We propose a new proxy that employs assemblages of fossil turtle shells to estimate the timing and depth at which fossilization and lithification occur in shallowly buried terrestrial strata. This proxy, the Turtle Compaction Index (TCI), leverages the mechanical failure properties of extant turtle shells and the material properties of sediments that encase fossil turtle shells to estimate the burial depths over which turtle shells become compacted. Because turtle shells are one of the most abundant macroscopic terrestrial fossils in late Mesozoic and younger strata, the compactional attributes of a suite of turtle shells can be paired with geochronologic and stratigraphic data to constrain burial histories of continental settings—a knowledge gap unfilled by traditional burial-depth proxies, most of which are more sensitive to deeper burial depths. Pilot TCI studies of suites of shallowly buried turtle shells from the Denver and Williston basins suggest that such assemblages are sensitive indicators of the depths (~10–500 m) at which fossils and their encasing sediment become sufficiently lithified to inhibit further shell compaction, which is when taphonomic processes correspondingly wane. This work also confirms previously hypothesized shallow Cenozoic burial histories for each of these basins. TCI from mudstone-encased turtle shells can be paired with thicknesses and ages of overlying strata to create geohistorical burial curves that indicate when such post-burial processes were active.

Fossils, along with sediment mineralogy and geochemistry, are useful proxies for understanding the evolution of basins and tectonic histories, because their decay and lithification processes are sensitive to increasing burial depths and thermal gradients. Unfortunately, in sedimentary rocks, most of these proxies for maximum burial depth and/or temperature (e.g., color alteration indices, vitrinite reflectance, low-T isotope, and fission-track thermochronology) only work in basins that have undergone relatively deep burial, typically in the realm of ~1–9 km (e.g., Epstein et al., 1977; Staplin, 1982; Suggate, 1998; Winkelstern and Lohmann, 2016; Wildman et al., 2019; Van Ranst et al., 2020). Yet, many basins, especially in epicontinental settings, are shallow, and may not contain sufficient chalk, shale or peat/lignite to leverage burial depth proxies tied to porosity, volatile matter content, or water content. Yet many of these basins contain fossils of known morphology and kinematics, and these fossils undergo measurable compaction and lithification at shallow depths. Understanding the timing and depth at which fossils decay and mineralize could help elucidate shallow basin histories (e.g., Lynn, 2005; Hartkopf-Fröder et al., 2015).

Constraining the timing and depth at which organisms decay and mineralize is also useful for quantifying biases in the fossil record. Much of this rich biological history is reconstructed from exceptional fossil deposits, known as Lagerstätten. Yet burial, decomposition, and mineralization in these deposits are commonly considered to be rapid and shallow, given the typically delicate and/or three-dimensional nature of their preserved specimens (see reviews in Bottjer et al., 2002; Fraser and Sues, 2017). Although the supposition that exceptional soft-tissue preservation results from rapid, shallow burial and/or early diagenetic mineralization, such hypotheses are rarely testable except with decay experiments on modern organisms (see syntheses in Allison and Briggs, 1991; Martin, 1999; Allison and Bottjer, 2011). In part, this knowledge gap exists because in continental settings, it is challenging to sequentially date deep-time (e.g., 50+ Ma) strata with the precision needed to address the short-term timescales (e.g., days, millennia, and more) over which taphonomic and lithification processes occur.

To address these challenges in assessing shallow-basin burial histories, we developed a novel method, the Turtle Compaction Index (TCI), which combines an understanding of how fossil turtle shells get compressed and ultimately become crushed (Fig. 1), with biomechanical properties of extant turtle shells and empirical relationships of sediment porosity to determine the burial-depth history of fossil-bearing deposits. Turtles were chosen as compaction proxies because their mineralized carapaces are frequently preserved in epicontinental basins and because their hemispherical shapes are straightforward to reconstruct, even when crushed. We tested this new TCI technique with two suites of fossil turtle shells from the Denver and Williston basins of the western United States, augmenting the database with older turtle shells from the same region and with other fossil turtle material from the San Juan and Kaiparowits basins.

Turtles are among the most abundant fossil vertebrate remains of Late Jurassic and younger continental facies. In addition, turtles have a high percentage of articulated remains, mainly in the form of shells. Shell-surface texture and patterning of the scales in hard-shelled turtles are commonly diagnostic to the species level. Compressed turtle shells are not only common, but show a stereotypical taphonomic pattern—namely, that the vertical bridge that connects the carapace and plastron in hard-shelled turtles breaks, shatters, and/or expresses itself on the relatively horizontal carapace as a result of compression (Fig. 1; figure 3 in Joyce et al., 2016).

The majority of specimens analyzed in this pilot study come from the Cretaceous-to-Paleogene D1 Sequence (i.e., Denver Formation) of the Denver Basin, a unit that is rich in fossil turtle shells and has a well-constrained framework for understanding its stratigraphy, geochronology, and burial history (Raynolds, 2002; Raynolds and Johnson, 2003; Raynolds et al., 2007; Fuentes et al., 2019). One of the most complete and best exposed outcrops of this unit is in the Corral Bluffs study area, where we were able to collect articulated turtle specimens spanning a wide geographic and stratigraphic range. Although soft-shelled turtles are present (Middleton, 1983; Hutchison and Holroyd, 2003; Lyson et al., 2019a; Lyson et al., 2021a, 2021b), we only analyzed the hard-shelled, aquatic turtles (n = 21) from this deposit, focusing on the abundant paracryptodiran (principally baenid) turtles as well as Adocus, Compsemys, and Hoplochelys (Table 1).

A complementary suite of 44 hard-shelled, aquatic turtle specimens was also examined from the Hell Creek Formation in the Williston Basin, a basin that is hypothesized to have had a relatively shallow burial history (Hartman et al., 2002; LeCain et al., 2014). This formation spans a similar time range as the succession in the Denver Basin (Hicks et al., 2002; LeCain et al., 2014; Sprain et al., 2018), has similarly abundant baenid (Holroyd and Hutchison, 2002; Lyson and Joyce, 2009a, 2009b, 2010, 2011; Joyce and Lyson, 2015; Lyson et al., 2019b) and other turtles (Knauss et al., 2011; Joyce and Lyson, 2011, 2017; Joyce et al., 2019; Holroyd et al., 2014), and has a well-constrained geochronologic, stratigraphic, and tectonic setting (Hartman et al., 2002; Wilson et al., 2014).

Both D1 and Hell Creek strata were deposited primarily in sandy riverine to muddier ponded-water environments, and their stratigraphy is well documented (Hartman et al., 2002; Johnson et al., 2002; Wilson et al., 2014; Lyson et al., 2019a). In addition, the turtle fauna from the two deposits is nearly identical in its mode of preservation (Holroyd and Hutchison, 2002; Hutchison and Holroyd, 2003). Only isolated turtle shells (i.e., not preserved with articulated appendicular elements) were used in this study; none of these shells showed signs of predation, abrasion, or weathering. The lack of weathering suggests the turtle shells were not subaerially exposed (Behrensmeyer, 1978; Brand et al., 2003a, 2003b) but rather buried in an aquatic environment. Combined, these data suggest the turtle shells used in this analysis share similar taphonomic histories that are common in aquatic reptiles (e.g., Syme and Salisbury, 2014). These include death in aquatic environment (ponded water or river and/or stream), bloat and float before sinking, and finally, disarticulation at the water/sediment interface. Moreover, these characteristics collectively suggest that the fossils considered in this analysis entered the depositional system, or sediment, in a similar state of preservation.

Despite these similarities in depositional environments and turtle fauna, most specimens from the Denver Basin are dorsoventrally compressed, whereas the baenid turtle shells from the Hell Creek Formation are mostly (nearly) uncompressed (meaning they have either not reached the threshold at which plastic deformation of the turtle shell begins, or have only been deformed by a small percentage) and better preserved (Tables S1 and S21). Minimal compaction in these specimens is based on the fact that the shells, skulls, limbs, pectoral and pelvic girdle, and caudal and cervical vertebrae are preserved three-dimensionally. Specimens from the “Turtle Graveyard” locality in the Hell Creek data set (DMNH Loc. 6301; included in our data set) contain intact cortical bone (the outer bone layer that defines the shape of a bone) with the cancellous marrow cavity inside it (Lyson et al., 2014). Although such bone tissue resists micro-structural alteration during diagenesis and fossilization, hollow spaces between cortical bone typically collapse under increasing pressure with burial depth. Presence of three-dimensionally preserved bones with an uncompromised marrow cavity signals that structural integrity of turtle bone tissue at the Turtle Graveyard locality is intact, which requires minimal compaction and relatively shallow burial. X-ray CT analysis of material from the Turtle Graveyard, together with another Hell Creek locality, “Turtle Ridge” (DMNH Loc. 6302), reveals additional fine anatomical structures that speak to minimal compaction and shallow burial depth, such as three-dimensional preservation of the internal carotid system (Rollot et al., 2018). The carotid system is a suite of arteries that serve as the major blood supplier to the brain, and its bony canals are typically compacted, fractured, and collapsed in fossils (see Joyce et al., 2018). Therefore, when these and similar structures are preserved three-dimensionally, it indicates that the fossils experienced minimal burial compaction. Considered together, these preservational features suggest little to no compressive stress for most of the baenid turtle shells from the Turtle Graveyard and Turtle Ridge localities.

These features make the suite of Hell Creek baenid turtle shells an ideal starting point for creating a baseline standard for the Turtle Compaction Index (TCI). Baenids are common enough in other basins and typically exhibit a greater diversity of compaction than seen in the Hell Creek Formation, thus offering an opportunity to apply the TCI to assess approximate pre-lithification burial depths in other tectonic settings. With this in mind, we augmented our Denver and Williston basin TCI analyses with turtle shells from the roughly coeval Fruitland Formation (n = 3; San Juan Basin) and Kaiparowits Formation (n = 1; Kaiparowits Basin), and from the Jurassic Morrison formation (n = 1) and the Cretaceous D1 Sequence elsewhere in the Denver Basin (n = 1). These data are summarized in Table 1.

Turtle shells are usually infilled and/or entombed in sediment prior to or shortly after burial (e.g., Brand et al., 2003a). As they are buried and gradually crushed, the height of any given turtle shell decreases; thus at first approximation, carapace height appears to be the key parameter to consider. The logic is that a suite of carapace heights could be measured and used to extrapolate the maximum amount of compaction that shells experienced, and hence, the maximum burial depth of that part of the basin. However, maximum compaction, and hence, TCI burial-depth estimates, are greatly dependent on the grain size of the surrounding sediment in uncemented clastic strata (Fig. 2A). Fine-grained sediment can contain larger amounts of fluid initially and thus can be reduced in volume more than coarse-grained sediment that cannot hold as much fluid initially (Fig. 2A). To wit, depth estimates in coarser-grained strata of the D1 Sequence and Hell Creek Formation are similar (Fig. 2B), whereas depth of mudstones of the D1 Sequence, Hell Creek, and from five samples from the Kaiparowits, Morrison, and Fruitland formations vary more. In the same vein, the maximum depth resolution to which TCI is sensitive is governed by the surface porosity of the sediment. For example, even a highly porous (45%) sandstone, in theory, should only allow a suite of turtle shells to undergo compaction to an estimated depth of 360 m, whereas in finer-grained (silt- and mud-dominated) sediments, turtle shells can theoretically be crushed much further, potentially undergoing compaction to depths of up to 1300 m (Fig. 3).

Density and porosity of the sediment above and encasing the turtle shell are likely to influence final burial-depth estimates. In order to understand the extent of this influence, we used two density estimates for the sediment surrounding each turtle shell (1820 kg/m3 and 2100 kg/m3 based on known sediment grain mineralogies and grain-size distributions for these rock units; Robson and Banta, 1993), and we examined the aforementioned surface porosity scenarios (Fig. 3). Overall, reasonable variations in density (~300 kg/m3) do not significantly impact the resulting compaction-depth estimates (Fig. 4), and comparison of the resulting depth to known thickness of the overlying strata suggests that our selected surface porosity model is satisfactory (Fig. 4). Because the TCI associates turtle-shell compaction with sediment porosity, our results conform to sediment-porosity specific burial-depth curves reported by Bridge and Leeder (1979) and Baldwin and Butler (1985).

We also analyzed a suite of turtle shells that were encased in apatite concretions for comparison. These specimens from the D1 Sequence are described in Lyson et al. (2019a). We found that the suite of turtle shells in concretions contained some specimens that were more compacted than in the other turtle-shell populations (Fig. 2D). This pattern is more pronounced in mudstones, where such concretions are more common (see analogous examples in Feldmann et al., 1993). This observation is somewhat surprising. Turtle shells in such concretions might have experienced greater diagenetic mineralization, which could extend the depth and/or taphonomic window under which burial compaction could have occurred. Alternatively, it is possible that early leaching of skeletal apatite during concretion formation may have weakened such turtle shells and made them more susceptible to greater fracturing and compaction.

We analyzed turtle shells that were buried at a variety of known minimum depths and of several different ages for further comparison. These include sandstone-hosted turtle-shell suites from the Paleocene–Cretaceous D1 Sequence (~590 m of burial based on thickness of overlying stratigraphy; Item S1, footnote 1), Cretaceous Hell Creek Formation (~990 m), Cretaceous Kaiparowits Formation of the Kaiparowits Basin (~1550 m), Cretaceous Fruitland Formation of the San Juan Basin (~1700 m), and Jurassic Morrison Formation of the Denver Basin (~2400 m). The more deeply buried turtle shells, as well as older and younger deposits, all plot on the same curve as the shallowly buried, mudstone-encased samples from the D1 Sequence and Hell Creek (Fig. 2B).

Our analysis included 21 hard-shelled turtles from the D1 Sequence, 44 from the Hell Creek Formation, and five from the outgroup of Fruitland, Kaiparowits, and Morrison formations. The turtle shells analyzed from each deposit appear to have similar taphonomic histories. All but one of the D1 Sequence turtle specimens are distributed across a geographic area of ~15 km2 and span 105 m of stratigraphy (Fig. 5), whereas the majority (n = 41) of Hell Creek turtle shells are from two distinct but geographically and stratigraphically equivalent localities located 400 m apart (Lyson and Joyce, 2009; Lyson et al., 2019b). The following parameters were measured directly on each of these turtle shells: (1) plastron length, (2) plastron width, (3) bridge length, (4) carapace length, and (5) shell height (Fig. 1E). Figure 6 illustrates relevant turtle anatomy discussed below. The degree of turtle-shell compaction was assessed quantitatively through calculation and qualitatively based on a typical pattern of turtle-shell failure under stress (Figs. 1A1D). We consider a turtle shell (nearly) uncompacted as long as the carapace is not fractured above the bridge (i.e., the ventral portion of the shell that connects the plastron with the carapace; Fig. 1A). Minimal cracking around the peripherals (i.e., the bones along the perimeter of the shell) may occur before shell failure and may indicate early onset of compaction (Figs. 1A1C). A turtle shell that has reached critical failure shows longitudinal fractures above the bridge (Fig. 1B), whereas a moderately compacted turtle shell exhibits an expansion of these fractures and fracturing on either side of the neurals (i.e., the midline bones overlying the vertebral column) parallel to the vertebral column (Fig. 1C). A severely compacted turtle shell shows a wall-like structure forming around the peripherals, as well as the previous fractures (Fig. 1D).

In the case of the D1 Sequence and Hell Creek Formation, we know the maximum thickness of strata that lie or could have plausibly lain above all fossil turtles in these successions. Supra-D1 stratigraphy could be as thick as ~1256 m, but well-log, facies, and isopach projections suggest a thickness closer to ~590 m; similarly, thicknesses of sediments deposited above the Hell Creek could be as thick as ~1411 m, but are likely closer to ~990 m (Item S1, footnote 1). With this information, we applied the shallow-burial-depth model curve of Bridge and Leeder (1979) to these successions:
where Φ is the porosity at depth ZF, and ΦS is surface porosity of the sediment (which Bridge and Leeder [1979] set to 78%). The formula from Bridge and Leeder (1979) has a 2% error. Surface porosity was estimated based on sediment composition and empirical data from the literature (e.g., McNeill, 1980; Table S3, footnote 1). We acknowledge that sediment composition is typically a mixture of clay, silt, sand, and gravel, and we use end-member compositions (mud and sand) for surface porosity in our calculations, which is not a perfect representation of the true surface porosity of the fossil-bearing strata, but is a starting point with which to begin refining the TCI. Measuring the porosity of every sedimentary layer above each turtle shell was not feasible; thus, we reasoned that porosity Φ in (1) represents a change in pore-space (factor F), which can be described as:
where any volume that behaves like its surrounding sediment could potentially be used to estimate Φ at depth ZF. Taphonomic studies have shown that turtles disarticulate in a pattern that results in an empty turtle shell (reviewed in Brand et al., 2003b). Therefore, turtle shells are a hollow body with the potential to behave in response to pressure like the surrounding sediment once the shell fractures. Complete turtle shells are abundant in both primary study areas, and they typically occur with their plastron (the ventral part of the shell) facing downward. As they are buried and gradually crushed, their shell heights decrease; thus, height of their resulting shell is inversely proportional to the maximum amount of compaction that the individual shell experienced. Comparison of various measurements on the turtle shell of uncompacted or nearly uncompacted turtle shells shows that plastron length correlates best with uncompacted shell height (Fig. 7). Carapace length can also be employed to assess original shell height, and subsequently to calculate depth values, with little statistical difference (Tables S4, S5, and Fig. S1, see footnote 1), but plastron length is a better metric for calculating original turtle-shell height because plastrons tend to be more completely preserved than entire carapaces.
It is possible that variations between different turtle genera in each of these deposits could also bias TCI calculations, but only one taxon, Eubaena, had sufficient representation for a meaningful linear model fit for pre-deformation shell height (HE):
where LP = plastron length and LC = carapace length.

We used the fit for Eubaena and a linear model calculated using all baenids for the remaining turtles (which include the kinosternid Hoplochelys, the adocid Adocus, and unprepared specimens). The fitted linear model for pre-deformation shell height (H) is described by the following equations:



Calculation of linear models requires uncompacted specimens. Modern and fossil relatives can be used for this purpose as long as the proportions between shell height and plastron and/or carapace length are similar.

We used the linear models to reconstruct shell height prior to deformation for all specimens. When the measured height of a (nearly) uncompacted specimen exceeded the calculated original shell height, we used the measured height to prevent values greater than 100% of the shell height of the living animal. The ratio of measured shell height (HM) to shell height prior to compaction (H) is a representation of the factor
which can be used in Equation (2) to estimate porosity at depth ZF. With all of these considerations, Equation (1) was solved for burial depth:


This equation calculates a depth at which compaction of a cracked turtle shell stopped. Magwene and Socha (2013) showed that turtle shells will undergo elastic deformation before cracking, and the depth at which critical shell failure takes place must be taken into account. Another important caveat is that Magwene and Socha (2013) analyzed “fresh” turtle shells, whereas the fossil turtle shells analyzed herein underwent subaqueous decay. However, given the similar depositional environment, turtle fauna analyzed, and taphonomic history of all turtle shells used herein, the differences between specimens are regarded as negligible. Force at critical turtle-shell failure:
is size-dependent (Magwene and Socha, 2013) and requires plastron length (in m) to calculate the critical force in newtons. In other words, a turtle shell must be buried to a specific, size-dependent depth before Equation (8) for burial depth can be applied. Critical force Fc corresponds to the depth at which the turtle shell would have cracked:
which uses stress σ (N/m2), sediment density ρ (kg/m3), and a gravitational constant (9.81 m/s2) to find depth at critical failure ZC (in m). We used Robson and Banta (1993) to estimate lower (1820 kg/m3) and upper bounds (2100 kg/m3) of sediment bulk density. Figure 4 shows that moderate density differences have very little to no impact on the final depth estimate, and that these density differences affect the depth estimate for (nearly) uncompacted turtle shells by <15% in our sample. Stress σ is derived from:
with turtle-shell area A (in m2) calculated using the equation for the area of an ellipse:
with carapace length (in m), shell width W (in m), and π. This equation represents the maximum turtle-shell area on which a force can act. Magwene and Socha (2013) point out that accounting for a continuously changing turtle-shell area under compressive force is difficult, and critical force can only be experimentally determined at shell failure using traction stress. We acknowledge that tensor stress is more precise, but this calculation affects only the depth of critical turtle-shell failure (typically 5–7 m). Adding up depths ZF and ZC results in a maximum depth at which the turtle shell stopped compacting. Figure 8A shows burial-depth estimates with error bars representing minimum and maximum compaction and burial depth for each specimen; Figure 8B shows only shallowly buried individuals. The greatest calculated errors for turtle-shell compaction are −14.1% and +23.4%, which would yield a range of calculated burial depths ranging from 6 m to +8.1 m around a mean calculated burial depth of 7.49 m. The greatest differences in burial-depth estimates were 507–80.5 m and 143+80.3 m. The mean error of all burial estimates is ±10.9 m.

We used RStudio (R Core Team, 2016; RStudio Team, 2020) to compile a script for all computations, which is provided in Item S2 (footnote 1).

The Turtle Compaction Index allows us to estimate the depths over which maximum compaction of a turtle shell and its surrounding sediment occurred and provides a minimum estimate of the amount of sediment that was deposited atop each turtle shell before it stopped collapsing. Because most fossil turtle shells do not ever get completely crushed, despite burial to substantial depths, we hypothesize that when their compactional trajectory is arrested, the onset of lithification of the unconsolidated sediments that encase them begins. The range of depths at which this occurs varies between individual specimens and between mudstone-versus-sandstone–encased assemblages (or suites). Yet within these two lithologic suites, all studied turtle shells plot along similar compaction-depth trajectories, regardless of age (Paleocene to Jurassic), thickness of overlying stratigraphy (~600 to ~2400 m), basin of origin (n = 4), or taxonomic group (n = 11).

In the Denver Basin, we compared the geochronology of the strata that buried the D1 turtle shells to the depths at which turtle shells became maximally crushed in order to estimate when the latter happened. For this suite of turtle shells, maximum compaction is clustered in several temporal intervals (Fig. 9). More than half of all D1 turtle shells reached maximum compaction between 65.9 and 65.0 Ma, a timing that is nearly syndepositional on geologic timescales. Three specimens reached this milestone shortly thereafter, between 64.5 and 64 Ma. The remaining specimens attained maximum compaction during two intervals of the Eocene (53.5–51.9 Ma, ~12–13.5 m.y. later), perhaps reflecting a depositional episode (Galloway et al., 2011), or pulse of deeper burial, at that time. This interval is suspiciously close in age to the timing of synorogenic sedimentation thought to be represented by the overlying D2 Sequence in the Denver Basin (Raynolds, 2002; Raynolds and Johnson, 2003; Dechesne et al., 2011). The Eocene phase(s) of compaction could also be associated with onset of more humid climates and/or tectonic uplift associated with the regionally extensive Eocene erosion surface (Epis and Chapin, 1975; Gregory and Chase, 1994).

All Hell Creek turtle shells achieved their maximum compaction geologically soon after burial, reflected by maximum compaction reached within depths of 20 m, which is within the realm of syndepositional compaction (red diamonds in Fig. 2B). This result also suggests that these fossils and encasing sediment began to lithify much more shallowly than the maximum amount of sediment that buried them (~990 m; Item S1, footnote 1). The suite of Denver Basin turtle shells, on the other hand, have compaction histories that suggest turtle shells experienced burial ranging from ~5–540 m before they became lithified (Fig. 2); these thicknesses are consistent with the ~590 m total thickness of strata thought to have mantled the D1 sequence in the Corral Bluffs region (Item S1, footnote 1).

Surprisingly, among the suite of concretion-encased D1 specimens are turtle shells that exhibit substantially more compaction than expected (Fig. 2). In our geohistorical analysis, these are the specimens that appear to have reached maximum compaction in the early Eocene, ~13–14 m.y. after their initial burial (Fig. 9). The exact reason for their increased compaction potential and their protracted journey through the burial process is not understood. Perhaps if phosphorous in such concretions was leached from turtle carcasses, this dissolution could have weakened the turtle shell further than normal, enabling further compaction than might otherwise be expected.

The TCI has potential to inform burial histories of turtle-bearing continental strata, as well as to better understand fossilization in the many turtle-rich Lagerstätten that anchor our understanding of Earth history (Table 2). In the case of the studied D1 and Hell Creek strata, the calculated maximum burial depths confirm previously hypothesized shallow burial histories for the Denver and Williston basins.

We recommend using a complete suite of mudstone-encased turtle shells to assess burial depths, rather than individual specimens or specimens encased in sandstone. When combined with traditional depth proxies, the TCI can provide an upper (minimum) burial-depth metric for continental deposits in which shallow burial has been suspected but has been challenging to confirm. Basins that contain exceptional fossil deposits such as the Hamilton Lagerstätte (Illinois Basin; Cunningham et al., 1993), Kinney Brick Company Quarry (Albuquerque Basin; Zidek, 1992), or Geiseltallagerstätte (Geiseltal Basin; Simoneit et al., 2021) are particularly ripe for testing this hypothesis (see also Table 2). Moreover, if distinct intervals of burial compaction are identified among a suite of turtle shells, there are opportunities to compare these to coeval depositional episodes (sensu Galloway et al., 2011) triggered by orogeny or climate.

Yet in the same way that conodont alteration, vitrinite reflectance, and palynological proxies underwent years of testing and refinement before being widely adopted by the geoscience community to assess burial and thermal histories (Wilson, 1964; Castaño and Sparks, 1974; Epstein et al., 1977), the Turtle Compaction Index also needs to be vetted. We present the TCI here as the first step in this process, and we encourage the community to adapt it to other continental basins, and to refine it in the field and in the laboratory. There is ample opportunity to refine the index by employing tensor stress calculations to calculate critical shell failures for specific turtle taxa, and by leveraging experimental approaches that integrate varying rates of deep burial of extant turtle shells across different turtle-shell morphologies and sediment rheologies.

Finally, predictable compaction patterns are not unique to turtle shells. Other fossil groups that are abundant in shallow continental basins exhibit stereotypical breakage patterns that could potentially reflect depth-dependent burial processes. Common examples include Cenozoic mammal and crocodile crania, which are commonly found flat and with a recognizable pattern of collapsed nasal cavities (mammals) and orbital regions (crocodilians). Similarly, compaction and lithification data from scientific, engineering or hydrogeologic drill cores in continental strata may provide a test of the validity of compaction profiles derived through the study of fossil vertebrates.

We thank Norwood Properties, City of Colorado Springs, Waste Management, Aztec Family Raceway, J. Hawkins, J. Hilaire, J. Carner, W. Pendleton, the Bishop Family, and H. Kunstle for land access; the State of Colorado, Office of the State Archaeologist for issuing collection permits; F. Koether, N. Toth, S. Bastien, S. Begin, B. Benty, T. Tucker, and D. Zelinski for preparation of specimens; R. Hess, S. Milito, Y. Rollot, P. Sullivan, L. Taylor, and K. Weissenburger for field assistance; R. Wicker and N. Neu-Yagle for photography; K. MacKenzie and N. Neu-Yagle for collections assistance; K. Weissenburger for assistance with Figure 2; D. Fastovsky, M. Lewan, S. Paxton, B. Raynolds, and an anonymous reviewer for helpful reviews and discussions; B. Snellgrove for logistics; and B. and W. Stevenson for lodging during fieldwork. Funding was provided by The Lisa Levin Appel Family Foundation, M. Cleworth, Lyda Hill Philanthropies, David B. Jones Foundation, M.L. and S.R. Kneller, T. and K. Ryan, and J.R. Tucker as part of the Denver Museum of Nature and Science No Walls Community Initiative.

1Supplemental Material. Figure S1: Comparison of lithification depths derived from plastron length and carapace length. Table S1: Plastron size data and plastron-based burial-depth estimates. Table S2: Carapace size data and carapace-based burial-depth estimates. Table S3: Different surface porosity values used to estimate burial depth. Table S4: Outcomes of similarity tests between plastron- and carapace-based depth estimates. Plastron and carapace depth models are similar. Item S1: Reconstruction of thickness of overlying sediment packages. Item S2: R Script. Please visit https://doi.org/10.1130/GEOS.S.20113886 to access the supplemental material, and contact editing@geosociety.org with any questions.
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