Decoding Deep‐Time Rhythms: Probing the Limit of Stratigraphic Correlation in the Time‐Specific Facies of the Late Devonian Usseln Limestone (Rhenish Massif, Germany)

The iso‐ or diachronous character of a geologic unit is scale‐dependent, especially for time‐specific facies. The Usseln Limestone is a Late Devonian time‐specific facies from Germany, occurring immediately below the Lower Kellwasser black shale. Here, we investigate whether cm‐scale rhythmical bands within the Usseln Limestone are correlatable across its depositional basin. Its facies were studied at three locations ca. 50 km apart, representing different depositional settings. Its cm‐scale alternations in lithological facies and elemental content (μXRF) form an excellent target for correlations on millennial timescales. Correlation attempts failed to converge to a solution at the cm‐scale of individual rhythmites. Dynamic Time Warping, however, provided convincing correlations at the dm‐scale, supporting its use as a high‐resolution correlation tool. The Usseln Limestone base may be diachronous, but the top is likely isochronous. This finding is in agreement with sudden basin‐wide black shale deposition at the onset of the Kellwasser Crisis.


Introduction
Time-specific facies are sedimentary rock units, characterized by distinct lithological, paleontological, and geochemical attributes, indicative of a particular interval in geologic time (Brett et al., 2012;Schindler, 2012;Walliser, 1984aWalliser, , 1984b)).Examples include temporally and geographically far-reaching deposits, such as Cretaceous Oceanic Anoxic Event-associated black shales and Precambrian banded iron formations (Brett et al., 2012), but also single beds that record briefly persisting conditions across a basin, such as the Late Devonian Usseln Limestone (Gereke, 2007;Gereke & Schindler, 2012).In their entirety, time-specific facies are considered isochronous.However, when considering their internal structures, isochroneity often breaks down.Here, we investigate how far the isochroneity of a rhythmically banded Devonian time-specific facies persists when comparing cm-scale units, and whether automated algorithms can help to elucidate these high-resolution correlations.
The Usseln Limestone represents the prelude to the Late Devonian Kellwasser Crisis sequence in northwestern Germany, and varies in thickness between 7 and 72 cm (Gereke, 2007;Gereke et al., 2014;Piecha, 1993;Rabien, 1954;Volk, 1939).It has a characteristic rhythmic appearance between clay-rich and carbonate-rich bands alternating on cm-scales.This limestone was deposited in both deep and shallow shelf basin environments.In siliciclastic sections, it is the only massive limestone that persists across significant distances throughout the Rhenish Massif (Gereke, 2007).The rhythmic character is particularly well-expressed in thicker Usseln Limestone units (Gereke, 2007;Gereke & Schindler, 2012).Its distinctive appearance and regional occurrence led Gereke and Schindler (2012) to designate the Usseln Limestone as a time-specific facies.
The environmental implications and correlatability of the Usseln Limestone rhythmites thus remain open questions.Here, we investigate three complete intervals of the Usseln Limestone with two distinct lithologies and from three different water depths.We employ thin section analysis, lithostratigraphy, μXRF scanning, and Dynamic Time Warping (DTW), an automated correlation algorithm, to probe the limit of layer-by-layer correlation within the Usseln Limestone.Therewith, our objective is to understand the degree of isochroneity within the Usseln time-specific facies on millennial timescales and infer on the fundamental question-do time-specific facies represent an equal amount of time?

Methods
Sedimentological descriptions were based on thin section microscopy (Figures S2-S4 in Supporting Information S1) supplemented with μXRF elemental maps.The μXRF scans were also used to generate depth records for selected elements and elemental ratios, to which DTW was applied.DTW is designed to automatically correlate depth or time series and is implemented in the R package "dtw" (Giorgino, 2009).DTW calculates the optimal match between two sequences while taking into account certain rules and constraints.In this case study, we avoid extreme sedimentation rates while correlating.All methods are described in detail in Text S1 in Supporting Information S1.

A Range of Depositional Settings
Three Usseln Limestone deposits were collected in their entirety: Winsenberg, Arfeld, and Steinbruch Schmidt (Rhenish Massif, Figures 1a-1c; Texts S1 and S2, Figure S5 in Supporting Information S1).Reconstructions place all three in the tropical seaway south of Euramerica, but at different distances from shore and at different water depths (Figures 1b and 1c).Winsenberg and Arfeld are shelf basin deposits that mostly consist of marls and shales.Steinbruch Schmidt represents a condensed submarine high that is entirely carbonate, except for the Kellwasser black shales (Figure 1a).Winsenberg was located near a volcanic seamount, receiving large amounts of carbonate input (Gereke, 2007).The Usseln Limestone is 72, 50, and 20 cm thick at Winsenberg, Arfeld and Steinbruch Schmidt, respectively (Figures 1a and 1c).The Usseln Limestone at Arfeld is thus considerably thinner than at Winsenberg despite the complete Kellwasser interval being more expanded (Figure 1a).This discrepancy is likely related to Arfeld receiving less carbonate export due to its deeper depositional setting (Gereke, 2007).The exact paleo water-depth of these two basinal settings is difficult to constrain due to a lack of diagnostic sedimentary structures or fauna, but is considered to be some hundreds of meters (Tucker, 1973).Steinbruch Schmidt was located seaward from the shelf basin (Figure 1c).The carbonate-rich and condensed nature of the section has been interpreted as representing deposition on a submarine high at ≤200 m water depth, with terrigenous siliciclastics bypassing the site (Devleeschouwer et al., 2002).

Different Expressions of Rhythmic Banding
The nature of the characteristic rhythmic banding differs between the studied sites.Winsenberg and Arfeld show cm-scale alternations of pure, gray to dark-gray limestone and light-gray to brown-gray, sometimes laminated, layers with a high clay content (Figures 2a and 2b, 2d and 2e).Importantly, the Usseln Limestone forms one cohesive bed, so both layer types are lithified to the same degree and rich in carbonate (Figures S6a and S6b in Supporting Information S1).We therefore refer to these alternating layers as "clay-poor/clay-rich," rather than "limestone/marl" or "limestone/shale."The cm-scale alternations in Steinbruch Schmidt consist of light-gray clotted micrite with sparry calcite cement and stromatactis, and dark-gray to brown-gray micritic wackestone with abundant sponge spicules (Figures 2c and 2f).Here, the Usseln Limestone contains very little detrital material (Figure 2f; Figure S6c in Supporting Information S1).Horizontal stylolites are pervasive and often separate the two layer types.The clotted micrite structures are interpreted as microbial deposits.Such microbialsponge associations, often with stromatactis, are common in the Devonian (Bourque & Boulvain, 1993;Brunton & Dixon, 1994;Flajs & Hüssner, 1993;Gischler et al., 2021;Shen et al., 2010).For additional thin section photos and detail descriptions, see Figures S2-S4, Text S3 in Supporting Information S1.

An Already Restricted Depositional Environment
The Usseln Limestone was deposited in an environment that was already restricted prior to the Lower Kellwasser Event.The scarce fossil-content at Winsenberg and Arfeld is dominated by offshore conodonts as nekton, and ostracods as benthos.Such a low diversity assemblage suggests unfavorable seafloor conditions for most marine life, including dysoxia (Flügel, 2010;Haq & Boersma, 1998).While the fossil diversity is higher at Steinbruch  S1 in Supporting Information S1 for their coordinates.Depositional settings after Meischner (1971).
Schmidt (Figures S4b-S4g in Supporting Information S1), including high numbers of offshore conodonts (Ziegler & Sandberg, 1990), the consistent preservation of microbial textures suggests an absence of grazers, and microbial deposits are generally indicative of hostile bottom environments including low oxygen levels (Browne et al., 2000;Chen & Lee, 2014;Garcia-Pichel et al., 2004;Levin et al., 2009;Noffke et al., 2016).The clay-rich layers in Arfeld lack bioturbation throughout.Winsenberg is mostly bioturbated, suggesting at least intermittent oxygenation.Pyrite crystals are scattered throughout all three Usseln Limestones.Large crystals occur at the base of Winsenberg and Arfeld, and oxidized crystals in Steinbruch Schmidt.Sometimes, pyrite is associated with organic matter degradation (Figures S3a and S3e in Supporting Information S1) but the larger crystals probably reflect diagenesis deeper within the sediment (Bond et al., 2004).The organic matter content increases halfway throughout the Winsenberg and Arfeld samples, as indicated by the darker color (Figures 2a and 2b).This organic matter increase suggests enhanced productivity and/or better preservation under low oxygen.The uppermost 0.5 cm of the Steinbruch Schmidt sample is also black (Figure 2c).However, this may represent a diagenetic incorporation of the overlying Lower Kellwasser black shale via calcite cementation.The same may be true for the top of the Arfeld sample (Figure 2b).Gereke (2007) observed the same in the uppermost 0.5 cm at Winsenberg, but this was not present in our sample.

Rhythmical Banding Reflects a Primary Environmental Signal
Attempts to correlate the Usseln Limestone at the dm-and cm-scale layer level require these layers to contain a primary signal that reflects basin-wide environmental changes, rather than local diagenetic changes.Both early and late diagenetic features are observed, but several lines of evidence point to a primary origin of these layers.
Early diagenesis is indicated by differential compaction at Winsenberg and Arfeld.Fractures in the clay-poor layers transition into soft-sediment deformation of the clay-rich layers, suggesting early cementation of the former (Figures S7a-S7b in Supporting Information S1).Similarly, preservation of the clotted texture at Steinbruch Schmidt suggests early cementation of microbial carbonate (Figure S7c in Supporting Information S1) (Dupraz et al., 2004).Sharp boundaries between clay-poor and clay-rich layers at Winsenberg and Arfeld, as well as nodule formation, also point to diagenetic enhancement of the original boundaries between the different sediment types.Later stage diagenesis resulted in calcite-filled subvertical fractures throughout all three samples that cut across the boundaries of the alternating layers.
The primary origin of the Steinbruch Schmidt Usseln Limestone alternations is evidenced by the preservation of original microbial textures.Moreover, bioturbation at Winsenberg caused mixing of the clay-rich and -poor zones, which necessitates the presence of a primary distinction between these two sediments (Figure S7d in Supporting Information S1) (Nohl et al., 2019).Laminae within the clay-rich layers at Winsenberg and Arfeld bend around the early cemented clay-poor layers instead of crossing the layer boundary, suggesting this was original bedding that was subsequently distorted.Finally, the abundance of ostracods seems to differ between clay-rich and clay-poor layers at Arfeld, pointing to different environmental conditions within these sediments.Ostracod shells are calcitic and therefore unlikely to be dissolved during early diagenesis (Nohl et al., 2019).In all three intervals, the rhythmic banding is preserved in one lithified limestone bed.The main diagenetic biases, early and late, are caused by CaCO 3 redistribution, though, this interval has imported CaCO 3 throughout, "cementing" original differences.We therefore infer that all three rock units preserve a primary signal of alternating depositional environments that has been subsequently diagenetically enhanced.

High-Resolution Correlations Within a Time-Specific Facies
We evaluate four scenarios concerning the internal correlation between Usseln Limestone samples: a) The Usseln Limestone is entirely isochronous.Top and bottom correlate across all three sites (Figure 3a); b) The top of the Usseln Limestone (and therefore the base of the Lower Kellwasser black shale) is isochronous, but the base is diachronous (Figure 3b); c) The base of the Usseln Limestone is isochronous, but the top is diachronous (Figure 3c); d) Both the top and base are diachronous (Figure 3d).
No evidence for erosional surfaces, hiatuses or handgrounds within the studied sections was found.We therefore do not consider any time within the limestones to be missing due to (a lack of) syndepositional processes.There is, however, missing time at Steinbruch Schmidt due to postdepositional pressure solution, as evidenced from stylolites (Section 5.1).

Number and Nature of Alternations
The number of alternations varies greatly between different sites: not just between Winsenberg, Arfeld, and Steinbruch Schmidt, but also between additional sites with alternation counts available from Gereke (2007) (Figure S1 in Supporting Information S1; see also Figure 1c).Winsenberg has the most layers (N = 42), followed by Steinbruch Schmidt (N = 27) and Arfeld (N = 21) (Figure 2; Figure S1 in Supporting Information S1), with the caveat that the Steinbruch Schmidt layers are the most ambiguous and thus most susceptible to miscounts (Text S1 in Supporting Information S1).In the absence of visible hiatuses, a mismatch in alternations could have arisen from different sedimentation rates, recording environmental changes of different duration.In this scenario, sites with lower sedimentation rates (Arfeld, Steinbruch Schmidt) would only have recorded low frequency fluctuations, while higher sedimentation rates at Winsenberg would have enabled the recording of higher frequency fluctuations.However, in this case one would expect both high and low frequency fluctuations to be visible at Winsenberg.As there is no such hierarchy visible in either elemental record fluctuations or facies alternations, the mismatch is unlikely to be caused by sedimentation rate differences between sites (Figures 2a-2c).This mismatch in alternations then argues against a completely isochronous Usseln Limestone (scenario a).At Steinbruch Schmidt, horizontal stylolites indicate missing material and time, potentially including entire layers.Additionally, the microbial component of the alternations may have accreted more rapidly than the abiotic component.Modern estimates for shallow water microbial mat growth are in the mm/yr range (Buffan-Dubau et al., 2001;Garcia-Pichel et al., 2004;Laval et al., 2000;Rasmussen et al., 1993), but it is unclear whether these are suitable analogs for ancient deeper water microbialites, which likely grew slower.These rates also include organic matter and original porosity, both of which have long disappeared here.Taking these factors and the presence of stylolites into account, the overall time represented by one alternation in Steinbruch Schmidt might still be comparable to Winsenberg and Arfeld.Yet, these factors certainly complicate layer-by-layer correlations.

Facies and Elemental Trends
Comparing facies and (Ti + K)/Ca trends in Figure 2, the base of the Winsenberg and Arfeld Usseln Limestone show striking similarities.Both Usseln Limestones start with a few thick (>2 cm) alternations, followed by an interval with thinner (1-2 cm) alternations and massive pyrite crystals, and then a monotonous, clay-poor interval (Figures 2a and 2b).The (Ti + K)/Ca record shows a decrease in amplitude of the first ∼9 alternations in Arfeld and Winsenberg prior to this monotonous interval.A similar trend in decreasing (Ti + K)/Ca amplitude can be seen at Steinbruch Schmidt, from ca. 0-12 cm (Figure 2c).In the second half of the record, an increase in organic material (dark color) is observed from 42 cm upward at Winsenberg and from 30 cm upward at Arfeld.These observations suggest that at least for Winsenberg and Arfeld, both the lower and upper part are roughly correlatable and therefore support scenario a.

Contextual Clues From Basin Geometries and Water Depth
The mismatch in alternation count between the sites makes an isochronous base and top (scenario a) unlikely.Winsenberg has the most alternations and is inferred to represent the longest duration.This raises the question of where time is missing at Arfeld and Steinbruch Schmidt-at the base, at the top, or both?

Time Is Missing at the Base
The Lower Kellwasser Event is sometimes associated with a brief transgression (Bond & Wignall, 2008;Buggisch, 1991;Johnson et al., 1985;Stephens & Sumner, 2003).A rapid transgression at the base of the Lower Kellwasser Event would make the Usseln Limestone's top isochronous, if the contact is conformable.A conformable contact fits with a deepening sequence seen in the uppermost few centimeters at Steinbruch Schmidt: The microbial layers make place for a darker bioclastic packstone prior to black shale deposition (Figure S4b in Supporting Information S1).In addition, the increase in organic carbon at Arfeld up into the overlying black shale appears gradual (Figure 2b).These observations argue for scenario b.The diachronous base in this scenario could be related to a carbonate productivity increase in shallower waters, which would have first been recorded in the shallower sites Winsenberg and Steinbruch Schmidt.

Time Is Missing at the Top
No indicators for hardground formation or scouring were identified at the top of any studied sample.Still, carbonate dissolution linked to an increased amount of organic matter input and degradation may have resulted in the loss of the upper part of the Arfeld and Steinbruch Schmidt Usseln, relative to Winsenberg.Such a mechanism fits scenario c, and an increase in organic matter is clearly seen in the upper part of all three samples (Figure 2).However, this mechanism is at odds with the basin geometry.Productivity is expected to have been highest near the coast and in surface waters.Therefore, Winsenberg and Steinbruch Schmidt would have been more affected by carbonate dissolution than Arfeld (Figure 1b).Even assuming miscounting of the alternations at Steinbruch Schmidt, this might reconcile Arfeld and Steinbruch Schmidt, but not Arfeld and Winsenberg.Similar geometryrelated issues arise when assuming a diachronous Lower Kellwasser black shale base.The number of alternations in that case suggests anoxia developed at Arfeld, Steinbruch Schmidt, and Winsenberg consecutively.However, neither anoxia rising up from the basin floor, nor anoxia extending from the continent, nor anoxia spilling over the submarine high from the open ocean explains this pattern (Figure 1b).A more complicated and speculative explanation could be that Winsenberg's location was protected longer from anoxic waters via oxygenated bottom currents.This hypothesis fits with the intermittent oxygenation inferred from bioturbation at Winsenberg, but the thin-sections show no current-induced microfacies.

High-Resolution Correlating With DTW
The above lines of evidence provide tentative support for a diachronous base.As an alternative approach to the problem, we experimented with DTW for Winsenberg-Arfeld, Winsenberg-Steinbruch Schmidt, and Arfeld-Steinbruch Schmidt correlations.One-to-one correlation with DTW is fast and more objective than manual correlation (see Text S1 in Supporting Information S1 for user inputs and constraints).The four hypotheses were tested by prescribing a closed start/end to represent an isochronous base/top, and an open start/end to represent a diachronous base/top (Figure 3).In the main text, results for DTW correlations using (Ti + K)/Ca are presented.

10.1029/2024GL109392
Additionally, we used Ca, Fe, Ti, K, and K/Ti depth-series for automated correlation, with their corresponding results reported in Tables S2-S5, Figures S8-S12 in Supporting Information S1.
As DTW optimizes correlations via distance minimization, normalized distances are one metric to evaluate performance (with a low distance corresponding to a good fit).However, this metric was not particularly useful here, as the normalized distance decreases when open starts or ends are allowed and the algorithm is given more freedom (Tables S2-S4 in Supporting Information S1).The consistency of correlations across proxies is a better metric to evaluate performance, as a real correlation would produce similar results for different proxies.We thus deem a consistent correlation across an ensemble of proxies more reliable, even if its mathematical fit is not as good as other options.For Winsenberg-Arfeld and Winsenberg-Steinbruch Schmidt, the correlation with an open (diachronous) start and closed (isochronous) end (scenario b) appears the most consistent (Figures S9 and S10 in Supporting Information S1).The Arfeld-Steinbruch Schmidt DTW solution is similar across all four options and suggests a correlation at both base and top (Figure S11 in Supporting Information S1).This similarity remains when the reference record is switched from Arfeld to Steinbruch Schmidt (Figure S12 in Supporting Information S1).The correlation is also internally consistent at dm-scale resolution, since the base of both Arfeld and Steinbruch Schmidt correlate to around 10 cm height within Winsenberg (Figures S9c and S10c in Supporting Information S1).We therefore present this DTW result as the most likely internal correlation of the Usseln Limestone, in alignment with scenario b (Figure 4).This outcome is consistent with inferences from the depositional context and layer counts.
We emphasize that this interpretation largely pertains to the dm-scale resolution.Figure 4a provides one correlation (with (Ti + K)/Ca), but cm-scale, layer-by-layer correlations vary per elemental record.This is to be expected, as in nature sedimentation style is not homogenous across a basin, and different regions produce material at a different reach and rate than others.Diagenetically induced condensation of the clay-rich facies (especially at the top of Arfeld and Steinbruch Schmidt) may also have obscured minor shifts in the elemental records.Which one of these layer-by-layer correlations is more realistic is difficult to answer with the data at hand.Dynamic Time Warping is a useful correlation tool to use alongside other approaches, but in this case, correlating the individual alternations proved to be too complex and perhaps impossible, owing to the different nature of accumulation at Winsenberg/Arfeld and Steinbruch Schmidt and the considerable distances (50 km at present) between sites.
The proposed scenario suggests a synchronous emergence of Lower Kellwasser black shales across the basin and at different depths, aligning with a transgressive mechanism.This scenario requires an abrupt increase in nutrient supply and enhanced surface productivity throughout the studied basin, leading to a rapid deoxygenation of large parts of the basin floor.Such swift changes are likely tied to a climatic or oceanographic mechanism, potentially involving increased nutrient input from the continent via runoff or aeolian influx, and/or from upwelling through basin circulation changes.The intermittent oxygenation observed during the Lower Kellwasser depositional interval (Gereke, 2007), as also documented in younger Devonian anoxic events (Becker, Piecha, et al., 2016;Boyer et al., 2014;Carmichael et al., 2016;Marynowski et al., 2010Marynowski et al., , 2012)), underscores the rapid oscillatory nature of the anoxia.Dysoxic conditions within the Usseln Limestone, prior to the onset of Lower Kellwasser deoxygenation, emphasize the environment's vulnerability to redox fluctuations.Furthermore, the observed rise in organic matter content within the Usseln Limestone prior to the rapid basin deepening suggests that enhanced productivity and/or deoxygenation was initiated prior to the Lower Kellwasser onset.These observations suggest that eustatic transgressions facilitated Kellwasser oxygen deficiencies rather than directly causing them.Our approach may be applied to different basins as well as other Late Devonian anoxic crises, so to better understand the Late Devonian climate system and its susceptibility to oceanic deoxygenation.

Conclusions
What "time-specific" in time-specific facies means, and whether a stratigraphic horizon is iso-or diachronous, always depends on the scale of interest.The Usseln Limestone is a good example of how a well-constrained regional time-specific facies is not necessarily isochronous throughout, despite its characteristic alternations likely being of primary origin.Although no layer-by-layer interpretation was reached, Dynamic Time Warping is shown to be a valuable tool to be used alongside other approaches in high-resolution correlation studies, as long as user input biases are taken into account.Thereby realistic sedimentation rates, as well as the allowance of hiatuses and immediate deposition need to be carefully considered.In general, an ensemble-approach to DTW is recommended over individual single-proxy correlations.For the Usseln Limestone, we infer that the top, but not the base, is likely isochronous.This is in agreement with a rapid onset of Lower Kellwasser black shale deposition across the depositional basin.

Figure 2 .
Figure 2. Usseln Limestone μXRF elemental depth-series and maps.(a-c): Thin section composites and (Ti + K)/Ca depthseries for Winsenberg, Arfeld and Steinbruch Schmidt.μXRF-derived (Ti + K)/Ca ratios serve as a proxy for the detrital fraction and show a clear correspondence to facies banding.At Steinbruch Schmidt, log 10 (Ca) is used instead of Ca to better visualize the variability throughout the record.Note that as the entire ratio is not log-scaled, the x-axis is not in log notation.μXRF-derived element ratios are unitless as they signify the division of counts by counts.The three intervals separated by dotted lines in panels a and b indicate similar facies alternations in Winsenberg and Arfeld (Section 5.2).(d-f) μXRF elemental maps of representative sections.μXRF measurements were done on thick sections with minimally different rock surfaces compared to the corresponding thin sections.

Figure 3 .
Figure 3. Correlation scenarios for the studied Usseln Limestones.For each scenario, a representative DTW correlation is shown between Winsenberg and Arfeld.SBS = Steinbruch Schmidt.(a) Base and top are isochronous.(b) Top is isochronous, while the base is diachronous.(c) Base is isochronous, while the top is diachronous.(d) Base and top are diachronous.Note the normalized (standard scores) y-axis values.