Novel method for determining 234 U-238 U ages of Devils Hole 2 cave calcite

Uranium-uranium (U-U) dating can determine the age of secondary carbonates over greater time intervals than the well-established Th-U dating method. Yet it is rarely applied due to unknowns surrounding the initial U (Ui) 10 value, which result in significant age uncertainties. In order to understand the Ui in Devils Hole 2 cave, we have precisely determined 110 Ui values from phreatic calcite crusts using a Th-U chronology. The sampled calcite crusts were deposited in Devils Hole 2 between 4 and 590 thousand years, providing a long-term look at Ui variability over time. We then performed multi-linear regressions among the Ui values and correlative O and C values. These regressions allow us to predict the Ui value of Devils Hole calcite based upon its O and C. Using this approach and measured present15 day U values, we calculate 110 independent U-U ages of Devils Hole 2 cave deposits. In addition, we used newly measured O, C, and present-day U values to calculate 10 U-U ages that range between 676 and 731 thousand years, thus allowing us to extend the Devils Hole chronology beyond the Th-U-dated chronology while maintaining an age precision of ~2 %. Our results indicate that calcite deposition at Devils Hole 2 cave began no later than 736  11 thousand years ago. The novel method presented here may be used in future speleothem studies in similar hydrogeological settings, 20 given appropriate calibration studies.


Introduction
The mid-20 th Century discovery of 234 U-238 U disequilibrium in natural waters (Cherdyntsev, 1955;Isabaev et al., 1960;Thurber, 1962) unlocked a new geochronometer for sediments and secondary deposits in marine and freshwater settings. The greatest limitation of the 234 U-238 U dating method, however, lies in the uncertainty of the initial  234 U at the time of deposition, as 25 shown in Eq. 1: where  234 Up refers to the present  234 U value,  234 Ui refers to the  234 U value at the time of deposition, λ234 is the decay constant of 234 U, and T refers to the time elapsed since deposition. In marine settings,  234 Ui can be approximated using the known excess 234 U activity in seawater. Ku (1965) was the first to test the 234 U-238 U geochronometer in marine sediments. 30 Although this method has been applied successfully in marine-sourced secondary carbonates (Veeh, 1966;Bender et al., 1979;Ludwig et al., 1991), it has largely been limited as it is now clear that uranium can be mobile subsequent to deposition, such as in mollusks (Kaufman et al., 1971) and corals (Bender et al., 1979;Gallup et al., 1994).
In contrast to seawater, surface and ground waters exhibit a wide spatial and temporal variability in  234 U. As a result, constraining the  234 Ui of freshwater-sourced secondary carbonates is difficult. Uncertainties in past  234 Ui result in 234 U-238 U 35 age uncertainties that are orders of magnitude greater than those common for 230 Th-234 U dating technique. 230 Th-234 U dating has thus remained the preferred method for determining the age of secondary carbonates that have been deposited between modern day and 600 thousand years (ka) before present (BP), when 230 Th and 234 U are very close to secular equilibrium.
However, with a firm understanding of past source water  234 Ui, the 234 U-238 U method represents a powerful geochronometer that can reach much deeper in time (Gahleb et al., 2019). 40 Devils Hole (DH) and neighboring Devils Hole 2 (DH2) caves are ideal settings for the study of groundwater  234 Ui variations over time. The walls of both steep fractures are coated with thick (up to ~90 cm) layers of calcite deposits that have precipitated subaqueously at a rate of approximately 1 mm per 1000 years Moseley et al., 2016). Small variations in calcite  234 Ui (1851-1616 ‰) over the last 500 ka BP have been precisely determined Wendt et al., 2019).
Due to the high initial 234 U excess in DH and DH2 calcite (mean  234 Ui = 1750 ‰), the 234 U-238 U method can be used to 45 determine the age of cave calcite as old as 2.5 million years. Ludwig et al. (1992) were the first to calculate 234 U-238 U ages from DH calcite. To do so, they derived the  234 Ui value from 21 230 Th-234 U ages between 60-350 ka. From this dataset they calculated the median  234 Ui value (1750 ‰) and associated uncertainty ( 100 ‰); the latter was derived from the range of  234 Ui over the selected time period. Using this  234 Ui value, 18 234 U-238 U ages were calculated. The ages ranged between 385-568 ka BP with mean uncertainties of 20 ka (3-5 % relative 50 uncertainty) .
Building upon the pioneering work of Ludwig et al. (1992), we aim to decrease the uncertainties of DH and DH2  234 Ui in order to improve the precision of 234 U-238 U ages. Previous work in DH cave revealed a negative correlation between  234 Ui and  18 O, and a positive correlation between  234 Ui and  13 C over the last 500 ka BP . Similar correlative patterns were obtained over the last 200 ka BP using independently obtained drill cores from DH2 (Moseley et al., 2016). In 55 this study, we show that by accounting for changes in  234 Ui with respects to  18 O and  13 C, we can reduce the uncertainty in https://doi.org/10.5194/gchron-2020-26 Preprint. Discussion started: 25 August 2020 c Author(s) 2020. CC BY 4.0 License.  234 Ui by 35 %, thereby reducing the uncertainty in 234 U-238 U ages to about ± 13 ka within a several hundred-thousand-year range. We then use this method to calculate the age of calcite that was deposited in DH2 prior to (older than) the limit of 230 Th-234 U dating (~600 ka BP). Doing so allows us to extend the independently derived radiometric chronology and determine the time at which calcite first deposited in DH2. 60

Regional Setting
DH and DH2 caves are located 100 m apart in a detached area of Death Valley National Park in southwest Nevada (36°25′ N, 116°17′ W; 719 m above sea level). Bedrock of the study area is composed of carbonates from the Bonanza King Formation of middle and late Cambrian age (Barnes and Palmer, 1961). The caves follow a pair of deep, planar, steeply dipping faultcontrolled open fissures roughly 5 m wide, 15 m long, and at least 130 m deep . Evidence for the tectonic 65 origin of these caves includes the spreading and the orientation of their planar opening, which is perpendicular to the northwestsoutheast principal stress direction that has prevailed in this part of the Great Basin for the last 5 million years (Carr, 1974).
DH and DH2 both intersect the water table of the Ash Meadows Groundwater Flow System (AMGFS), which is a large (~12,000 km 2 ) aquifer hosted in Paleozoic limestones (Winograd and Thordarson, 1975). The AMGFS is primarily recharged by infiltration of snowmelt and rainfall in the upper elevations of the Spring Mountains (~500 mm a -1 ; Winograd and 70 Thordarson, 1975;Thomas et al., 1996;Winograd et al., 1998;Davisson et al., 1999). Quaternary extensional tectonics in this area has produced an underground network of open fractures which contribute to the high transmissivity of the aquifer.
Previous studies suggest groundwater transit times of < 2000 years from the Spring Mountains to DH/DH2 caves (Winograd et al., 2006). Due to the long flow path (> 60 km), prolonged residence time, and the retrograde solubility of calcite, the groundwater flowing southwest through both caves is very slightly supersaturated with respect to calcite (SI = 0.2; Plummer 75 et al., 2000). The caves are < 1.5 km upgradient from a line of springs that represent the primary discharge area of the AMGFS.
Calcite has been continuously depositing as dense mammillary crusts on the submerged walls DH and DH2 over much of the last 1 million years at a very slow rate of roughly 1 mm ka -1 Winograd et al., 2006;Moseley et al., 2016).
The thickness (≤ 90 cm) of mammillary calcite crusts implies a long history of calcite-supersaturated groundwater. Regional groundwater transmissivity is maintained despite calcite precipitation due to active extensional tectonics . 80

Methods
A 670 mm-long core was drilled from the hanging wall of DH2 cave at + 1.8 m relative to the modern water table (r.m.w.t.).
The first 654 mm of the core consists of calcite; the last 16 mm of the core consists of bedrock. The core consists of two types of calcite: folia and mammillary calcite. For a full description of the petrographic and morphological differences between both forms of calcite see Wendt et al. (2018). Briefly, mammillary calcite precipitates subaqueously, while folia calcite forms at the 85 water table in a shelf-like formation. The presence of folia in the core is an indicator of paleo-water table near + 1.8 m r.m.w.t. https://doi.org/10.5194/gchron-2020-26 Preprint. Discussion started: 25 August 2020 c Author(s) 2020. CC BY 4.0 License.
The selected core was cut longitudinally and polished. The core was surveyed for growth hiatuses and features indicative of changing deposition mechanisms and rates (such as folia). Folia was identified at 77.7-97.4 mm (as reported in Moseley et al., 2016), 171.4-199.2 mm, 209.4-229.0 mm, and 305.0-323.0 mm (distances are reported from top of the calcite sequence). In addition, a growth hiatus was discovered between 587.4 and 589.0 mm (supplementary Fig. 1). 90 The mammillary calcite portions of the core were 230 Th-234 U dated at regular intervals (n = 110). As described in Moseley et al. (2016), folia calcite cannot be reliably dated. Results for the first 91 230 Th-234 U ages were published by Moseley et al. (2016) and Wendt et al. (2019). Nine additional 230 Th-234 U ages were measured between 351.0 and 562.0 mm using identical methodology to the aforementioned publications. The purpose of additional 230 Th-234 U ages is to extend the DH2 chronology toward secular equilibrium (about 600 ka BP). Between 608.2-652.0 mm, 10 new  234 U measurements were collected for this 95 study. To do so, calcite powders were hand drilled at approximately 1 cm intervals and spiked following the 230 Th-234 U methods cited above. The uranium aliquots were then extracted and measured following the methods described in Cheng et al. (2013).
Chemical blanks were measured with each set of 10-15 samples and were found to be negligible (< 50 ag for 230 Th, < 100 ag for 234 U, and < 1 pg for 232 Th and 238 U).
Samples for stable isotope measurements were micromilled continuously at 0.1-0.2 mm intervals along the core axis between 100 0-158 mm and presented by Moseley et al. (2016). The values of two to three stable isotope measurements (0.1-0.2 mm in width) were averaged in order to pair with 230 Th-234 U subsamples, which averaged 0.3 to 0.5 mm in width. Between 169.8-652.0 mm, 66 new stable isotope samples were micromilled at the location of each 230 Th-234 U and  234 U measurement published by Wendt et al. (2019). Similarly, 2-3 stable isotope measurements were averaged to encompass the width of uranium isotope subsamples. Calcite powders were analyzed using a Delta V plus isotope ratio mass spectrometer interfaced with a Gasbench 105 II. Values are reported relative to VPDB with 1-sigma precisions of 0.06 and 0.08‰ for  13 C and  18 O, respectively.
A statistical model was built to predict  234 Ui values using  18 O and  13 C based on the correlation observed between measured  234 Ui and stable isotope values from 4 to 590 ka BP. Software OriginPro (version 2015) was used to conduct all correlation and regression analyses (Moberly et al., 2018). Several types of models fitted with linear, quadratic, and cubic regression methods were built. The model that provided the best estimate of the measured  234 Ui values was selected. Using this model, 110 a statistically derived (SD)  234 Ui value can be determined based on known  18 O and  13 C values. The SD  234 Ui and measured  234 Up can then be used to calculate 234 U-238 U ages (Eq. 1). The 234 U decay constant of 2.82206  0.00302 10 -6 a -1 (Cheng et al., 2013) was used. We validated our methodology and uncertainty estimates by comparing 230 Th-234 U and 234 U-238 U dates obtained for samples younger than 590 ka BP.
Using this dataset, we calculated 120 234 U-238 U ages for samples in total. With these 234 U-238 U ages as input, we calculated an 115 age model using the Bayesian statistical software OxCal version 4.2 (Bronk Ramsey and Lee, 2013). Age models were https://doi.org/10.5194/gchron-2020-26 Preprint. Discussion started: 25 August 2020 c Author(s) 2020. CC BY 4.0 License. calculated under deposition sequence "P" with k-parameter set to 0.1 (Bronk Ramsey and Lee, 2013). The positions of growth hiatuses, including folia calcite, were incorporated into the age model as growth boundaries.

Results
The new 230 Th-234 U ages (denoted in subsequent text as 230 Th ages for simplicity) are in stratigraphic order within uncertainties. 120 238 U and 232 Th concentrations fall within the range of previous data published by Moseley et al. (2016) and Wendt et al. (2019).
The time-depth consistency and reproducibility of ages argue against open-system processes. The existence of a ca. 67-kalong growth hiatus between 587.4-589.0 mm is supported by U-series ages (see supplementary materials).
In this study we split the  234 Ui dataset into three sections (4-309 ka, 309-355 ka and 355-590 ka BP). The sections were divided according to the level of uncertainty in  234 Ui derived from 230 Th ages (see Table 1 and Supplementary Table 2). The 125 average  234 Ui was the same within uncertainties regardless of how we grouped the data, implying no detectable trend in  234 Ui with time. DH2 oxygen isotope values reveal a negative correlation with  234 Ui over the last 590 ka BP (0-578 mm along the core axis; r = -0.52 (n = 110, p  0.05)), whereas carbon isotopes reveal a positive correlation (r = 0.71 (n = 110, p  0.05); Fig. 1 and 130 Table 2). The linear relationships presented here are consistent with results from Moseley et al. (2016) and Ludwig et al. (1992) in DH2 and DH cave, respectively. The anti-correlation between  18 O and  234 Ui is consistent with the interpretation presented in Wendt et al. (2019) such that periods of increased regional moisture availability (due to cooler, wetter conditions favoring depleted  18 O values) are associated with increased DH  234 Ui values. A full list of correlation calculations among  234 Ui,  18 O and  13 C is presented in Table 2. The linear relationship between  13 C and  234 Ui is closer than that between  18 O and  234 Ui 135 for the same period. This is likely due to the fact that  13 C and  234 Ui are forced by local processes, including changes in vegetation density at the principle recharge zone and groundwater interaction with bedrock in the vadose zone (see Coplen et al., 1994 andWendt et al. 2019 for proxy interpretation). Since changes in the local environmental and hydrological regime are closely interconnected, we expect similar trends in the timing and pattern of  13 C and  234 Ui signals. In contrast, DH/DH2  18 O reflects the  18 O of meteoric precipitation, which is sensitive to atmospheric temperatures and changes in moisture source 140 https://doi.org/10.5194/gchron-2020-26 Preprint. Discussion started: 25 August 2020 c Author(s) 2020. CC BY 4.0 License. (Winograd et al., 1998;Mosley et al., 2016). Evidence suggests no secular temperature changes in the local aquifer over the last several glacial-interglacial cycles (Kluge et al., 2014;J. Fiebig, pers. comm.), thus DH/DH2  18 O is expected to be minimally influenced by aquifer-related processes. Overall, we expect a greater scatter in the  18 O vs.  234 Ui regression due to the compounding forcings that influence  18 O on a much larger spatial scale.  regardless of  234 Ui precision. We therefore explored various time ranges and types of regressions in order to determine the most precise predictor of  234 Ui based upon  18 O and/or  13 C.

Regression Analysis
We evaluated the linear and polynomial (quadratic and cubic) regression methods primarily by calculating the coefficient of determination (COD), i.e. R 2 . The R 2 value represents the percentage of variation of the SD  234 Ui in terms of the total of 155 https://doi.org/10.5194/gchron-2020-26 Preprint. Discussion started: 25 August 2020 c Author(s) 2020. CC BY 4.0 License.
observed  234 Ui. To further compare the robustness between different models, we adjust the R 2 values from the different numbers of predictors, i.e. the degree of freedom (DF) of the predictors. The adjusted R 2 (Adj. R 2 ) values is shown in Table 3. Note: the robustness of the regression model can be evaluated by coefficient of determination (COD), R 2 , which is defined as R 2 = 1 -(residual sum of squares, RSS)/(total sum of squares, TSS). Adj. R 2 = 1-(RSS/(DF of residual))/(TSS/(DF of total predictors)).

160
Among the various models, the multiple linear regression (MLR) for the time period of 4-309 ka BP in terms of both  18 O and  13 C yielded the highest Adj. R 2 value of 0.63, such that over this time span the model accounts for 63 % of the  234 Ui variability (Table 3). The corresponding equation is as follows (cf. We then applied statistical methods to test the robustness of the chosen model, starting with the F test. This tests whether the 165 model differs significantly from a 'y = constant' model. The F value is computed by dividing the mean square of the fitted model by the mean square of the residual. The more this ratio deviates from 1, the stronger the indication that the model differs from the 'y = constant' model. The test returned F = 52.5, far larger than the critical value of the F test at a significance level of α = 0.01 (DF of numerator = 2; DF of denominator = 65) (Fcrit = 4.95), indicating that the model is tenable. Second, we performed a "t-test" to check if every term in the MLR for 4-309 ka is significant. The t value is the ratio of the fitted value to its standard error. As shown in the Table 4, all the fitted values (coefficients and intercept) are significant at a significance level of α = 0.001. Thus, the regression model is robust.

Residual Analysis 175
We now estimate the uncertainty of the SD  234 Ui values by analyzing the residuals, defined as the differences between the observed and predicted values. Figure 2 reveals that the residuals are basically normally distributed. Thus, we conclude that the regression model captures the dominant characteristic of variability of the observations. The estimate of the residuals yields uncertainty of  60.5 ‰ (95 % confidence interval) with an average of essentially zero (4.4E-13). We take the  60.5 ‰ value to represent a constant uncertainty for all the SD  234 Ui values, amounting to a ~40 % reduction in  234 Ui uncertainties (the 180 original estimate of uncertainty from Ludwig et al. (1992) was 100 ‰). Figure 3 plots residuals versus time. The residuals have a full range of about 120 ‰ and exhibit multi-millennial to orbital scale variability.

234 U-238 U Ages
Using Eq. 1 and 2, we can calculate the 234 U-238 U ages (denoted in subsequent text 234 U for simplicity) for each data point for which  234 Up,  18 O and  13 C are measured. The final uncertainty of 234 U ages comes from two sources: 1) the uncertainty of the model and 2) the uncertainty in determination of  234 Up. Combined, the final uncertainty of 234 U ages before 590 ka BP is approximately ± 13 ka (2σ), which represents a 35 % improvement relative to previously reported 234 U ages from DH (± 20 190 ka;Ludwig et al., 1992).
The 234 U and 230 Th ages between 4 to 590 ka BP are consistent within uncertainties (Fig. 4), with the exception of 4 ages (out of 110) at 27 ka, 348 ka, 410 ka and 503 ka BP). Since uncertainties are reported at the 95 % confidence level, we would expect this number of statistical outliers and conclude that our analysis is overall internally consistent. Alternately, there may be some unknown underlying process not captured by our analysis, which may be consistent with the variability of the residual 195 (Fig. 3).

234 U ages beyond 230 Th-234 U secular equilibrium
The consistency between 234 U and 230 Th ages within the time range 4 to 590 ka BP suggests that it is reasonable to utilize this model to calculate ages that are close to or beyond 230 Th-234 U secular equilibrium. Using measured  234 Up,  18 O and  13 C 205 values, we calculated 10 234 U ages for DH2 cave deposits older than 600 ka BP over the depth of 608 to 652.0 mm ( Table 5).
The 234 U ages are in stratigraphic order within uncertainty.  (Fig. 5) is due to the fact that ≥ 10 215 half-lives of the 234 U will have elapsed and the  234 Up values increasingly approach the uncertainty of their measurement. Figure 6 shows an OxCal-derived age model with 95 % confidence intervals plotted over depth using all 234 U ages with their 2σ uncertainties. Location of folia and a growth hiatus are highlighted. Two lines of evidence suggest that the resulting time series is reasonable. Firstly, the average growth rate during the whole period is at 0.9  0.3 mm ka -1 (1σ uncertainty; Fig. 7), 220 which is broadly consistent with growth rates reported by Moseley et al. (2016). Secondly, all 234 U ages are in stratigraphic order within uncertainties and fall within the 95 % confidence interval of our age model, implying no major outliers.  Previous investigations revealed that DH2 cave opened to the surface at approximately 4 ka BP (Moseley et al., 2016), likely due to surface collapse processes . The timing at which the main fissure opened, however, remains largely unknown. By 234 U dating the oldest calcite deposited on our studied core (at the calcite-bedrock boundary), we can determine 235 the earliest-possible timing at which the DH2 fissure existed (without which calcite cannot precipitate). 234 U ages in the last 170 mm of the core are in stratigraphic order within uncertainties (Fig. 8) yet due to the slight scatter of absolute ages, we utilize our OxCal age model to extrapolate the age at calcite-bedrock boundary. In doing so, we determine the earliest calcite deposition at our study location (+ 1.8 m) to 736 ± 11 ka BP (Fig. 8).

Timing and rate of calcite deposition
The onset of calcite deposition in DH2 cave is in agreement with the recent geologic history of this region. The orientation of 240 DH and DH2 are in accord with the principal northwest-southeast stress direction in this part of the Great Basin that has prevailed over the last 5 Ma (Carr, 1974), suggesting that one or both fissures formed after 5 Ma BP. Abundant calcareous and siliceous spring and marsh deposits in Ash Meadows and the Amargosa Desert of Pliocene age (2.1 to 3.2 Ma BP; Hay et al., 1986) and groundwater-deposited calcite veins in alluvium and colluvium of Pleistocene age (500 to 900 ka BP; Winograd and Szabo, 1988) indicate that groundwater in the discharge zone of AMGFS has been continuously supersaturated with respect 245 to calcite for at least the last 3 Ma. Our results, which suggest that the DH2 fissure opened no later than 736 ka BP, is therefore in agreement with the modern understanding of the AMGFS' geological history.