the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Novel method for determining ^{234}U–^{238}U ages of Devils Hole 2 cave calcite (Nevada)

### Kathleen A. Wendt

### Yuri Dublyansky

### Gina E. Moseley

### Christoph Spötl

### R. Lawrence Edwards

Uranium–uranium (^{234}U–^{238}U) disequilibrium
dating can determine the age of secondary carbonates over greater time
intervals than the well-established ^{230}Th–^{234}U dating method. Yet
it is rarely applied due to unknowns in the initial *δ*^{234}U
(*δ*^{234}U_{i}) value, which result in significant age
uncertainties. In order to understand the *δ*^{234}U_{i} in Devils
Hole 2 cave, Nevada, we have determined 110 *δ*^{234}U_{i} values
from phreatic calcite using ^{230}Th–^{234}U disequilibrium dating. The
sampled calcite was deposited in Devils Hole 2 between 4 and 590 ka,
providing a long-term look at *δ*^{234}U_{i}
variability over time. We then performed multi-linear regression among the
*δ*^{234}U_{i} values and correlative *δ*^{18}O and
*δ*^{13}C values. The regression can be used to estimate the *δ*^{234}U_{i} value of Devils Hole calcite based upon its measured
*δ*^{18}O and *δ*^{13}C values. Using this approach and the
measured present-day *δ*^{234}U values of Devils Hole 2 calcite, we
calculated 110 independent ^{234}U–^{238}U ages. In addition, we used
newly measured *δ*^{18}O, *δ*^{13}C, and present-day *δ*^{234}U values to calculate 10 ^{234}U–^{238}U ages that range
between 676 and 731 ka, thus allowing us to extend the Devils Hole
chronology beyond the ^{230}Th–^{234}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 kyr ago. The novel method presented here may be applied to future
speleothem studies in similar hydrogeological settings, given appropriate
calibration studies.

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^{234}U–

^{238}U ages of Devils Hole 2 cave calcite (Nevada), Geochronology, 3, 49–58, https://doi.org/10.5194/gchron-3-49-2021, 2021.

The mid-20th 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 in marine and freshwater
settings. The greatest limitation of the ^{234}U–^{238}U dating method,
however, lies in the uncertainty of the initial *δ*^{234}U (*δ*^{234}U_{i}), as shown in Eq. (1):

where *δ*^{234}U_{p} refers to the present *δ*^{234}U
value, *δ*^{234}U_{i} refers to the *δ*^{234}U value at
the time of deposition, *λ*_{234} is the decay constant of
^{234}U, and T refers to the time elapsed since deposition. In marine
settings, *δ*^{234}U_{i} 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. 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
by the potential mobility of U following deposition, as observed in mollusks
(Kaufman et al., 1971) and corals (Bender et al., 1979; Gallup et al.,
1994).

In freshwater settings, constraining the *δ*^{234}U_{i} of
secondary carbonates is further complicated by the fact that, in contrast to
seawater, terrestrial surface and groundwaters exhibit a wide spatial and
temporal variability in *δ*^{234}U. Uncertainties in
determining past *δ*^{234}U_{i} result in ^{234}U–^{238}U age
uncertainties that are orders of magnitude greater than those common for
^{230}Th–^{234}U disequilibrium dating. ^{230}Th–^{234}U dating has
thus remained the preferred method for determining the age of secondary
carbonates that have been deposited between the modern day and ∼ 600 ka,
at which secular equilibrium between ^{230}Th and ^{234}U has been nearly restored. However, with a firm understanding of past source-water *δ*^{234}U_{i}, the ^{234}U–^{238}U disequilibrium method is a
powerful geochronometer that can reach deeper in time than
^{230}Th–^{234}U disequilibrium dating (e.g., Gahleb et al., 2019).

The Devils Hole (DH) and neighboring Devils Hole 2 (DH2) caves are ideal
settings for the study of groundwater *δ*^{234}U_{i} 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 (Ludwig et al.,
1992; Moseley et al., 2016). Small variations in calcite *δ*^{234}U_{i} (1851 ‰–1616 ‰) over the last 500 kyr
have been precisely determined by Ludwig et al. (1992) and Wendt et al. (2020).
Due to the high initial ^{234}U excess in DH and DH2 calcite (mean
*δ*^{234}U_{i}=1750 ‰), the
^{234}U–^{238}U disequilibrium method can theoretically
determine the age of DH and DH2 calcite as old as 2.5 Ma.

Ludwig et al. (1992) were the first to calculate ^{234}U–^{238}U ages
from DH calcite. To do so, they derived the *δ*^{234}U_{i} value
from 21 ^{230}Th–^{234}U ages between 60 and 350 ka. From this dataset, they
calculated the median *δ*^{234}U_{i} value (1750 ‰) and
associated uncertainty (±100 ‰); the latter was derived from the range of *δ*^{234}U_{i} over the selected time period. Using this *δ*^{234}U_{i} value, 18 ^{234}U–^{238}U ages were calculated. The
ages ranged between 385 and 568 ka with mean uncertainties of 20 kyr (3 %–5 %
relative uncertainty) (Ludwig et al., 1992).

Building upon the pioneering work of Ludwig et al. (1992), we aim to
decrease the uncertainties of DH and DH2 *δ*^{234}U_{i} in order
to improve the precision of ^{234}U–^{238}U ages. A negative correlation
between DH *δ*^{234}U_{i} and *δ*^{18}O, and a positive
correlation between *δ*^{234}U_{i} and *δ*^{13}C, is
observed over the last 500 kyr (Ludwig et al., 1992). Similar correlative
patterns were obtained over the last 200 kyr using separate drill cores
from DH2 (Moseley et al., 2016) and were shown to be independent of U
concentrations (Fig. S1; Wendt et al., 2020). In this study, we show that by
accounting for changes in *δ*^{234}U_{i} with respect to
*δ*^{18}O and *δ*^{13}C, we can reduce the uncertainty in
*δ*^{234}U_{i} by 40 %, thereby reducing the uncertainty in
^{234}U–^{238}U ages to about ± 13 kyr 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 disequilibrium dating (∼ 600 ka).
Doing so allows us to extend the radiometric chronology and determine the
time at which calcite first deposited in DH2.

## 1.1 Regional setting

The 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 fault-controlled open fissures roughly 5 m
wide, 15 m long, and at least 130 m deep (Riggs et al., 1994). Evidence for
the tectonic origin of these caves includes the spreading and the
orientation of their planar opening, which is perpendicular to the
northwest–southeast principal stress direction that has prevailed in this
part of the Great Basin for the last 5 Myr (Carr, 1974). Parts of these
extensional fractures were later modified by condensation corrosion
(Dublyansky and Spötl, 2015).

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 limestone (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 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)
and prolonged residence time, the groundwater flowing southwest through
both caves is very slightly supersaturated with respect to calcite (SI of 0.2;
Plummer 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 of DH and DH2 over much of the last 1 Myr at a very slow rate
of roughly 1 mm kyr^{−1} (Ludwig et al., 1992; 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 (Riggs et al., 1994).

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 consist of calcite; the last 16 mm of the core consist of bedrock. The core consists of two types of calcite: mammillary calcite and folia. 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 forms at the water table in a shelf-like formation. The presence of folia in the core is an indicator of the paleo-water table near +1.8 m r.m.w.t. at the time of deposition.

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, 209.4–229.0, 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 (Fig. S2).

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. (2020). 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 to the near limit of
^{230}Th–^{234}U dating (about 600 ka). Between 608.2 and 652.0 mm, 10 new
*δ*^{234}U measurements were collected for this study. To do so,
calcite powders were hand drilled at approximately 1 cm intervals and spiked
following the ^{230}Th–^{234}U dating method cited above. The U 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 0 and 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 and 652.0 mm, 66 new stable isotope samples were micromilled at
the location of each ^{230}Th–^{234}U and *δ*^{234}U measurement
published by Wendt et al. (2020). Similarly, two to three stable isotope measurements
were averaged to encompass the width of U isotope subsamples. Calcite
powders were analyzed using a Delta V plus isotope ratio mass spectrometer
interfaced with a Gasbench II. Values are reported relative to Vienna Pee Dee Belemnite (VPDB) with
1*σ* precisions of 0.06 ‰ and 0.08 ‰ for *δ*^{13}C and *δ*^{18}O, respectively.

A statistical model was built to predict *δ*^{234}U_{i} values
based on the correlation
observed between measured *δ*^{234}U_{i} and stable isotope values
from 4 to 590 ka. To calculate the correlation analysis for unevenly
spaced time series, we chose the Fortran 90 program PearsonT3, which can
provide the 95 % calibrated confidence intervals (Olafsdottir and
Mudelsee, 2014). OriginPro software (version 2015) was used to conduct the
regression analyses (Moberly et al., 2018; see detailed description in the
Supplement). Several types of models fitted with linear,
quadratic, and cubic regression methods were built. The model that provided
the best estimate of the measured *δ*^{234}U_{i} values was
selected. Using this model, a statistically derived (SD) *δ*^{234}U_{i} value can be generated based on known *δ*^{18}O and
*δ*^{13}C values. The SD *δ*^{234}U_{i} and measured
*δ*^{234}U_{p} 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.

Using this dataset, we calculated 120 ^{234}U–^{238}U ages for samples
in total. With these ages as input, we calculated an age model using the
OxCal version 4.2 Bayesian statistical software (Bronk Ramsey and Lee,
2013). Age models were calculated under deposition sequence “P” with
the *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.

The new ^{230}Th–^{234}U disequilibrium ages (denoted in subsequent text
as ^{230}Th ages for simplicity) are in stratigraphic order within
uncertainties. ^{238}U and ^{232}Th concentrations fall within the range
of previous data published by Moseley et al. (2016) and Wendt et al. (2020).
The time–depth consistency and reproducibility of ages argue against
open-system processes. The existence of an approximately 67 kyr growth hiatus
between 587.4 and 589.0 mm is supported by ^{234}U–^{238}U ages (see
the Supplement).

In this study, we split the *δ*^{234}U_{i} dataset into three
sections (4–309, 309–355, and 355–590 ka). The sections were divided
according to the level of uncertainty in *δ*^{234}U_{i} derived
from ^{230}Th ages (see Tables 1 and S4). The average *δ*^{234}U_{i} was the same within uncertainties regardless of how we
grouped the data, implying no detectable trend in *δ*^{234}U_{i}
with time.

DH2 oxygen isotope values reveal a negative correlation with *δ*^{234}U_{i} over the last 590 kyr (0–578 mm along the core axis; $r=-\mathrm{0.52}$ with the 95 % confidence interval of [−0.81; −0.06]), whereas
carbon isotopes reveal a positive correlation (*r*=0.71 with the 95 %
confidence interval of [0.57; 0.81]; Fig. 1 and Table 2). The interpretation
of *δ*^{18}O and *δ*^{13}C in DH and DH2 calcite has been
extensively discussed in Winograd et al. (1988, 1992, 2006), Coplen et al. (1994),
and Moseley et al. (2016). DH/DH2 *δ*^{18}O is a reflection
of meteoric precipitation at the principal recharge zones of the AMGFS.
Modern meteoric *δ*^{18}O varies seasonally by *>*10 ‰ in southern Nevada (Ingraham et al., 1991). Winter
precipitation (−12 ‰ to −14 ‰ Vienna Standard Mean Ocean Water; VSMOW) is sourced from
the Pacific and provides the dominant fraction (∼ 90 %) of
aquifer recharge, while summer precipitation (0 ‰ to −3 ‰
VSMOW) is sourced from monsoonal systems from the
gulfs of Mexico and California (see Winograd et al., 1998, for details). We
interpret past variations in DH/DH2 *δ*^{18}O to be the result of
(i) changes in temperature and variations in the path length of moisture
transport through Rayleigh fractionation processes, (ii) changes in *δ*^{18}O values at moisture source regions, and (iii) changes in the
relative contributions of summer versus winter precipitation (see Moseley et
al., 2016, for details). Past DH/DH2 *δ*^{13}C variations have been
argued to reflect the extent and density of vegetation in the recharge zones
of AMGFS, such that *δ*^{13}C minima correspond to periods of
maximum vegetation (Coplen et al., 1994).

Note that all the 95 % confidence intervals do not cross zero,
indicating that all the *r* values are significant.

The linear relationships presented here are consistent with results from
Moseley et al. (2016) and Ludwig et al. (1992) in the DH2 and DH caves,
respectively. The anti-correlation between *δ*^{18}O and *δ*^{234}U_{i} is consistent with the interpretation presented in
Wendt et al. (2020) such that periods of increased regional moisture availability
(due to cooler, wetter conditions favoring depleted *δ*^{18}O
values) are associated with increased DH *δ*^{234}U_{i} values. A
full list of correlation calculations among *δ*^{234}U_{i},
*δ*^{18}O, and *δ*^{13}C is presented in Table 2. The linear
relationship between *δ*^{13}C and *δ*^{234}U_{i} is
closer than that between *δ*^{18}O and *δ*^{234}U_{i} for
the same period. This is likely due to the fact that *δ*^{13}C and
*δ*^{234}U_{i} are forced by local processes, including changes in
vegetation density at the principal recharge zone and groundwater
interaction with bedrock in the aquifer. Since changes in the local
environmental and hydrological regime are closely interconnected, we expect
similar trends in the timing and pattern of *δ*^{13}C and *δ*^{234}U_{i} signals. In contrast, DH/DH2 *δ*^{18}O reflects the
*δ*^{18}O of meteoric precipitation, which is sensitive to regional
atmospheric temperatures and changes in moisture source (Winograd et al.,
1998; Moseley et al., 2016). Evidence suggests no secular temperature
changes in the local aquifer over the last several glacial–interglacial
cycles (Kluge et al., 2014); thus, DH/DH2 *δ*^{18}O is expected to be
minimally influenced by aquifer-related processes. Overall, we expect a
greater scatter in the *δ*^{18}O vs. *δ*^{234}U_{i}
regression due to the compounding forcings that influence *δ*^{18}O on a much larger spatial scale.

From Table 2, we can see that the modulus value $\left|r\right|$ for
*δ*^{18}O and *δ*^{234}U_{i} is greatest in the 4–309 ka
dataset, which represents the time span with the highest precision
*δ*^{234}U_{i} values. In contrast, the $\left|r\right|$
values for *δ*^{13}C and *δ*^{234}U_{i} are similar
regardless of *δ*^{234}U_{i} precision. We therefore explored
various time ranges and types of regressions in order to determine the most
precise predictor of *δ*^{234}U_{i} based upon *δ*^{18}O
and/or *δ*^{13}C.

## 3.1 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 *δ*^{234}U_{i} in terms of the total of observed
*δ*^{234}U_{i}. To further compare the robustness between different
models, we adjusted 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. All models were
calculated without considering the analytical uncertainty of *δ*^{234}U_{i} values (see the Supplement for more
information).

Note that the robustness of the regression model can be evaluated by the
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)).

Among the various models, multiple linear regression (MLR) for the time
period 4–309 ka in terms of both *δ*^{18}O and *δ*^{13}C yielded the highest adj. *R*^{2} value of 0.613 (rounded to 0.61), such that over
this time span the model accounts for 61 % of the *δ*^{234}U_{i} variability (Table 3). The corresponding equation is as
follows (Table 4):

Note that (1) the standard error of fitting parameters was calculated based on
the standard deviation of the residual from the model and used only for the *t* test;
(2) a smaller *p* value represents a decreased likelihood that the
parameter is equal to zero.

We then applied statistical methods to test the robustness of the chosen
model, starting with the *F* test. The *F* value is the ratio of the mean square
of the fitted model to the mean square of the residual. A ratio that
deviates greatly from 1 indicates that the model differs significantly from
the “*y* = constant” model. The test returned *F* equal to 52.5, far larger than
the critical value of the *F* test at a significance level of *α*=0.01 (DF of the numerator is equal to 2; DF of the denominator is equal to 65; *F*_{crit} is 4.95),
indicating that the model is tenable. Additional confidence in the
robustness of the chosen model is derived from the autocorrelation results
(see the Supplement).

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, we conclude the regression model to be robust.

## 3.2 Residual analysis

We now estimate the uncertainty of the SD *δ*^{234}U_{i} values
over the past 309 kyr by analyzing the residuals, which are defined as the
differences between the observed and predicted values. Figure 2 reveals that
the residuals are approximately normal in distribution. Thus, we conclude
that the regression model captures the dominant characteristic of
variability in the observed values. The estimate of the residuals yields an
uncertainty of ±61 ‰ (95 % confidence
interval) with an average of essentially zero (*<*10^{−12}). We
take the ±61 ‰ value to represent a constant
uncertainty for all the SD *δ*^{234}U_{i} values, amounting to a
∼ 40 % reduction in *δ*^{234}U_{i} uncertainties
(the original estimate of uncertainty from Ludwig et al. (1992) was 100 ‰). The analytical uncertainty of ^{230}Th-derived
*δ*^{234}U_{i} is combined with (i) uncertainty of measured
*δ*^{234}U_{p}, which is incorporated into the ^{234}U–^{238}U
ages (see the following section), and (ii) the uncertainty of ^{230}Th
ages which is negligible relative to uncertainty of the model over the past
309 kyr (see Tables 1 and S4 for details). Therefore, we do not take
this analytical uncertainty into account.

## 3.3 ^{234}U–^{238}U ages

Using Eqs. (1) and (2), we then calculated the ^{234}U–^{238}U disequilibrium
ages (denoted in subsequent text as ^{234}U ages for simplicity) for each
data point for which *δ*^{234}U_{p}, *δ*^{18}O and *δ*^{13}C
are measured. The final uncertainty of ^{234}U ages comes from
two sources: (i) the uncertainty of the model and (ii) the uncertainty in
determination of *δ*^{234}U_{p}. Combined, the final uncertainty
of ^{234}U ages before 590 ka is approximately ± 13 kyr (2*σ*; Table S4), which represents a 35 % improvement relative to previously
reported ^{234}U ages from DH (±20 kyr; Ludwig et al., 1992).

The ^{234}U and ^{230}Th ages between 4 and 590 ka are consistent
within uncertainties (Fig. 3), with the exception of four ages (out of 110) at
27, 348, 410, and 503 ka. 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 residuals
(see Fig. S3).

## 3.4 ^{234}U ages beyond ^{230}Th–^{234}U secular equilibrium

The consistency between ^{234}U and ^{230}Th ages within the time range of
4–590 ka suggests that it is reasonable to utilize this model to
calculate ages that are close to or beyond ^{230}Th–^{234}U secular
equilibrium in DH/DH2. Using measured *δ*^{234}U_{p},
*δ*^{18}O, and *δ*^{13}C values, we calculated 10 ^{234}U
ages for DH2 cave deposits older than 600 ka over the depth of 608 to
652.0 mm (Table 5). The ^{234}U ages are in stratigraphic order within
uncertainty.

## 4.1 Uncertainties of ^{234}U ages

Due to the high initial *δ*^{234}U values (1760 ± 61 ‰),
DH/DH2 calcite can theoretically be dated up to 2.5 Ma, assuming that
measured *δ*^{234}U_{p} values have about 1 ‰ absolute uncertainty. By including all the uncertainty described
above, we obtain the following age uncertainty (2*σ*):
∼ 13 kyr uncertainty for a sample *<*500 ka, 16 kyr at
1.0 Ma, 26 kyr at 1.5 Ma, 70 kyr at 2.0 Ma, and 290 kyr at 2.5 Ma.
The rapid increase in uncertainty after 2.5 Ma (Fig. 4) is due to the
fact that ≥ 10 half-lives of the ^{234}U will have elapsed and the
*δ*^{234}U_{p} values increasingly approach the uncertainty of
their measurement.

## 4.2 Timing and rate of calcite deposition

Figure 5 shows an OxCal-derived age model with 95 % confidence intervals
plotted over depth using all ^{234}U ages with their 2*σ*
uncertainties. Locations 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 kyr^{−1}
(1*σ* uncertainty; Fig. 6), which is 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 the DH2 cave opened to the surface at
approximately 4 ka (Moseley et al., 2016), likely due to surface collapse
processes (Riggs et al., 1994). The timing at which the main subsurface
fissure opened, however, remains largely unknown. By ^{234}U dating, the
oldest calcite in our studied core (at the calcite–bedrock boundary), we can
determine 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. 7), yet
due to the slight scatter of ages we utilize the OxCal age model to
extrapolate the age at the calcite–bedrock boundary. In doing so, we
determine the earliest calcite in this core (+1.8 m r.m.w.t.) to 736 ± 11 ka (Fig. 7).

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

We have developed a novel method to determine the *δ*^{234}U_{i}
values in DH/DH2 calcite. We established a robust multiple linear regression
model between *δ*^{234}U_{i}, *δ*^{18}O, and *δ*^{13}C values of DH2 calcite deposited between 4 and 309 ka. We
applied this model to estimate the *δ*^{234}U_{i} of DH2 calcite
using the respective *δ*^{18}O and *δ*^{13}C values. We
refer to the statically derived initial values as SD *δ*^{234}U_{i}. Uncertainty associated with SD *δ*^{234}U_{i}
is ±61 ‰, thereby improving precision by
40 % relative to Ludwig et al. (1992). We then calculated 120 ^{234}U
ages by determining the *δ*^{234}U_{p} and SD *δ*^{234}U_{i} at each age location. Average relative ^{234}U age
uncertainties are 2 %. The concordance between the ^{234}U and the
^{230}Th ages younger than 600 ka indicates that the DH2 calcite
behaves as a closed system. Overall, 10 of the 120 ^{234}U ages are located in the
oldest portion of the studied DH2 calcite core and range from 676 to 730 ka.
Thus, the ^{234}U ages allow us to extend the DH2 chronology beyond
the limits of ^{230}Th dating (*>*600 ka). Using our time
series, we determined that calcite at the base of the studied core was
deposited at 736 ± 11 ka. We argue that this age marks the earliest
possible time at which the DH2 fissure existed.

All the data used in this paper are available in the Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/gchron-3-49-2021-supplement.

RLE conceptualized the project and XL carried it out. KAW, XL, and
RLE prepared the manuscript with contributions from all co-authors. XL
conducted the formal analysis. CS and YD provided the cave samples. KAW and
GEM conducted the ^{230}Th dating work and contributed to stable isotope
measurements. All authors discussed the results and provided input to the
manuscript and technical aspects of the analyses.

The authors declare that they have no conflict of interest.

This research was conducted under research permit nos. DEVA-2010-SCI-0004 and DEVA-2015-SCI-0006 issued by the Death Valley National Park. We thank K. Wilson for assistance in the field and M. Wimmer for assistance in the laboratory. Finally, we would like to thank two anonymous reviewers for their insightful comments on the manuscript.

This research has been supported by the National Science Foundation (NSF) (project no. 1602940) (to R. Lawrence Edwards) and the Austrian Science Fund (FWF) (project nos. P263050 and P327510) (to Christoph Spoetl).

This paper was edited by Norbert Frank and reviewed by two anonymous referees.

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^{234}U in submerged calcite crusts that coat the walls of Devils Hole 2 (DH2) cave (Nevada, USA) and, using a

^{234}U–

^{238}U dating method, extended the chronology of the calcite deposition beyond previous well-established

^{230}Th ages and determined the oldest calcite deposited in this cave, a time marker for cave genesis. The novel method presented here may be used in future speleothem studies in similar hydrogeological settings.

^{234}U in submerged calcite...