ogg, 2012) has a relatively incomplete reversal record (Hounslow et al., 2018). Although it is sufficiently well understood to provide accurate estimates of reversal frequency across the entire period, its incomplete nature has resulted in various proposed magnetostratigraphic sequences (Hounslow & Muttoni, 2010;Hounslow et al., 2018;Maron et al., 2019). The lack of an agreed upon geomagnetic polarity timescale (GPTS) for the Triassic has hindered its use for timescale definition, spawning the suggestion to describe Triassic magnetostratigraphy as a set of multichrons (Lucas, 2010;Lucas & Tanner, 2014). Such a description would contain less information than would be available from traditional chron to chron correlation, highlighting that although the number of reversals occurring during the Triassic is reasonably well constrained, the exact ages of the reversals are not.
The Earth's magnetic field is often described as a geocentric axial dipole (GAD). This description is believed to be accurate when a sufficient amount of time can be averaged (Schneider & Kent, 1990) but non-dipole contributions are ever present in the instantaneous field configuration. Studying the dispersion of virtual geomagnetic poles (VGPs) can provide an estimate of the extent of this contribution (Biggin et al., 2020;Veikkolainen & Pesonen, 2014). Analyzing PSV in this way provides a measure of field stability and many recent studies have investigated a possible association between PSV and reversal frequency (Biggin et al., 2008;de Oliveira et al., 2018;Doubrovine et al., 2019;Franco et al., 2019;Veikkolainen & Pesonen, 2014).
Investigations into the relationship between PSV and reversal frequency have tended to focus on the CNS, PCRS, and Jurassic due to their nature as extreme high and low reversal frequency regimes (Biggin et al., 2008;de Oliveira et al., 2018;Doubrovine et al., 2019). Similarly, Franco et al. (2019) investigated PSV in the Illawarra Hyperzone of Mixed Polarity (IHMP; ∼266.7-228.7 Ma), beginning after the PCRS, stating an average reversal rate of ∼5.9 Myr −1 . Many of these studies have focused on sequential time periods resulting in a near continuous record of VGP dispersion from the CNS going back to the PCRS, with the exception of almost the entirety of the Triassic. Despite this, it is still unclear whether a relationship does exist between PSV and reversal frequency. McFadden et al. (1991) concluded that low reversal regimes would exhibit lower VGP dispersion at low latitudes, and a high latitudinal dependence. Both Biggin et al. (2008) and Doubrovine et al. (2019) described the occurrence of this behavior during the CNS, while de Oliveira et al. (2018) obtained a similar, more extreme result for the PCRS. Other results suggest near latitudinal invariance during the Jurassic  and IHMP (Franco et al., 2019) and therefore, it might be claimed that studies of extreme reversal regimes support the original claim of McFadden et al. (1991). Discrepancies appear when comparing these results with those from more recent time intervals, however Doubrovine et al. (2019) found that the relationship between PSV and latitude for the last 5 or 10 Ma was similar to that observed for the superchrons, despite average reversal frequencies of ∼4.4-4.8 Myr −1 . In contrast, Franco et al. (2019) concluded that the last 5 Ma exhibited comparable behavior, and a similar reversal rate, to that which they described for the IHMP.
In addition to our lack of knowledge regarding PSV behavior during the Triassic, and historically uncertain magnetostratigraphy, there is a significant shortage of paleointensity data for this period. The Triassic is a period bounded by mass extinction events that coincided with eruptions of huge volumes of flood basalts . It also comprises an interval of time in which all continents were arranged as  (Lucas, 2005). This tectonic setting resulted in little large-scale volcanism after the Siberian Traps (ca. 252-251 Ma; Burgess et al., 2017;Wignall, 2015) until the eruption of the Central Atlantic Magmatic Province (CAMP; ca. 201.5 Ma; Ogg et al., 2016), associated with the break-up of Pangaea (Benton, 2016). This provides an explanation as to why a relatively minor proportion of known Triassic rocks are volcanic (Lucas, 2005). As a result, there is a ∼50 Ma gap in the paleointensity record (Anwar et al., 2016) due to the nature of absolute paleointensity experiments which are heavily reliant on volcanic recorders and their associated intrusions (Donadini et al., 2007;Lerner et al., 2017). An incomplete reversal record, very few paleointensity estimates, and a lack of PSV analysis have all resulted in a limited understanding of geomagnetic field behavior during the Triassic when compared to other periods since the latest Carboniferous. As we will demonstrate here, however, there are a sufficient number of Triassic-aged rapidly cooled igneous units distributed globally to provide a first order description of the geomagnetic field through this period.
The last decade has provided many investigations into Triassic magnetostratigraphy with sufficient progress to justify a revised Triassic GPTS (Haque et al., 2021;Kent et al., 2017Kent et al., , 2018Kent et al., , 2019M. Li et al., 2016;Maron et al., 2019;Zhang et al., 2020). These advancements present the opportunity to analyze Triassic PSV behavior within the context of the average reversal frequency for the period. Such an investigation would result in a continuous record describing PSV behavior from the PCRS through to the CNS, whilst also facilitating an investigation into PSV behavior between two prominent features of the reversal record: the PCRS and the high reversal rate values associated with the Jurassic. At the same time this offers the potential to categorize geomagnetic field behavior during a time period still characterized by much uncertainty. In this study, an updated Triassic paleomagnetic directional and VGP database is presented, using results taken from existing publications, and combined with data previously compiled for the late Permian. An analysis of VGP dispersion at different paleolatitudes for this newly studied time interval,  referred to as the "Post-PCRS," is compared to data from a revised PCRS database using the same analytical process. Furthermore, comparisons are then carried out against previously published databases for the , CNS , and the last 10 Ma (Cromwell et al., 2018) before a discussion on the pattern of VGP dispersion with latitude during times of differing reversal frequencies and how this may relate to field morphology.

Sourcing Data
Information from PSV analysis comes in two distinct forms: time series of magnetic field variations, such as information from long sediment cores, and statistical descriptions which rely on geologically instantaneous spot readings, such as those associated with lava flows (Johnson & McFadden, 2015). Data derived from sedimentary rocks are susceptible to smoothing of the recorded field during remanence acquisition, resulting in at least partial averaging of PSV (Lund & Keigwin, 1994) and inclination shallowing, affecting the final estimate of paleolatitude (Tauxe & Kent, 2004). The general consensus is that igneous rocks, and in particular volcanic rocks, are a more reliable source of PSV information in older geologic periods (Biggin et al., 2008;Cromwell et al., 2018;, provided that they cooled quickly and that the group of rocks spans sufficient time to provide representative variability. As such this study exclusively uses data from igneous rocks, avoiding large, slow cooling intrusions that would not provide a spot-reading of the field. All datasets have been taken from lava flows, sills, dykes, or pyroclastic flow deposits with supporting evidence for fast cooling rates where appropriate and for the occurrence of welding when pyroclastic flow deposits have been used. Triassic datasets were compiled from papers published up to and including those from March 2020. Most data arose from a literary search but a small number of datasets were sourced using the Global Paleomagnetic Database (iggl.no/resources.html, Ivar Giaever Geomagnetic Laboratory). Datasets from the late Permian, after the PCRS, were sourced from the database compiled by Franco et al. (2019). The revised PCRS database was built around the work of de Oliveira et al. (2018) with the addition of a few new datasets. Following the approach of Biggin et al. (2008) site-mean directions of a similar age and geographic location were grouped into the same data set.
After these initial constraints, both the PCRS and Post-PCRS databases were filtered using selection criteria in order to remove low quality data and potentially unsuitable studies. This study applied the selection criteria below. These are the same as used by Doubrovine et al. (2019) but with a few additional requirements.
1. The age of the rock formation must be reasonably well constrained, preferably by the application of radiometric dating techniques. There must be no doubts that the data set might not represent the geomagnetic field during the time interval to which it has been assigned that is the PCRS or Post-PCRS. 2. There must be no evidence that the characteristic remanent magnetisation (ChRM) directions are of secondary origin. 3. Data from igneous formations that were tectonically tilted or folded post-emplacement must have an associated structural correction. Where there was evidence of local block rotation between sampling sites, data were not used. A commentary outlining the reasoning behind the inclusion of each data set, with respect to its tectonic setting, can be found in Table S2. 4. Each data set is composed of at least nine paleomagnetic sites (N ≥ 9), and each site-mean direction is calculated from the ChRM of a minimum of 3 independently oriented samples (n ≥ 3). 5. ChRM components must have been isolated using stepwise demagnetization techniques. Principal component analysis should have been utilized for at least one specimen per site and agree with any ChRM components inferred by other methods. This corresponds to a "demagnetization code" greater than or equal to 3 (McElhinny & McFadden, 2000). 6. The uncertainties of the site-mean directions must be presented in the original study as either the Fisher concentration parameter (k) or the angle of 95% confidence about the mean direction (α 95 ). 7. The total Q score based on the first 6 Van der Voo criteria must be equal to or greater than 3. 8. All site-mean ChRM directions within a data set have a k-value greater than or equal to 10.
In Supporting Information S1, the effects of accounting for serial correlation and the removal of data derived from great circle analysis were considered, separately, for datasets which satisfied selection criteria 1-8. Serial correlation identifies cooling units that are likely representative of the same event in time, and as such may not be considered as individual paleomagnetic data points (Cromwell et al., 2018;Watson & Beran, 1967). Meanwhile, obtaining directions from great circle analysis often results in the inability to obtain rigorous confidence limits for K . The inclusion of great circle derived data has the potential to allow datasets to fulfill selection criteria 1-8 which may not have a well-defined Fisher concentration parameter and thus could be of lower quality than desired. In both cases the overall effects on the calculated VGP dispersions were minor (Figures S1 and S2 in Supporting Information S1). As a result, neither the inclusion of serial correlation or the exclusion of great circle derived data was utilized in the final data selection process due to the benefits associated with a greater N, and total number of datasets (Biggin et al., 2008).

Investigating Robustness With Additional Criteria
McElhinny and McFadden (1997) explored the possibility that PSV studies may be strongly biased by the quality of the data used, concluding that the resulting dispersion was at least partly due to the incorporation of lower-quality data. Additionally, the use of sampling site paleolatitude during the conversion process of magnetic directions into VGPs causes any latitudinal independent within-site dispersion of directions to result in latitudinal dependent VGPs (Biggin et al., 2008). This is mitigated by an inbuilt correction to the conversion process but, in order for it to be effective, n must be sufficiently large so that k is a good estimate of its true value (Biggin et al., 2008). In order to assess the robustness of the resulting VGP distribution, and the influence of data quality, further selection criteria have been applied to produce a second, higher quality database. These selection criteria have been chosen as they mitigate bias associated with low n and/or k values (Biggin et al., 2008). 9. ChRM site-mean directions used must have an associated estimated Fisher concentration parameter of at least 50 (k ≥ 50). 10. Each site-mean direction is calculated from the ChRM of a minimum of five independent samples (n ≥ 5).
The resulting datasets from the application of selection criteria 1-8 are termed Group 1 and where selection criteria 1-10 have been applied the datasets are termed Group 2. Group 2 datasets have been analyzed in an identical process to those from Group 1 to ensure that a direct comparison of results is possible.

Measuring PSV
PSV is a measure of the variability of all of the geomagnetic field's observables; the most common way in which it is measured and assessed is by analyzing VGP dispersion (Hulot & Gallet, 1996). This VGP dispersion, otherwise known as angular dispersion, is calculated using the following equation (Cox, 1970) where S is the angular dispersion, N is the total number of VGPs in a given data set, and Δ i is the angular deviation of the ith pole from the mean paleomagnetic pole, in this case the mean VGP of the data set.
The calculated VGP dispersion is the result of dispersion from two sources: a minor contribution from within-site dispersion, S W , and a major contribution from between-site dispersion, S B . S W is the result of measurement errors and variations in the initial recording of the field. S B is the dispersion between VGPs calculated from measurements at different sites due to the recording of a different field. S B, therefore, is a measure of PSV and can be extracted by removing the contribution of S W using the following equation In order to calculate S W , an estimate of the precision parameter in pole space, K, is required. This is achieved by translating k, from directional space, under the reasonable assumption that the VGP distribution is Fisherian in nature.
Finally, S W is approximated by the following equation and the contribution of within-site dispersion can be removed using Equation 2 isolating the VGP dispersion due to PSV. This process is carried out individually for each data set in order to obtain an estimate of the dispersion associated with the PSV. This study used a non-parametric bootstrap in order to obtain 95% uncertainty estimates for S B .
When conducting a study into VGP dispersion, it is desirable to remove VGPs that are likely to have resulted from excursional or transitional behavior. The identification and removal of outlying VGPs is done in accordance with a cut-off angle. VGPs calculated using data from a time where the field was undergoing normal secular variation tend to cluster around a mean VGP, fit by a Fisherian distribution. Any VGPs lying farther from this mean VGP than the cut-off angle are deemed to be outliers and excluded. This separation between normal secular variation and that attributed to reversals is not grounded in a fundamental understanding of the physical system; reversals and excursions are probably natural outgrowths of normal secular variation. As measurements of S B are strongly influenced by these outlying VGPs, however, and because the time that the field spends in such states is relatively short, they are removed. Moreover, it has been shown to be an effective approach to assessing characteristics of PSV produced by numerical dynamo simulations (Biggin et al., 2020). This study applies a variable cut-off (Vandamme, 1994), calculating the optimum Δ max for the VGPs of a given data set using the following equation Following the approach of Biggin et al. (2008) this study opts to use average magnetic latitude calculated from the angular distance between the mean VGP and the sampling site, rather than geographic paleolatitude. The latter would require the use of plate reconstructions which would require some circular reasoning as they are often largely based on paleomagnetic studies (Biggin et al., 2008).

Modeling VGP Dispersion
For ease of comparison with the results of previous studies (de Oliveira et al., 2018;Doubrovine et al., 2019), Model G (McFadden et al., 1988) has been used to parameterize the latitudinal dependence of PSV. It is widely accepted as a useful but imperfect descriptive tool  and also has predictive power in determining the average axial dipole dominance of the ancient field (Biggin et al., 2020). Model G is described by the following equation where a and b are known as the Model G shape parameters. These shape parameters have been determined by carrying out a least-squares fit between the estimated dispersion values and the model, and uncertainties in these coefficients were estimated using a jack-knife technique as carried out by .

Datasets
The datasets that satisfied the Group 1 selection criteria for the Post-PCRS and PCRS time intervals are listed in Table 1. The corresponding site-level information is available in Data Sets S1 and S2. Table 1 provides background information regarding the lithology and rock units sampled, the source study, and country of origin. Most of the estimated ages presented for the Post-PCRS are the result of radiometric investigations; this is often not the case for the final PCRS datasets. Where there is no assigned numerical age, the age estimate was considered sufficient for the purpose of this study so long as the formation could be confidently attributed to the time interval in question. Within each data set, the site co-ordinates associated with the site-mean directional information have been used; however, when this was not possible, the mean site location was attributed. In either case average site co-ordinates are contained within Table 1 and displayed in Figure 1 along with the corresponding site identification code.
Also presented in Table 1 are the Van der Voo (1990) quality ratings assigned to each data set, breakdowns of which can be found in Data Set S3, the number of site-mean directions/VGPs, and the total number of samples per data set.
Data that passed the two additional selection criteria (9 & 10) are presented in Table 2 for both the Post-PCRS and PCRS. This table provides the same information regarding the datasets as in Table 1 and is presented in the same format. For both time intervals there is a reduction in the number of datasets compared with the Group 1 results, as removal of site-mean data resulted in some datasets failing criteria 4 (N ≥ 9). The reduction of site-mean data is displayed visually in Figure 2 with sites grouped according to their associated geological epoch. Overall the amount of site-level data decreases by about one-third after Group 2 selection criteria are applied ( Figure 2). Both the Post-PCRS and PCRS databases display too great a hemispherical bias to make a formal assessment of equatorial symmetry. Since the available data did not support any significant asymmetry however, we decided to display VGP dispersions on one-hemisphere projections (Figures 3 and 4). Note.
Site ID refers to an identification system used within this study, sites with codes beginning PT (Permo-Triassic) belong to the Post-PCRS database, sites with codes beginning K (Kiaman) belong to the PCRS database. Lat and Long are the mean site co-ordinates for the data set, and Age is the nominal assigned age for the data set. N is the number of site-mean directions within a data set, and n tot is the total number of directions. S B is an estimate of virtual geomagnetic pole dispersion calculated using the process set out in the method, likewise Plat is the estimated magnetic paleolatitude. "References" refer to the original studies from which the data was sourced. All of the provided information relates to site-mean directions from the referenced studies that pass Group 1 selection criteria.

Post-PCRS
There is a relatively even spread of formation dates from ∼200 Ma back to ∼264 Ma within the Post-PCRS compilation. This is despite a moderately large number of datasets associated with the Siberian Traps and with CAMP (Table 1). Reviewing the data at the site-mean level, it is noticeable that over half of the sites representing the Post-PCRS are early Triassic in age ( Figure 2). This is testament to the volume of work conducted on the Siberian Traps and the importance of this event in geological history. The mean time interval between the ages of subsequent datasets is just over 5 Ma, and the greatest time gap exists during the late Triassic where magnetic field behavior is unaccounted for about 22 Ma (Table 1). This is also the case for the late Permian for which there is no contributing data ( Figure 2).
Latitudinal coverage is good with the number of low (<30°), mid-(30°-60°), and high latitudinal sites (>60°) almost evenly split, although each of these latitude bands is dominated by data from one hemisphere. Unsurprisingly, all of the high latitude datasets are related to the Siberian Traps. For low-latitude sites, the temporal range is greater, being derived from unrelated volcanic events. The mid-latitude data are primarily from South America and associated with the regional Permo-Triassic volcanism. There is also agreement in estimated dispersion values from Eurasia, however, one being late Triassic in age.
The PSV behavior appears consistent at low-mid latitudes. Figure 3a shows closely grouped VGP dispersion values for latitudes <50° lying within error of one another. Datasets from high paleolatitudes display a far less consistent dispersion pattern despite all originating from the same volcanic event. Overall, only a weak latitudinal dependence of VGP dispersion is observed; estimated dispersion values commonly lie between 10° and 15° regardless of paleolatitude.
The more robust Group 2 selection criteria remove 6 Group 1 datasets including those two with the greatest associated uncertainty of VGP dispersion (PT05 and PT11, Tables 1 and 2). From the 15 remaining datasets, just four are unaffected by the additional Group 2 selection criteria. The difference in the site-mean directional data comprising each data set does not only change the estimated values of VGP dispersion but also the estimates of paleolatitude (Tables 1 and 2).
While Group 2 data do agree better at high-latitudes, the overall observed PSV behavior of the Post-PCRS remains largely unchanged regardless of whether Group 1 or Group 2 data are used (Figure 3). The Model G a parameter decreases slightly from 14.2° (11.3°-18.1°; Group 1) to 13.3° (9.8°-18.7°; Group 2). Modeling VGP dispersion using Group 2 datasets produces an even weaker latitudinal dependence than Group 1 data-

PCRS
According to the numerical age estimates that are available, the database spans nearly all of the PCRS, starting from 265 Ma going back to at least 306 Ma. Within that time interval, coverage is consistently good through the middle and final stages of the PCRS but lacking slightly for the first few million years following its onset at ∼318 Ma. The "late Carboniferous" (323.2-298.9 Ma; Davydov et al., 2012) and "early Permian" (298.9-272.3 Ma; Henderson et al., 2012) aged datasets (Table 1) are likely to have formed in and around this time interval, however, and likely ensure that the temporal representation is reasonable.
The range of latitudinal coverage is very good at low and mid-latitudes. Unlike the Post-PCRS, there is representation from very low-latitude sites (<10°). The PCRS database is lacking information at higher latitudes, however, with just two datasets above 60°. Both of these originate from Australia (Table 2) but are otherwise unrelated and separated by at least 40 Ma. Again, there is a hemispheric bias amongst the datasets with only five from 16 originating from the southern hemisphere. Figure 4a displays a very strong relationship between VGP dispersion and latitude showing a very clear upwards trend. PSV behavior is very consistent, particularly at low-mid latitudes, but even the high latitude estimates of VGP dispersion are within error of one another. The behavior at mid-latitudes is also particularly consistent considering the seven datasets represent formations from five different countries: three from the northern hemisphere and two from the southern hemisphere.
All of the PCRS datasets are affected by the use of the Group 2 selection criteria and the subsequent removal of site-mean data; furthermore, four of the datasets are removed entirely (K02, K08, K13, K16, Tables 1 and 2). The difference between the observed dispersion patterns, when the two different sets of selection criteria were used, appears to be greater for the PCRS than for the Post-PCRS for which some datasets were unaffected. In the PCRS, estimated dispersion values are, themselves, more dispersed when Group 2 datasets are used (Figures 4a and 4b). Despite neither of the high-latitude datasets being completely removed (K09 & K10, Tables 1 and 2), the removal of site-mean data within them has altered their estimated scatter values so they are less consistent with one another (Figure 4b). Only datasets from low-latitudes display consistent estimates, although these have shifted, leading to an increased estimate of the Model G a parameter from 5.5° (0.8°-8.6°; Group 1) to 7.2° (2.0°-10.6°; Group 2). A clear trend still exists for the PCRS showing an increase in VGP dispersion with latitude, though this is slightly less well-established than in the Group 1 data as demonstrated by the increased uncertainty in estimated Model G parameters.

Assessing the Robustness of VGP Dispersion
PSV analysis of the Post-PCRS paleomagnetic directional and VGP database, containing the first compilation of Triassic data, documents a S B -λ relationship similar to those from times of claimed high reversal frequency (Biggin et al., 2008;Doubrovine et al., 2019;Franco et al., 2019). By contrast, the PCRS demonstrates a much stronger latitudinal dependence of PSV demonstrated by the estimates of Model G b parameter which are approximately twice those estimated for the Post-PCRS (Figures 3 and 4). The Model G a parameter is also substantially lower. Both of these relationships can be thought of as robust features of their respective time intervals due to the general agreement when utilizing databases of differing quality.
In the Post-PCRS, the use of higher quality Group 2 datasets reduces the estimates of both a and b relative to the Group 1 datasets.
The strong dependence of VGP dispersion with paleolatitude observed for the Group 1 PCRS datasets is in general agreement with the results of a recent study of this superchron (de Oliveira et al., 2018). The use of Group 2 datasets somewhat reduces this agreement, though not significantly. The greatest difference observed when analyzing Group 2 datasets is a rise in the Model G a parameter, suggesting higher dispersion at the lowest latitudes. This could be a more accurate representation of the field than that presented by Group 1 datasets but here the issue of analyzing a smaller amount of data is highlighted. The database has been reduced to 12 datasets and the removal of 1 data set at very low latitude produces an estimate of the Model G a parameter which is much less well constrained by the paleomagnetic data.
Although slight differences exist between the VGP dispersions observed using either Group 1 or Group 2 datasets, which can both strengthen and weaken proposed relationships, they are not significant and there is a general agreement for both the Post-PCRS and the PCRS. The higher quality datasets were compiled in order to significantly reduce the effects of bias, and their agreement with the lower quality, more numerous databases suggest that both observed VGP dispersions are unlikely to be an artifact of small N or n (Biggin et al., 2008). This establishes the respective features of both the Post-PCRS and PCRS as robust and justifies the use of Group 1 datasets for further analysis.

Comparison With Other Time Intervals
The associated Model G shape parameters (a, b, and the b/a ratio) for the Post-PCRS and PCRS intervals have been compared with those from previously compiled databases representing different time intervals.
Here, we applied the Group 1 selection criteria, and the same initial constraints and method for the modeling of VGP dispersion, to the datasets from later time periods. This produced recalculated parameters which allow for a direct comparison of results. The recalculated shape parameters are given in Table 3 alongside the associated study, the time interval that they represent, and the estimated uncertainties on each parameter. The time interval studied for the Post-PCRS has some crossover with the IHMP studied by Franco et al. (2019) and, as such, some of the datasets are shared. Franco et al. (2019) reported a low paleolatitudinal dependence of VGP dispersion when analyzing datasets from 265 Ma to 240 Ma, very similar to the results presented in this study for the Post-PCRS. This is further demonstrated by the similar estimates calculated for the Model G shape parameters (Table 3), suggesting consistent PSV behavior throughout the Post-PCRS.
The study of de Oliveira et al. (2018) includes sedimentary-derived data and uses less-stringent selection criteria when analyzing the PCRS. This is advantageous as more datasets are presented with increased representation at higher latitudes. The observed VGP dispersions may be compared in a similar manner to Group 1 and Group 2 datasets. There is a strong relationship between VGP dispersion and latitude with similarly low values at low latitudes presented by de Oliveira et al. (2018). This further suggests that the observed PSV behavior is a robust feature of the geomagnetic field during the PCRS.
Previous studies have used the b/a ratio as a way of quantifying the type of PSV behavior across a given time interval and have explored the possibility of a correlation with mean reversal frequency (de Oliveira et al., 2018;Doubrovine et al., 2019;Franco et al., 2019;McFadden et al., 1991). Figure 5a plots the b/a ratio values for the recalculated CNS and Pre-CNS intervals , the PCRS and Post-PCRS intervals (this study), and a combined database for the Post-PCRS and Pre-CNS. Model G shape parameters have also been recalculated and plotted for the PSV10 database of Cromwell et al. (2018). All databases are of equal quality and represent the highest quality studies from 318 Ma to the present. Plotted alongside this is the same reversal frequency model previously presented in Figure 2.
Immediately obvious is the consistent b/a value throughout the Post-PCRS and the Pre-CNS and the higher values associated with the superchrons on either side (Figure 5a). During the newly combined interval, reversal frequency shows a wide range of values (Figure 5a) which would appear to contradict the idea that an inverse relationship exists between the b/a ratio and reversal frequency (Franco et al., 2019).  Note. AD/NAD median is the estimation of the ratio of non-axial dipole field to axial dipole field (Biggin et al., 2020) with the associated uncertainty limits where reasonable. Italicized parameters are associated with time intervals that were the subject of previous studies and contain data which has been incorporated into either the Post-PCRS or PCRS database of this study.

Table 3 Comparison of Model G Shape Parameters and Axial Dipole Dominance Recalculated Using Our Selection Criteria Applied to the Datasets Originally Selected in the Studies Given
Rather, it supports the hypothesis that any potential relationship must be less straightforward . The stronger latitudinal dependence of dispersion (i.e., the Model G b parameter) during both the PCRS (Figure 5a) and CNS  are responsible for the higher b/a ratio compared to the times of geomagnetic reversals. This could suggest that the different behaviors are indicative of a low/absent reversal regime and one in which reversals are present. However, the indistinguishable b/a ratio for the last 10 Ma, when compared to that of the CNS, is not consistent with this hypothesis .
If the b/a ratio does not have a straightforward relationship with the average reversal frequency, then the consistently low value between the two superchrons must have an alternative explanation. Interestingly, there is an ongoing discussion around a proposed feature of the paleointensity record across a similar time interval, the Mesozoic Dipole Low (MDL). This feature was first proposed by Prévot et al. (1990) and was defined as a period in which the virtual dipole moment (VDM) was one third of its present-day value between ∼180-135 Ma (McElhinny & Larson, 2003;Prévot et al., 1990). This hypothesis was broadly supported by the work of Tanaka et al. (1995), in their construction and analysis of a global palaeointensity database, and low paleointensity estimates obtained from the Siberian Traps Shcherbakova et al., 2015).
Subsequent studies have suggested an MDL ∼180-120 Ma (Perrin & Shcherbakov, 1997), and recent low VDM estimates obtained from Permo-Triassic boundary rocks (∼250 Ma) have led to proposals of an MDL extending back to this time (Anwar et al., 2016). The time interval corresponding to this longer MDL is largely encompassed by the time interval of low b/a ratios compiled for this study. Exploring this relationship further is very challenging due to the current global paleointensity record. As it stands there are almost no VDM estimates for the entirety of the Triassic (Anwar et al., 2016). Furthermore, there is the possibility that the MDL is not a time interval of low intensity but rather represents the long-term average (Selkin & Tauxe, 2000). Another possibility is that the real MDL is a time of low field strength associated solely with the Jurassic hyperactivity period (Kulakov et al., 2019).
Obtaining new estimates of absolute paleointensity values during the Triassic will be crucial in making possible the assessment of any relationships between geomagnetic observables and the paleointensity record. The compilation of data from Triassic aged volcanic rocks and small-scale intrusions in Table 1 (Shaar & Tauxe, 2015;Thellier & Thellier, 1959) some formations that are suitable for paleomagnetic studies are not suitable for paleointensity studies, however. Nevertheless, we highlight the potential for future work to characterize the Triassic dipole moment using paleointensity studies performed on such targets as identified in Table 1.

Implications for Field Morphology
A recent study by Biggin et al. (2020) investigated, across a wide range of models, the possibility of using Model G shape parameters to provide information about field morphology and, specifically, the dominance of the axial dipole contribution. Their finding was a strong, positive relationship between axial dipole dominance and the Model G a parameter. In order to assess what this would mean for the time intervals considered in this study, the different estimated a values must be analyzed in a similar manner to that done for the b/a ratios (Figure 5b). The relationship between estimated a values and apparent average reversal frequency does not appear to be strongly inverse to that observed when analyzing the b/a ratio ( Figure 5), as would be expected if the parameters co-varied inversely. The superchrons do display the lowest a values alongside higher estimated b values. Nevertheless, the estimated a value for the last 10 Ma is more comparable to that observed during the Pre-CNS, despite the associated estimated b value more closely resembling those of the two superchrons (Table 3). This would appear to support the conclusion of Biggin et al. (2020) that only a weak relationship exists between Model G shape parameters. The consequence of a relationship of this nature is that the original interpretation of the Model G shape parameters, as representing independent families of equatorially symmetric and equatorially anti-symmetric terms (McFadden et al., , 1991, is not well-supported (Biggin et al., 2020). A similar conclusion regarding the physical meaning of Model G shape parameters was reached by Doubrovine et al. (2019) who suggested that in strong-field, Earth-like dynamos the separation between the symmetric and anti-symmetric dynamo families becomes improbable despite being theoretically plausible.
Estimates of the Model G a parameter were used to establish the relative contribution of the axial dipole using the power law established by Biggin et al. (2020). The output is the median ratio of axial dipole to non-axial dipole contribution across the time interval (AD/NAD median ), with the median being used to avoid biasing due to brief, extreme events. The estimated ratios are displayed in Table 3. For the PCRS and Post PCRS, it is the first time that the field behavior has been analyzed in this way. The relative contribution of the axial dipole component of the field is somewhat similar for the Post-PCRS and Pre-CNS (Table 3) although a small increase is observed. Axial dipole dominance has since decreased, with the field over the last 10 Ma demonstrating a relative dipole contribution level similar to that during the Pre-CNS (Table 3). The most remarkable finding is the very strong axial dipole dominance of the PCRS field (Table 3), which is far greater than for any of the other ancient time intervals studied here or by Biggin et al. (2020). The closest values to this have come from much more recent, shorter time intervals on the order of 10 kyr (Biggin et al., 2020). The enhanced axial dipole dominance of the PCRS suggests that the Earth's magnetic field, during time instances within this interval, more closely resembled that of a GAD field than during any other time interval comparably studied. Put another way, dipole tilt (produced by the equatorial dipole terms) and all components of the nondipole field appear to have been heavily diminished relative to the axial dipole term during much of the PCRS. This offers a possible explanation for the enhanced duration of the PCRS, when compared to that of the CNS. Since collapse of the axial dipole is required to trigger a reversal (e.g., Olson et al., 2009), it being stronger and more dominant through most of the time interval would reduce the number of opportunities for a transitional field to dominate. The estimate of AD/NAD median for the PCRS is a factor of 5 larger than the estimates for the other intervals since 265 Ma, with the upper range essentially describing a pure GAD field (Table 3). Associated uncertainty estimates for AD/NAD median are inflated through incorporation of uncertainties associated with both the Model G a parameter and the power law fit of Biggin et al. (2020) that relates this to AD/NAD median . Nevertheless, these uncertainty bounds still only narrowly incorporate the AD/NAD median for the CNS and exclude the estimates for all intervals during which magnetic polarity reversals takes place. Therefore, although the formal establishment of the axial dipole dominance of the PCRS as statistically distinct from that of all other intervals must await the addition of further PSV data, we nevertheless consider it likely that, during the PCRS, the field was on average more axially dipolar field than at any subsequent time.
The possible relationships between axial dipole dominance and VDM can be illustrated as two end-member scenarios with a spectrum between. In the first, the non-axial dipole field remains approximately constant through time with changes in the VDM being entirely accounted for by shifts in the median axial dipole component. In the second, all components of the field vary in unison. Our new findings regarding the PCRS appear to rule out the second scenario (since the axial dipole does appear to have been enhanced at the expense of the rest of the field during this time). The observation that average VDM also appears to have been elevated during the PCRS (Hawkins et al., 2021) rather supports the first scenario, or somewhere on the spectrum near to it. Likewise, if the duration of the MDL was shown to coincide with the time interval represented by the combined Pre-CNS and Post-PCRS then this could suggest that an increased contribution from the non-axial dipole field was a factor in the lower average VDM.

Conclusions
PSV behavior during the Post-PCRS is very similar to that observed for the Pre-CNS despite these two intervals being characterized by different mean reversal rates. In terms of their PSV behavior, we suggest that they can adequately be represented as a single interval. The variable reversal frequency and consistent b/a ratio is not consistent with the hypothesis that an inverse relationship exists between the two (Franco et al., 2019). This observation is further demonstrated by the indistinguishable estimates of b/a ratio for the CNS and the last 10 Ma . Detailed analysis of PSV behavior during the Jurassic hyperactivity period could help reveal whether PSV behavior was, indeed, consistent throughout the Post-PCRS and Pre-CNS, and contribute to the ongoing discussion surrounding the nature of the relationship between VGP dispersion and reversal frequency. In order to conduct such a study, more high quality VGP datasets representing Jurassic hyperactivity behavior are required than are currently available.
It would appear that the original interpretation of Model G shape parameters in terms of competing and co-varying contributions from quadrupole and dipole family harmonic terms (McFadden et al., , 1991 is not appropriate. Over at least the last 318 Ma, superchrons seem to be characterized by a lower a parameter, which can likely be attributed to a more axial dipole dominated field (Biggin et al., 2020). This enhanced dipole dominance suppresses dipole tilt and the nondipole field, in turn suppressing VGP dispersion and the frequency of reversals. It appears that this behavior was much more enhanced during the PCRS, in contrast to previous comparisons that have argued for similar PSV behavior in the CNS and PCRS (de Oliveira et al., 2018;Haldan et al., 2014). The enhanced dipole dominance could go towards explaining the apparent longer duration of the superchron. It is also possible that the MDL is characterized by near latitudinal invariance of VGP dispersion and partially reduced axial dipole dominance as attested to by the marginally higher Model G a parameter. Testing this hypothesis will require a much greater insight into global dipole moment variability, in particular for the Triassic, in order to better constraint the extent of the MDL. Considering the viability of the formations in Table 1 as potential targets for future paleointensity studies would be a good first step towards addressing some of the gaps in the VDM record.
The low VGP dispersion at low-latitudes and the strong latitudinal dependence of VGP dispersion previously observed for the PCRS (de Oliveira et al., 2018) is a robust feature, demonstrated by the similarity in the pattern observed in this study using a higher-quality database. This behavior is distinguishable from that observed during the Pre-CNS and Post-PCRS and is the most extreme example of latitudinal-dependent VGP dispersion. This would suggest that the PCRS occurred during a time interval in which the Earth's magnetic field was greatly dipole dominated, and potentially of high intensity, making it a time interval worthy of intensive future study.

Data Availability Statement
The original datasets compiled for this research are available through EarthRef Digital Archive (https:// earthref.org/ERDA/2481, ERDA), and are also provided in the Supporting Information S1. A complete breakdown of the Supporting Information is available in "Supporting Information S1." Previously compiled data are available through their respective publications, Cromwell et al. (2018)