Definitions: Stage and substages, magnetostratigraphy, and ammonite biostratigraphy.

The chart follows The Geological Time Scale 2012 (GTS2012 [23]) for definitions of stage and substage boundaries [24], magnetostratigraphic boundaries [25], and ammonite biostratigraphy [24]. Although more recent revisions of these definitions are available, GTS2012 integrates all these defined units with chronostratigraphic dates that use the ⁴⁰Ar /³⁹Ar standard and decay constant pairing of Kuiper et al. [16] and Min et al. [19], which are also used here. A second magnetostratigraphic column is also offered containing some revised chron boundaries and includes many of the very short duration cryptochrons that have not yet been officially recognised, but are often named in magnetostratigraphic analyses (e.g. [26]). Individual definitions and discussion (where appropriate) can be found in the pop-up notes in the respective parts of the chart.

In some places it is necessary to provide a compromise in stratigraphic placement, generally where a magnetostratigraphic assertion does not match, say, the ammonite zonation (e.g. age of the Dorothy bentonite in the Drumheller Member, Horseshoe Canyon Formation, Alberta [27, 28]. In such cases, the pop-up note text boxes provide explanation of the problem, and references.

Positioning of geological units and dinosaur taxa.

The stratigraphic ranges of geological units and fossil taxa are plotted as a solid bordered white cell with the lower and upper borders representing the lower and upper contacts of the geological unit, or first and last documented taxon occurrences (respectively).

If stratigraphic position is not sufficiently documented, the possible or likely stratigraphic range is illustrated as a block arrow. For example, if we know a taxon occurs in a given formation, but not the precise stratigraphic position within that formation (or if the age of the formation itself is only roughly known), then the block arrow would show the possible range being equivalent to the full duration of the formation. A combination of a solid cell and block arrow may be used if a taxon or geological unit comprises some specimens or horizons for which stratigraphic position is precisely known (depicted by the solid cell) and some specimens or horizons for which stratigraphic position is unknown (block arrows). Periods of non-material time (lacunae) are represented by blank spaces. In the aforementioned cases, explanation for the plotting of geological units, lacunae, and taxa is given in the corresponding note A graded block arrow is used for units which may continue for a long time below the period of interest (typically used for thick marine shales). The ranges and boundaries of each taxon or geological unit are discussed on a case-by-case basis in S1 Table.

Issues with lithostratigraphy.

Some features of typical lithostratigraphic units are not possible to depict properly on the stratigraphic chart format. In the Western Interior, many terrestrial packages form clastic wedges thinning basinward. Where possible, it is attempted to represent this in the chart, although for the most part depicted stratigraphic sections are based on single well-sampled sections, cores, or geographic areas, so the wedge-shaped overall geometry might not be visible.

Limitation of scope & future versions.

There are some limitations of scope for this initial version of the correlation chart.

The chart is currently mostly limited to units of Santonian age (86.3 Ma) up to the K-Pg boundary (66.0 Ma). There are a few exceptions (e.g. Moreno Hill Formation, New Mexico; Straight Cliffs Formation, Utah), which are included because they have yielded important specimens, or provide stratigraphic context for overlying units.

Geological units featured in the correlation chart are currently limited to those for which dinosaurian material has been collected, or which provide contextual information for surrounding units (e.g. intertonguing marine units with biostratigraphically informative fauna, and overlying or underlying units with chronostratigraphic marker beds).

Dinosaurian fossils are limited to Neoceratopsia, Pachycephalosauridae, Sauropoda, and Hadrosauridae. This is partly to limit the amount of data in this first published version of the chart. Thus, the chosen clades represent the most abundant taxa, and also include taxa considered biostratigraphically informative by previous workers (e.g. [1, 3, 4, 29, 30]).

Future versions of the chart are intended to extend the stratigraphic range down to the Jurassic-Cretaceous boundary. However, the plans for the first expansion concern inclusion of more Upper Cretaceous formations from North America, and also similarly aged deposits in Asia. Initial work on expanding faunal coverage has already begun concerning the addition of all remaining dinosaur taxa (including birds), crocodylians, and mammals, with the intent of eventually incorporating all useful taxa if possible.

Institutional abbreviations.

A list of institutional abbreviations used in the correlation chart are provided in a separate tab of the correlation chart Excel sheet (S1 Table) labeled "repository codes".

Taxa display format- phylogenies and lineages.

It is not the intention of this project to make significant comment on phylogenies per se. However, precise stratigraphic placement of taxa permits testing of speciation hypotheses (see Discussion), and so the arrangement of taxa on the chart should reflect up-to-date phylogenies or other hypotheses of descent. In this current version, this only affects Ceratopsidae and Hadrosauridae. For ceratopsids, the general arrangement follows the chasmosaurine phylogeny from Fowler [31], and for centrosaurines the arrangement follows the phylogeny of Evans and Ryan [32]. For hadrosaurids, the general arrangement of hadrosaurines follows Freedman Fowler and Horner [13], and lambeosaurines follows Evans and Reisz [33].

Magnetostratigraphy.

The conventional methodology used for delineating magnetostratigraphic chron boundaries can create problems. In magnetostratigraphic analysis, if two stratigraphically adjacent sample points yield opposite polarities (i.e., they are recognisable as different chrons), then it is convention to draw the chron boundary stratigraphically halfway between the two points. However, an issue can arise if these lower and upper sample points are separated by a sandstone from which it is difficult or impossible to extract a magnetostratigraphic signal. In terrestrial floodplain deposition (typical of the units studied in this work), the bases of depositional cycles are characterized by a surface of non-deposition or erosion overlain by a low accommodation systems tract, typically comprising an amalgamated channel sandstone. The combination of the depositional hiatus at the base of the sandstone, and the sandstone itself, means that there may be a considerable time gap (up to millions of years) between the last sampled horizon immediately below the sandstone, and the first sampled horizon immediately above the sandstone. If opposite polarities are recorded for the two sampled horizons on either side of the unsampled sandstone, then the chron boundary would be drawn halfway, within the sandstone, whereas it might be more likely to occur at the base of the sandstone, as this is where the hiatus occurs. This would have the effect of making a unit appear older or younger than it really is. For example, the mudstone immediately beneath the Apex sandstone (basal unit of the upper Hell Creek Formation, Montana [34]) is of normal polarity, assigned to C30n, whereas the mudstone immediately above the Apex Sandstone is of reversed polarity (assigned to C29r [35]). The C30n-C29r boundary is therefore drawn within the Apex Sandstone, whereas it is more likely that it occurs at the hiatus at the base of the sandstone. A more significant case arises with the contact between the Laramie Formation and overlying D1 sequence in central Colorado: here, because of the halfway convention, the uppermost part of the Laramie is drawn as being within the lowermost C31r zone [36], whereas in actuality, all magnetostratigraphic samples recovered by Hicks et al. [36] from the Laramie are normal, and it might therefore be entirely C31n. The effects of this issue are best examined on a case by case basis; the reader is referred to the stratigraphic chart (S1 Table) where more examples are highlighted in pop-up text boxes. It should be noted that this issue is purely an artifact of conventional methodology, not any mistake by a given researcher. So long as the reader is careful and remains cautious of this issue, then mistaken correlation and / or artificial age extension can be avoided.

U-Pb and K-Ar.

Most radiometric dates reported for Upper Cretaceous units use either U-Pb, K-Ar, or ⁴⁰Ar / ³⁹Ar dating methods. U-Pb and K-Ar are primary dating methods, which directly determine the age of a sample and do not require recalibration (unless decay constants change, which is rare); whereas relative or secondary methods (such as ⁴⁰Ar / ³⁹Ar dating) require use of a monitor mineral of known or presumed age ("standard"). It is the recent changes to the recognized age of these standards that has been the cause of changing ⁴⁰Ar / ³⁹Ar dates.

U-Pb dating actually analyses two decay series (²³⁵U decay to ²⁰⁷Pb, and ²³⁸U decay to ²⁰⁶Pb), such that there are two independent measures of age, the overlap of which is the concordant age of the sample [37]. Recent improvements in analytical techniques (High-Resolution–Secondary Ion Mass Spectrometry: SHRIMP; and Chemical Abrasion Thermal Ionization Mass Spectrometry, CA TIMS) have brought greater precision and accuracy to U-Pb dating, and it remains one of the best methodologies currently available [37]. The decay constant for U-Pb analysis is well established [38], and known to better than 0.07% accuracy [37].

K-Ar dating is an older method of radiometric dating that was commonplace up until the end of the 1980's when it was essentially replaced by the more precise and accurate ⁴⁰Ar / ³⁹Ar method [37]. K-Ar had a range of benefits, including a large number of possible datable minerals (due to the common occurrence of potassium in many rock-forming minerals), but among its drawbacks was a relative lack of precision, largely due to the requirement to run two separate analyses per sample for K and ⁴⁰Ar. As such, analytical precision was never better than 0.5%, and with the development of new technologies K-Ar dating was quickly replaced by ⁴⁰Ar / ³⁹Ar in the early 1990's [37]. Even so, some K-Ar dates are still the only dates available for a given unit, and so are included in the chart. K-Ar dates typically have error in the region of 1–2 m.y. for Upper Cretaceous units, so are useful indicators as to a general age range for a unit, but not for precise correlation.

40Ar / 39Ar.

Detailed reviews of ⁴⁰Ar / ³⁹Ar dating have been published elsewhere (e.g. [39, 40]). Notes given here are for the purpose of aiding the reader in understanding the recalculation of radiometric dates reported in this work, how ⁴⁰Ar / ³⁹Ar dates are affected by changing standards and decay constants, and comparability of radiometric dates recovered by different methods (e.g., ⁴⁰Ar / ³⁹Ar vs U-Pb).

40Ar / 39Ar standards (neutron fluence monitor).

As ⁴⁰Ar / ³⁹Ar dating is a secondary dating method, every unknown sample needs to be analysed alongside a sample of known age: a standard. Primary standards are minerals from specific rock samples that have been directly dated by ⁴⁰K / ⁴⁰Ar dating or another method; whereas secondary standards are based on ⁴⁰Ar / ³⁹Ar intercalibration with a primary standard [41]. The following list includes (but is not limited to) some of the more popular standards that have been used historically (see McDougall and Harrison [39] for a more complete list):

1. MMhb-1 McClure Mountain hornblende, primary standard: ~420 Ma
2. GA-1550 Biotite, monazite, NSW, Australia, primary standard: ~98 Ma
3. TCR Taylor Creek Rhyolite (or sanidine, TCs), secondary standard: ~28 Ma
4. FCT Fish Canyon Tuff (or sandine, FCs), secondary standard: ~28 Ma
5. ACR Alder Creek Rhyolite (or sanidine, ACs), secondary or tertiary standard: ~1 Ma

Standards are chosen depending on availability, and should be of an age comparable to the unknown sample [41]. Hence, for Upper Cretaceous deposits, usually the secondary standards TCR or FCT have been used, typically themselves being calibrated against a primary standard (historically, the MMhb-1 is commonly used, although this depends on the preference of the particular laboratory). Many historically popular standards are no longer used, as repeated calibration studies have found the original sample to give inconsistent dates. For example, Baksi et al. [42] found the widely used MMhb-1 primary standard to be inhomogenous, making its use as a standard no longer tenable. Further, intercalibration studies have continually honed and refined the ages of standards (especially the more widely used secondary standards), with the result that radiometric dates published years apart are typically not precisely comparable without recalibration (e.g. [41, 43, 44]).

For ⁴⁰Ar / ³⁹Ar analysis, a significant issue concerns the changing age of the Fish Canyon Tuff (FCT: the relative standard used for most ⁴⁰Ar / ³⁹Ar analyses of Cretaceous rocks), and to a lesser extent, the associated decay constants (λβ: β- decay of 40K to 40Ca; and λε: electron capture or β+ of 40K to 40Ar; which combined are referred to as λT or λtotal [45].

Cebula et al. [46] first proposed an age of 27.79 Ma for the Fish Canyon Tuff. This was quickly refined to 27.84 Ma by Samson and Alexander [43], which remained the standard used by ⁴⁰Ar / ³⁹Ar analyses published up to the mid 1990’s (e.g., [47]). Renne et al. [44] revised the FCT to 27.95 Ma (although this new figure was not commonly used at the time). The next major update was that of Renne et al. [41], whereupon the FCT was revised to 28.02 Ma, which was widely accepted up to 2008 when Kuiper et al. [16] published the current standard of 28.201 Ma. This also brought ⁴⁰Ar / ³⁹Ar dates into line with U-Pb dates, unifying these two major chronostratigraphic dating systems [16]. Two further revisions have been offered by Renne et al. in 2010 [40] and 2011 [20], of 28.305 Ma, and 28.294 Ma (respectively). Rivera et al. [22], Meyers et al. [48], Singer et al. [49], and Sageman et al. [18] all found independent support for Kuiper et al.'s [16] 28.201 Ma age for the Fish Canyon Sanidine (and therefore rejected Renne et al.'s [40] further revised 28.305 Ma standard as too old). These analyses also used three methods (⁴⁰Ar / ³⁹Ar, U-Pb, cyclostratigraphy) to reach consensus, confirming alignment of U-Pb and ⁴⁰Ar / ³⁹Ar dates.

When applied to Upper Cretaceous units, a ~0.2 m.y. difference between the age of two different standards corresponds to ~0.4–0.5 m.y. difference in the ⁴⁰Ar / ³⁹Ar age of the analysed sample, and this is exacerbated if the standards used were further apart. For example, using the 27.84 Ma standard of Samson and Alexander [43], Rogers et al. [50] published an ⁴⁰Ar / ³⁹Ar date of 74.076 Ma for a bentonite at the top of the Two Medicine Formation, MT. This becomes 75.038 Ma if using the current Kuiper et al. [16] standard, and 75.271 Ma under the less commonly used Renne et al. [20] standard, a difference of 1.28 m.y. from the originally published date.

40Ar / 39Ar decay constants.

The ⁴⁰Ar / ³⁹Ar method depends upon the β- decay of ⁴⁰K to ⁴⁰Ca (λβ), and electron capture or β+ of ⁴⁰K to ⁴⁰Ar (λε), which combined are referred to as λT or λtotal [45]. The value of the decay constant λT (and its components) has historically been subject to fewer changes than the standards listed above, but has come under increased scrutiny since the late 1990's. The currently accepted standard is 5.463 E-10/y [19], although alternatives are available, and refinement of this figure is the subject of active research (see S1 Table).

The decay constant used for an analysis is not always reported, although it has much less effect on the final calculated age than variations in fluence monitor mineral ages. For example, the difference between using 5.543 E-10/y [38] and 5.463 E-10/y [19] is 0.02%, equating to a difference of 0.013 Ma for a sample from the late Campanian (~75 Ma). It should be noted that different values of λT have been used historically by geochronologists compared to physicists and chemists; this is pointed out by Renne et al., [41] who note that (for example) Endt [51] used a λT value of 5.428 +/- 0.032 E^-10/y which "is more than 2% different from the values recommended by Steiger and Jaeger (1977) [38]". Thus, there is no guarantee that, unless otherwise stated, a lab that performed an ⁴⁰Ar / ³⁹Ar analysis in the 1990's will be using the λT of 5.543 E^-10/y of Steiger and Jaeger [38], although all dates recalibrated here use either this, Min et al. [19], or Renne et al. [20]. Further details and a history of decay constant values can be found in the corresponding note within S1 Table.

40Ar / 39Ar, recalibration & current standards.

In order to compare ⁴⁰Ar / ³⁹Ar dates, it is essential to ensure that the same standards and decay constants were used in their calculation, which may require recalibration. If the standards used are different (for example, if an old analysis used the TCR standard, and a more recent one used the FCT), then it will be necessary to find what the equivalent FCT value was to the TCR used in the original analysis. This is usually achieved by referencing either the original publication of the standard, or the relevant published intercalibration analysis (e.g., [44]). It is critical to understand that recalculation cannot simply be performed by entering the original standard used (e.g., TCR = 28.32 Ma) into the equation provided on the recalculation sheet from McLean and EARTHTIME [21] (or the adapted spreadsheet used here); the equivalent FCT value is what must be entered, as the formula only uses FCT.

The decay constant absolute value has only a small effect on the absolute age of a sample, but decay constants contribute a greater amount to the error range of a radiometric date.

There are two current prominently used pairings of standard and decay constant. Kuiper et al. [16] combined an FCT standard age of 28.201 +/-0.023 Ma with the decay constant of Min et al. [19], λT = 5.463 +/- 0.214 E-10/y. Renne et al. [20] use an FCT standard age of 28.294 +/- 0.036 Ma, with a λT of 5.5305 E-10/y. The dates used here in the correlation chart (S1 Table) are calibrated to the Kuiper et al. [16] standard, paired with the Min et al. [19] decay constant. This is not a reflection on the reliability of one method over another; rather it is out of convenience, because the various ammonite biozones and magnetochrons detailed in The Geological Time Scale 2012 ([23]; upon which this chart is based) use the Kuiper et al. [16] FCT standard, and Min et al. [19] decay constant.

40Ar / 39Ar, choice of mineral.

Direct comparisons between ⁴⁰Ar / ³⁹Ar dates require not only the same standard and decay constant pairing, but also that the subject mineral is the same. Although it is theoretically possible that a date obtained from biotite crystals might be comparable with one from sanidine, in practice the difference in closure temperature (the temperature at which the mineral no longer loses any products of radioactive decay [37]) and other factors such as recoil effects [52] mean that (for example) biotite dates are typically ~0.3% older than sanidine dates (e.g., see [50]). The current "gold standard" mineral for ⁴⁰Ar / ³⁹Ar dating is sanidine, and most modern analyses use this mineral exclusively; however, plagioclase and biotite dates are quite common in literature from the 1990's. Here these non-sanidine dates are recalibrated, and they are comparable to each other (i.e., biotite dates can be directly compared with other biotite dates), but caution is advised when comparing non-sanidine dates with those of sanidine (although this is sometimes unavoidable).

40Ar / 39Ar, reporting of uncertainty / error.

Reporting of error associated with ⁴⁰Ar / ³⁹Ar derived ages is not standardized and varies in the inclusiveness of sources of error, the statistical method used to calculate error, the type of error, and in the amount of analytical information provided.

Sources of error in ⁴⁰Ar / ³⁹Ar analyses include analytical error (e.g., J-value), uncertainty in the standard used (e.g., age of the Fish Canyon Tuff, FCT is 28.201 +/- 0.23 Ma at 1σ [16]), uncertainty in the decay constant (e.g., λ_T of 5.463 +/- 0.214 E-10/y [19]), and geological processes that may lead to post-crystallization alteration of isotope ratios [37]. Most older publications do not explicitly state what is included in the reported error, but newer studies (e.g., [53]) report both analytical and systematic error.

The statistical method used to report error is not standardized, and is typically given in one of three forms; some authors report 1 or 2 standard deviations (σ); Standard Error is also commonly reported (especially for population means); finally, some authors report the 95% confidence interval for the population mean, which is roughly equivalent to 2σ (= 95.45% confidence interval).

It is common for published radiometric dates to lack associated details of the analysis, by either the date being given as a personal communication, or simply the omission of analytical details. Consequently, it is sometimes unclear as to whether (for example) a stated error of +/- 0.15 Ma refers to 1σ, 2σ, Standard Error, or whether it includes analytical and systematic error.

As such, it is not possible to make the error consistent between each recalibration (although the effects are relatively minor). Where possible, recalibrated error is reported to 1σ analytical error, but generally the original reported error is simply processed through the recalibration spreadsheet, noting wherever possible all details and any issues that may arise. Direct comparison of error between dates (both recalibrated and unrecalibrated) should therefore be approached with caution.

Agreement of 40Ar / 39Ar dates with U-Pb dates.

⁴⁰Ar / ³⁹Ar dates have historically tended to be younger than U-Pb dates by about 1% [54], equating to ~750 k.y. difference in a 75 m.y. old sample (i.e., the approximate age of the units studied here). Possible explanations include longer zircon magma residence times prior to an eruption [37], error in the ⁴⁰K decay constant [55], or interlaboratory bias and geological complexities [16]. Recent revisions of standards and decay constants for ⁴⁰Ar / ³⁹Ar dating have closed the gap to within ~0.3% [16, 20]. This led Kuiper et al. [16] to suggest that ⁴⁰Ar / ³⁹Ar dating has improved "absolute uncertainty from ~2.5% to 0.25%".

It should be noted [37, 41], that when comparing dates within the same system (i.e., ⁴⁰Ar / ³⁹Ar compared to ⁴⁰Ar / ³⁹Ar; and U-Pb dates compared to other U-Pb dates) then it is accepted practice to not include internal error (such as data uncertainties in K-Ar, decay constants, and intercalibration factors [41]) as both dates are subject to the same uncertainty, effectively canceling it out. However, when directly comparing dates derived from different systems (i.e., ⁴⁰Ar / ³⁹Ar dates with U-Pb dates), then internal error should be included. An example from Renne et al. [41] showed that when reported separately, and therefore without internal error, the age of a biotite-derived ⁴⁰Ar / ³⁹Ar date for the Permo-Triassic Siberian Trap basalt was 250.0 +/- 0.1 Ma, whereas a zircon and baddeleyite U-Pb date from the same intrusion was 251.2 +/- 0.2 Ma. When properly compared with the internal error included, the ⁴⁰Ar / ³⁹Ar dates became 250.0 +/- 2.3 Ma, whereas the U-Pb date was recalculated as 251.2 +/- 0.3 Ma, such that the error ranges of the dates now overlap. In the case of this current work, only three U-Pb dates are plotted in S1 Table, all of which are from the Javelina and Aguja formations of Texas. The reader should therefore take care when comparing these units directly with other units based on ⁴⁰Ar / ³⁹Ar geochronology.

Other general comments.

The number of decimal places for reported dates and error are left in their original published form where possible.

In previous publications, a number of radiometric dates are reported as personal communication or featured only in abstracts. Such references typically lack any analytical data, so original standards (etc.) must be assumed based on the year in which the analysis was (likely) conducted, and any details of the typical standards used by the scientist and laboratory that carried out the analysis (if known; see individual notes for details of sleuthing).

Various analyses published by J. D. Obradovich.

Many critical ⁴⁰Ar / ³⁹Ar dates have been published by J. D. Obradovich (United States Geological Survey, Colorado), not the least of which his 1993 work, "a Cretaceous time scale" [52] which presented over 30 ⁴⁰Ar / ³⁹Ar dates for many key horizons or ammonite biozones, establishing a robust framework for the Late Cretaceous of the U.S. Western Interior. As such, recalibration of Obradovich radiometric dates is of great importance, but requires special caution due to the particular methodology of Obradovich during the 1990's (and possibly early 2000's), which differs slightly from what might be expected. During this time, Obradovich typically used the TCR as the standard for his analyses, but the equivalent age of the FCT (required for recalibration) is not typical. Indication of this is noted by Hicks et al. ([56] p.43) who state:

“The TCR (Duffield & Dalrymple, 1990) [57] has been used exclusively since 1990 by one of us (Obradovich) with an assigned age of 28.32 Ma normalized to an age of 520.4 Ma for MMhb-1 (Samson & Alexander, 1987) [43]. This age differs from that of 27.92 Ma assigned by Sarna-Wojcicki and Pringle (1992) [58]. The choice of 28.32 Ma was entirely pragmatic because this monitor age provided the best comparison with ages delivered by Obradovich and Cobban (1975) [59]. In an intercalibration study […] Renne et al. (1998) [41] obtained ages of 28.34 Ma for TCR and 28.02 Ma for FCT when calibrated against GA1550 biotite as their primary standard with an age of 98.79 Ma. This value of 28.02 agrees quite well with […] 28.03 Ma obtained through calibration based on the astronomical time scale (Renne et al., 1994) [44]. On the basis of unpublished data, one of us (Obradovich) obtained an age of 28.03 Ma for the FCT […] of W. McIntosh (Geoscience Department, New Mexico Institute of Mining and Technology, Socorro, New Mexico), calibrated against an age of 28.32 Ma for TCR.”

However, Obradovich-published analyses from this time do not exclusively use the TCR at 28.32 Ma, as Izzett and Obradovich [60] state that they use FCT sanidine at 27.55 Ma, and TCR sanidine at 27.92 Ma, both relative to MMhb-1 at 513.9 Ma (in conjunction with λT = 5.543 E-10/y). They note that the 513.9 Ma age of MMhb-1 differs from the then standardized age of 520.4 Ma [43] as the former age was calibrated in the lab where their current samples were analysed [61, 62].

This creates a problem when recalibrating ⁴⁰Ar / ³⁹Ar ages that used TCR as the fluence monitor (standard). The "official" TCR age of 27.92 Ma has a corresponding FCT age of 27.84 Ma [41, 43]. However, since most analyses by Obradovich use TCR at 28.32 Ma, then the question remains as to what number to use for the equivalent FCT when performing recalibrations. Renne et al. [41] provide an intercalibration factor for FCT:TCR of 1:1.00112 +/- 0.0010, which simply calculated is FCT = 28.32 / 1.100112 = 28.006 Ma. This agrees well with an FCT equivalent of 28.03 Ma (as calculated by Obradovich; see above [56, 63]) and a value of 28.02 Ma of Renne et al. [41]. In The Geological Time Scale 2012 [23], Schmitz [17] recalibrates a selection of dates from Obradovich [52], and Hicks et al. [64, 65] using a legacy FCT age of 28.00 Ma (not stated, but retrocalculated here). Sageman et al. ([18]; cited as Siewert et al., in press, by Schmitz [17]) recalibrate Obradovich's older dates using a legacy FCT age of 28.02 Ma (thereby agreeing with Renne et al. [41]).

In this analysis, when recalibrating an ⁴⁰Ar / ³⁹Ar date that was calculated by Obradovich using TCR = 28.32, I use an FCT value of 28.03, as this is the equivalent FCT explicitly stated by Obradovich [63]. This is a very close value to the FCT value of 28.02 in Renne et al. [41] (where the TCR equivalent is 28.34 +/- 0.16 Ma; 1σ, ignoring decay error) so confusion between the two should be avoided, although the difference between ages calculated using 28.03 or 28.02 Ma standards would correspond to only 0.02 to 0.04 m.y. for ages in the Late Cretaceous (100.5–66 Ma [24]).

Roberts et al. (2013).

Roberts et al. [6] present a table of recalibrated radiometric dates from a selection of important dinosaur-bearing formations of the North American Western Interior. Unfortunately, 11 out of 18 dates are incorrectly recalibrated, producing dates that are incorrect by up to a million years.

For recalibrated dates of the Judith River Formation (originally published by Goodwin and Deino in 1989 [66]), the study [6] utilizes an incorrect original (legacy) FCT standard of 28.02 Ma (i.e., from Renne et al., 1998 [41], published after the original 1989 analysis). For the recalibration to be correct, the legacy standard must be the value of FCT that was equivalent to the MMhb-1 at 420.4 Ma, which is FCT = 27.84 Ma ([43]; see Renne et al. [41]). This produces recalibrations for the Judith River Formation that are nearly half a million years different from the corrected recalibrations calculated in the current article. For example, the sample 84MG8-3-4 was originally published as 78.2 Ma [66]; Roberts et al. [6] recalibrate it as 78.71 Ma, whereas the recalibration offered in the current work (see S1 and S2 Tables) is 79.22 Ma.

The same error was made for recalibrations from the Bearpaw, Dinosaur Park, and Oldman formations as the Renne et al. 1998 [41] FCT date of 28.02 was also input as the legacy FCT for dates originally published by Eberth and Deino in 1992 [67] and Eberth and Hamblin in 1993 [68]; i.e. before the 1998 paper was published. The correct legacy standard to be used for these recalibrations is again FCT = 27.84 Ma ([43]; confirmed by Eberth, pers. comm., 2017; in prep.)

When recalibrating ⁴⁰Ar / ³⁹Ar dates for the Fruitland and Kirtland formations, New Mexico (originally published by Fassett and Steiner in 1997 [69]), incorrect values are input for the original (legacy) decay constant (λ) and standard [6]. First, the legacy λ used by Roberts et al. [6] is 4.962E-10/y, which was presumably copied from the bottom of the chart on p. 243 of Fassett and Steiner [69], where it is labeled as the value of λβ (ie. the probability of β- decay of 40K to 40Ca), and is printed below the value of λε (0.581 E-10/y; probability of electron capture or β+ of 40Kto 40Ar). In this case, the correct λ value to use for recalibration is 5.543 E-10/y [38], which is the total (λT) of λβ plus λε. Second, Roberts et al. [6] correctly state that the legacy standard used by Fassett and Steiner [69] for fluence monitoring was the TCR at 28.32 Ma; however, this number is then input directly into the recalibration formula with the new FCT standard (28.201; [16]). This is incorrect as recalculation must use the same standard mineral (e.g., FCT) for both legacy and recalibrated dates. For the recalculation to be correct, the legacy standard must therefore be the value of FCT that was equivalent to the TCR at 28.32 at the time of the 1997 analysis, which is either FCT = 27.84 Ma or ~28.03 (see S1 Table; above note on Obradovich), both of which produce recalibrated ages ~1 million years older than the dates presented by Roberts et al. [6]. The resultant misrecalibrated dates are actually younger than the original legacy dates, which should have been more difficult to overlook as the standards for ⁴⁰Ar / ³⁹Ar dating have been getting progressively older, so all recalibrations should produce older dates.

The recalibrated dates of Roberts et al. [6] were replicated (therefore confirmed) by rerunning the legacy values through the recalibration spreadsheet provided by the EARTHTIME institute [21].

Seven recalibrations were performed correctly; four from the Kaiparowits Formation, Utah, one from the Wahweap Formation, Utah, and two from the Two Medicine Formation, Montana. All other recalibrated dates are incorrect and should be discarded.