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Estimating rock cooling rates by using multiple luminescence thermochronometers
Accepted Manuscript Estimating rock cooling rates by using multiple luminescence thermochronometers Jintang Qin, Jie Chen, Pierre G. Valla, Frédéric Herman, Kechang Li PII:
S1350-4487(15)30025-1
DOI:
10.1016/j.radmeas.2015.05.002
Reference:
RM 5420
To appear in:
Radiation Measurements
Received Date: 15 October 2014 Revised Date:
5 April 2015
Accepted Date: 10 May 2015
Please cite this article as: Qin, J., Chen, J., Valla, P.G., Herman, F., Li, K., Estimating rock cooling rates by using multiple luminescence thermochronometers, Radiation Measurements (2015), doi: 10.1016/ j.radmeas.2015.05.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Estimating rock cooling rates by using multiple luminescence thermochronometers
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Jintang Qin1, Jie Chen1*, Pierre G. Valla2, Frédéric Herman2, Kechang Li3
State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing, China
Institute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerland
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Qinghai Earthquake Administration, Xi’ning, Qinghai Province, China
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*Corresponding author: [email protected], phone number: +86-10-62009093; Postal address: Prof. Jie Chen
Institute of Geology, China Earthquake Administration 903,
P.O.Box 9803,
Huayanlijia
No.1,
Beitucheng
West
Street
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Room
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Chaoyang District, Beijing 100029,China
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ACCEPTED MANUSCRIPT Abstract The potential of luminescence thermochronology is characterized by diverse luminescence signals with different thermal stabilities available for a single rock sample. These signals may
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be exploited together to constrain rock cooling rates. In this study, we performed numerical synthetic experiments to assess the advantages and limitations of using multiple luminescence thermochronometers (MLT) of a hypothetical single rock sample to constrain its cooling rate.
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A series of luminescence traps with typical depths of quartz mineral are investigated (i.e. 1.55
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to 1.70 eV). We use synthetic luminescence saturation ratios predicted from imposed cooling scenarios to assess the benefits of MLT-based forward modeling on constraining rock cooling rates. Our results show that the prescribed cooling rates can be constrained by applying the MLT approach to a single sample, without the requirement of a priori knowledge on the
luminescence
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present-day temperature, which is mandatory for the approach only using a single thermochronometer.
Due
to
the saturation
effect
of luminescence
thermochronometers, the minimum cooling rates that can be constrained with given trap
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depths are also investigated for the MLT approach.
Keywords: Thermochronology; multiple luminescence thermochronometers; cooling rate; numerical sensitivity analysis; present-day temperature
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ACCEPTED MANUSCRIPT 1. Introduction Rocks cool as they travel towards the Earth’s surface in response to exhumation. Their cooling histories can be inferred by measuring radiogenic isotopes or lattice damages in
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mineral crystals (e.g. Braun et al., 2006; Reiners and Brandon, 2006 for reviews). The net accumulation of such radiogenic products is determined by the balance between their production and loss, the latter generally following an Arrhenius relationship (e.g. Dodson,
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1973). The ultimate concentration of radiogenic products can be converted into an apparent
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age, which corresponds to the time since the rock temperature cooled through its closure temperature (Dodson, 1973). Given the geothermal gradient is known, one can then convert apparent ages into an exhumation rate (e.g. Braun et al. 2006). However, this heavily depends on a good knowledge of the thermal conditions of the Earth’s crust. To reduce such a
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dependence, age-elevation profiles or using several thermochronometric systems are possible ways (e.g. Herman et al., 2013).
While most thermochronometric techniques rely on radiogenic isotopes, it has been
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proposed to use luminescence signal as a thermochronometer (e.g. Prokein and Wagner 1994;
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Herman et al. 2010; Li and Li 2012). In particular, optically stimulated luminescence (OSL) thermochronometry is featured by its potential low closure temperature (~40 oC, Guralnik et al. 2013), providing high sensitivity to change in surface topography and potential applicability to constrain recent and/or high-temporal-resolution geological events (Herman et al., 2010). OSL and thermoluminescence (TL) signals of quartz have already been used for exploring basin geothermal evolution or retrieving mountain long-term erosion and relief history (Ypma and Hochman, 1991; Prokein and Wagner, 1994; Herman et al., 2010; Wu et
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ACCEPTED MANUSCRIPT al., 2012; Sarkar et al., 2013). In this study, we exploit the fact that various luminescence signals have different thermal stabilities (Murray and Wintle, 1999; Spooner and Questiaux, 2000; Bailey, 2001; Li and Chen, 2001) to introduce a multi-thermochronometric approach
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based on luminescence dating, as proposed in Li and Li (2012). Here we assess the advantages and limitations of using multiple luminescence thermochronometers (MLT) together to constrain rock cooling rates through numerical synthetic experiments. We test the
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possibility of incorporating two or more thermochronometers to avoid the requirement of
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closure or present-day temperatures estimates, since they are not easy to be precisely constrained (Grün et al., 1999; Li and Li, 2012; Guralnik et al., 2013).
2. Methods
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2.1 Theory
The theoretical framework of dynamics of charges’ responsible for quartz luminescence signals has already been established for first-order kinetics by the following
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equation (Randall and Wilkins, 1945; Kallmann and Spruch, 1956; Christodoulides et al., 1971; Li and Li, 2012; Guralnik et al., 2013):
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( ⁄ )
1 = − + , = 1,2 … (1)
where i denotes the type of electron traps, Ni is the total number of traps, ni is the number of trapped charges at time t (ka), ni/Ni is the saturation ratio of traps, (Gy.ka-1) is the ionizing dose rate, Doi (Gy) is the characteristic saturation dose, and τi (ka) is the lifetime of trapped charges, which is defined by the Arrhenius relationship (Christodoulides et al., 1971): =
!(")
(2) 4
ACCEPTED MANUSCRIPT where si (ka-1) is the frequency factor of trapped charges, Ei (eV) is the trap depth, kB is the Boltzmann constant (8.617*10-5 eV.K-1) and T(t) is the rock temperature (K) at time t (ka). A long-term linear and constant cooling scenario is assumed in this study, in which the
#() = # − $ (3)
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temperature evolution is described as follows:
where T0 (°C) is the initial temperature at the beginning of the rock cooling and β (oC.ka-1) is
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the constant cooling rate.
In the equations shown above, D0i can be obtained experimentally by fitting the
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luminescence dose response curve with a saturating exponential equation, while can be calculated based on the concentration of radioactive elements in the rock and grain sizes considered (e.g. Aitken, 1985). Ei and si are usually determined by pulse annealing or
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isothermal decay experiments (Li et al., 1997; Murray and Wintle, 1999; Li and Li, 2013). The saturation ratio ni/Ni can be determined experimentally by dividing the natural luminescence intensity by the maximum saturation intensity of the regenerated dose response
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curve (e.g. Guralnik et al., 2013). The cooling rate β, cooling period t and initial temperature
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T0 are the unknown geological parameters, which are expected to be derived from inverting the saturation ratios (ni/Ni). Clearly, it is a non-unique problem.
2.2 Forward modeling
The numerical forward modeling approach (e.g., Herman et al. 2007; Valla et al., 2010; Braun et al. 2012) is employed to find all possible combinations of T0, β and t in a given parameter space that generate the synthetic “observed” n/N,. In practice, we first
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ACCEPTED MANUSCRIPT numerically integrate equation (1) with respect to t under an imposed cooling scenario (given T0 and β) to generate the “observed” n/N values as our synthetic data for each trap. Then, the equation (1) is numerically integrated with prescribed T0 and β, and the integration interval
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(tint) is determined by the ratio of (T0 + 60) to the assigned cooling rate β, since the possible lowest present-day temperature is rarely lower than -60 oC at the Earth’s surface. The integration time-step is 2 ka, and thereafter the synthetic saturation ratios are correspondingly
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recorded in an interval of 2 ka. An exhaustive search is then performed to compare these
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saturation ratios with the “observed” n/N values. If the difference between the modeled and “observed” n/N values is less than 5%, the corresponding assigned T0, β as well as the present-day temperature Tp (Tp= T0-β*t) are recorded. Subsequently, this iterative process is repeated with all possible combinations of T0 and β within the given parameter space. All
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combinations of T0, β and Tp that generate n/N values being consistent with the synthetic “observed” saturation ratios are clustered to construct a solution space for each single luminescence thermochronometer (SLT). For the MLT approach, only the combination of T0,
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β and Tp, which generate n/N values that are consistent with the synthetic “observed” values
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for two or more kinds of traps, are clustered as the solution space for our MLT approach. In this study, we test two strategies for the MLT approach by adopting either two or four traps. We specify them as the “double luminescence thermochronometers” (DLT) and “four luminescence thermochronometers” (FLT) method, respectively. Finally, the solution space is compared with the prescribed cooling scenarios to evaluate the performance of corresponding approach in quantitatively retrieving the prescribed cooling rate.
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ACCEPTED MANUSCRIPT 2.3 Parameters for the numerical calculation Here, we employed a set of trap depths (1.55, 1.60, 1.65 and 1.70 eV) as potential candidates for our MLT approach, which are typical values for the quartz mineral (Bailey,
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2001; Li and Li, 2012). The 1.55-eV trap may correspond to the 230 oC TL peak while the 1.70-eV trap may correspond to the fast component OSL signal, which is usually assumed to correspond to the 325 oC TL peak (Bailey, 2001). The frequency factor (si) is assumed to be
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1013 s-1(Murray and Wintle, 1999; Bailey, 2001; Li and Li, 2012). The dose rate ( ) is
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assumed to be 3.3 Gy.ka-1, which is estimated based upon the typical environmental radioactive elements concentrations (U~3 ppm, Th~11 ppm and K~1.8%) with a grain size of 90-125 µm. The characteristic doses (D0i) are assumed as 200 Gy for all traps, although they can vary in practice (Zhou and Shackleton, 2001; Li and Li, 2012; Guralnik et al., 2015). All
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numerical calculations shown thereafter are implemented using MATLAB ©.
3. Results and discussion
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3.1 Evolution of saturation ratios during the rock cooling
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Firstly, we integrate equation (1) numerically for the different traps mentioned in section 2.3 under different imposed cooling scenarios with an initial temperature T0 of 200 oC and cooling rates β ranging from 0.01 to 2 oC.ka-1. Fig. 1a, b show the evolution of saturation ratios for the 1.55-eV and 1.70-eV traps under various cooling rates β, respectively. Electrons started to accumulate at ambient temperatures of ~70 oC and ~100 oC for the 1.55-eV and 1.70-eV traps, respectively. It is expected that the saturation ratios would differ for different traps during rock cooling before they all reach saturation, and such a difference is depending
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ACCEPTED MANUSCRIPT on the cooling rate. To visualize it, we extracted snapshots at Tp = 30 oC in Fig. 1a, b as well as for similar evolutions using the 1.60- and 1.65-eV traps (not shown) and combine these snapshots together to generate Fig. 1c, which shows the saturation ratios of these four traps at
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Tp = 30 oC under different cooling scenarios. Fig. 1c shows the different traps have various resolutions in resolving cooling rates. It is clear from this result that the uncertainty of the constrained β could be potentially diminished by incorporating more than one trap into
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Fig. 1
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analysis, therefore further justifying the use of our MLT approach.
The co-evolution of n/N values of two traps under different cooling rates is shown by the contours of cooling rate (iso-β curves) in Fig. 1d. Two types of combination are shown: 1.55-1.60 eV (thin and red lines) and 1.55-1.70 eV (thick and black lines). The n/N values of
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relatively shallow (1.55 eV) and relatively deep (1.60 or 1.70 eV) traps are shown on x-axis and y-axis, respectively. The shaded area is the forbidden zone where the deep trap is saturated (n/N > 0.86, Wintle, 2008) or the shallow trap is empty (n/N < 0.05). The 1.55 - 1.70
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combination is applicable when β is higher than 0.2 oC.ka-1, while the 1.55 - 1.60 combination
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is applicable to all investigated scenarios. However, β is better resolved by the former combination since the intervals between iso-β curves are larger. For real rock samples, since we do not know a priori the cooling rate, it seems reasonable to incorporate a range of traps to allow the MLT approach being compatible with a larger range of cooling scenarios. Besides improving the resolution, and more importantly, Fig. 1d seems to show that no priori knowledge about Tp is needed to constrain the cooling rate once we get n/N values of two different traps. In the following, we employed the forward modeling to demonstrate the
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ACCEPTED MANUSCRIPT feasibility and performance of the MLT approach on constraining rock cooling rate.
3.2 Constraining rock cooling rates using the MLT approach
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Suppose a rock cooled from 200 to 30 oC, the synthetic saturation ratios (Fig. 1c) modeled under a range of cooling scenarios (β = 0.01, 0.1, 0.2, 0.5, 1.0 and 1.5 oC.ka-1) were used as input observables for forward modeling to assess the potential of the MLT approach in
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constraining cooling rates. For the parameter space of forward modeling, T0 ranged from 30 to
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250 oC in steps of 5 oC; β ranged from 0.005 to 3 oC.ka-1 in steps of 0.005 oC.ka-1 when applying the forward modeling to the n/N values predicted with β = 0.01 oC.ka-1, while it ranged from 0.02 to 3 oC•ka-1 in steps of 0.02 oC•ka-1 for n/N values predicted with higher β values to reduce the computational cost. It should be emphasized that in the current numerical
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study, we only want to demonstrate the performance of the MLT approach, for which the coarse sampling interval does not matter, but a narrow sampling interval of β is preferred
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when applied to real rock samples.
Fig. 2
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The solution spaces (T0, Tp and β) are shown in Fig. 2. The prescribed β are 0.01 (slow cooling), 0.1 (medium cooling) and 1.0 (fast cooling) oC.ka-1 for the left, middle and right columns. From the first to the fourth row, the solution spaces are for SLT (1.55 eV), SLT (1.70 eV), DLT (1.55 and 1.70 eV) and FLT (1.55, 1.60, 1.65 and 1.70 eV) approaches, respectively. Since the choice of T0 does not affect constraint of β when T0 is high enough (well above the closure temperature, i.e. >100 oC), we only show the solution space with T0 bounded between 30 and 120 oC in Fig. 2.
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ACCEPTED MANUSCRIPT The solution space is wide if only the 1.55- or 1.70-eV trap is employed. The information of Tp helps greatly narrowing the solution space. Although the 1.70-eV trap helps better constraining the cooling rate β than 1.55-eV trap for the slow (Fig. 2b) and medium
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(Fig. 2f) cooling scenarios, its solution spaces are complicated by the saturation effects (n/N > 0.86, Fig. 1c). In fact, the saturation of 1.70-eV trap sets an upper limit for β. Under the fast cooling scenario, these two traps perform similarly on constraining β, however, the range of
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permitted Tp is much narrower for the 1.55-eV trap than that for the 1.70-eV trap (Fig. 2i and
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2j). Tp constrained by the 1.55-eV trap can be effectively regarded as the boundary Tp for the 1.70-eV trap. Therefore, the uncertainties in β are expected to be reduced by using these two or more traps together in a MLT approach. It is somewhat similar to the SLT approach of Li and Li (2012), but here we do not need external information on Tp anymore.
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For the slow and medium cooling scenarios (Fig. 1c, prescribed β = 0.01 and 0.1 o
C.ka-1), the DLT-constrained β range from 0.005 to 0.325 oC.ka-1 and from 0.02 to 0.24 oC.ka-
1
, respectively. Correspondingly, the permitted Tp are constrained in the range of 9 to 31 oC
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and 23 to 34 oC (Fig. 2c and 2g). For the fast cooling scenario (prescribed β = 1.0 oC.ka-1), the
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permitted β and Tp are bounded in the range of 0.08 to 1.18 oC.ka-1 and 24 to 41 oC with the DLT method (Fig. 2j). Two more traps (1.60 and 1.65 eV) are incorporated for the FLT method. For slow and fast cooling scenarios, the permitted β and Tp are substantially narrowed. The β values are constrained in the range of 0.005 to 0.175 oC.ka-1 and 0.8 to 1.18 o
C.ka-1, while the permitted Tp values are in the range of 19.3 to 31.2 oC and 24.2 to 31.6
o
C.ka-1, for slow and fast cooling scenarios, respectively (Fig. 2d and 2l). However, for the
medium cooling rate, the constraints on the permitted β and Tp are not significantly improved
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ACCEPTED MANUSCRIPT by using the FLT method (Fig. 2h). The β and Tp constrained by the MLT approach (both the DLT and FLT methods) for other prescribed cooling scenarios are summarized in Table 1. In summary, the β and Tp are significantly better constrained by the FLT than by the DLT method
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for almost all cooling scenarios except the case with prescribed β = 0.1 oC.ka-1. The FLT method improves the potential overestimation of DLT constrained β values for the scenarios with prescribed β = 0.01 and 0.1 oC.ka-1, while it improves a potential underestimation of the
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DLT constrained β values if the prescribed β is higher than 0.1 oC.ka-1. For the former two
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scenarios, the improvement is due to the incorporating traps suffering less from the saturation effect (Fig. 1d). However, for other scenarios, the improvement is due to the narrower bound of the permitted lowest initial temperature T0 (Table 1).
We mentioned earlier that the choice of T0 does not affect the constrained β, if T0 is
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high enough (i.e. > 100 oC). However, the lowest permitted T0 is constrained by the DLT and FLT methods, and the increase of this lower limit eliminates the low cooling rates for the FLT method (Fig. 2 and Table 1). If the initial temperature T0 is higher than 75 oC, then the DLT
C.ka-1 (Table 1).
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o
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and FLT methods would perform similarly if the prescribed cooling rate is not lower than 0.2
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3.3 Minimum cooling rate constrained by MLT approach Thermochronometers with different thermal stabilities are required for the MLT approach. However, it is possible that the relatively stable traps are getting saturated while the most unstable traps are still empty at low cooling rate. Therefore, the dose saturation of
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ACCEPTED MANUSCRIPT luminescence signal sets a lower limit for cooling rate that can be effectively constrained by the MLT approach, which was therefore investigated numerically with a range of difference in traps’ thermal stabilities.
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The difference in thermal stabilities was depicted by different trap depths. For a specified β, the equation (1) was numerically integrated for the relatively stable trap with a given depth of dS and the relatively unstable trap with a depth of dS - δE. Then, we examined
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whether the n/N value of the unstable trap was < 0.05 (taken as the criteria for an empty trap)
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when the n/N value of the stable trap was just > 0.86 (criteria for trap saturation). We increased δE from 0.01 eV to 1.00 eV in steps of 0.01 eV. The minimum δE predicting the n/N value just <0.05, as well as the corresponding β and dS, were recorded. The above iterative process was repeated with dS varing from 1.5 to 2.5 eV in steps of 0.05 eV, and β
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ranging from 0 to 2 oC•ka-1 in steps of 0.01 oC.ka-1, respectively. The integration interval was also taken as the ratio of (T0 + 60) to the assigned cooling rate β, and other parameters were
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taken as following: T0 = 250 oC, D0 = 200 Gy, = 3.3 Gy•ka-1 and s = 1013 s-1. Fig. 3
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Fig. 3 shows the relationship among all recorded δE, β and dS. Different colors indicates the minimum cooling rate (βmin) that can be constrained by the traps with depth of dS and dS – δE, e.g., in the case of trap depths of 1.8 and 1.6 eV, the minimum cooling rate that can be effectively constrained is ~ 0.2 oC.ka-1. Clearly, βmin increases significantly with the δE for any dS. For a given δE, the βmin decreases with the depth of relatively stable trap (dS). For instance, we took a profile across the color map of Fig 3a at δE = 0.21 eV (AA’). As shown in Fig.3b, βmin decreases from 0.25 to 0.01 oC.ka-1 with dS increasing from 1.5 to 2.5 eV. Such a
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ACCEPTED MANUSCRIPT difference decreases along with the increase of δE. With δE increasing to 0.4 eV, βmin decreases from 0.63 to 0.52 oC•ka-1 with dS increasing from 1.5 to 2.5 eV. Such sensitivity analyses can also provide guidance to properly select luminescence thermochronometers with
3.4 Advantages and limitations of the MLT approach
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applying the MLT approach.
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different thermal stabilities based on a priori estimate of the expected cooling rates, before
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In this study, we tested the potential of the MLT approach to constrain rock cooling rates using a numerical investigation. To apply the MLT approach to natural samples, the natural intensities of multiple luminescence signals could be converted into either 1) De values, and thereafter apparent closure ages (i.e. De/ ) or 2) saturation ratios (n/N) (Guralnik
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et al., 2013). For both cases, the thermal kinetic parameters (E and s) of the multiple luminescence signals have to be determined experimentally for each individual sample (Chen and Pagonis, 2011; Guralnik et al., in press). Combining these data all together, the thermal
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history of the sample can be constrained in two ways correspondingly: 1) by confronting the
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apparent closure ages against the associated closure temperature (Braun et al., 2006; Guralnik et al., 2013); or 2) by numerical forward modeling approach exploiting MLT as we proceeded for the synthetic data in section 3.2. Indeed, by incorporating the experimentally derived parameters (D0, E, s and ) into equations (1) – (3), forward modeling allows to compute modeled n/N values with every combination of T0, β in the given parameter space [T0, β] for each luminescence trap. One can then search numerically in the parameter space for the bestfit combinations generating modeled n/N values consistent with the observed n/N values for
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ACCEPTED MANUSCRIPT all investigated traps. The ensemble of such T0, β, the corresponding cooling period t and the resulting Tp cover all possible cooling history generating the observed n/N. In that framework, any knowledge/assumption on both the apparent closure temperature and present-day
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temperature Tp is not required. Further, our approach also enables to estimate the Tp as a model output. Finally, if T0 is high enough, a rough cooling rate can also be read out directly from a plot similar to Fig. 1d based on DLT method. The next step will be to test our MLT
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approach on natural samples to fully infer its potential in constraining rock cooling histories.
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For the MLT approach, different methods can be adopted considering the available number of traps as well as the trap depths. For the quartz system, if the initial temperature T0 is high enough (> 100 oC), the constrained cooling rates are independent of the choice of T0, therefore, the unknown parameters in equations (1) – (3) reduce to two (only the cooling rate
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and the cooling period). In this case, the DLT method constrains the cooling rate satisfactorily. However, more than two thermochronometers are preferred if we are not sure whether or not the T0 is possibly low (e.g. reheating thermal event). The FLT method exploited here could
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eliminate such possibilities for the cooling scenarios with prescribed cooling rate being higher
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than 0.1 oC.ka-1 (Fig. 2 and Table 1). When the cooling rate is lower than 0.1 oC.ka-1, we should be cautious about the saturation effect, which would limit the application of the MLT approach. For the slow cooling scenarios, a small difference in the traps thermal stability is preferred (Fig. 3), although the associated resolution in the output cooling rate will get worse (Fig. 1d). For application to real rock samples, more than two thermochronometers are recommended with consideration of balancing the potential saturation and resolution of the multiple thermochronometers. An expected cooling rate could provide guidance to optimize
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ACCEPTED MANUSCRIPT the experimental parameters to isolate multiple luminescence signals with appropriate differences in their thermal stabilities. TL signals and different components of the OSL signal for quartz are suitable
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candidates for the MLT approach, since luminescence signals with different thermal stabilities can be isolated during a single measurement sequence (e.g. Aitken, 1985; Singarayer and Bailey, 2003). However, Guralnik et al. (2015) demonstrated the complexities of using
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bedrock quartz OSL signal as a potential thermochronometer through a comprehensive
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investigation on its basic luminescence characteristics, which may also be applied to the TL signals of bedrock quartz. The development of non-fading post-infrared infrared stimulated luminescence (pIR IRSL, Thiel et al., 2011) and multiple elevated temperature (MET)-pIR IRSL (Li and Li, 2011) signals of potassium feldspars (K-feldspars) are of great potential for
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the MLT approach, since signals with different thermal stabilities can be simply isolated by changing the IR stimulation temperature (Thomsen et al, 2011; Li and Li, 2013). The conventional low temperature IRSL signal is generally less thermally stable than the post-IR
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IRSL signals, and it may play an important role for the MLT approach of K-feldspars. Since
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new generic models have been developed to describe the trapping and anomalous fading processes of the IRSL signal (Huntley, 2006; Kars and Wallinga, 2009; Jain et al., 2012), they may enable the use of IRSL signals without fading correction. By using the IRSL and pIR IRSL signals together, we will have more candidates for the MLT approach. Li and Li (2012) investigated the effects of the dose rate ( ) and characteristic saturation dose (D0) on resolving rock cooling rates using luminescence thermochronometers. Such effects also hold for each single thermochronometer of the MLT. In fact, the ratio of to 15
ACCEPTED MANUSCRIPT D0, which is the “probability per unit time of an empty trap being filled by the radiation”, is the ultimate controlling factor (Huntley and Lian, 2006). It implies that the luminescence signal with a smaller /D0 is preferred to serve as a relatively stable thermochronometer for
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the MLT approach.
4. Conclusions
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In this study, the applicability and advantage of the multiple luminescence
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thermochronometers (MLT) approach to constrain rock cooling rates from a single sample is demonstrated through numerical forward modeling with different electron trap depths typical for the quartz mineral. The rock cooling rates are independently constrained by MLT saturation ratios without a priori knowledge on the present-day temperature. If we
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independently know that the initial temperature has been high enough (i.e. > 100 oC), two thermochronometers with sufficient difference in their thermal stabilities can constrain the cooling rate satisfactorily. Otherwise, more thermochronometers may help reducing the
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uncertainty in cooling rate predictions. Due to the saturation effect of luminescence signals,
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the minimum cooling rate that can be constrained should be evaluated before applying the MLT approach to natural rock samples.
Acknowledgments
We are thankful to an anonymous reviewer for his/her constructive comments, which greatly help us clarifying our manuscript. We also thank Dr. Shenghua Li for his inspirational suggestions during revisions. This work was supported by the National Science Foundation of
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ACCEPTED MANUSCRIPT China (41272195), SKLED grant (No. LED2010A04), IGCEA grant (No. 1417), China Postdoctoral Science Foundation (2013M540997), and the Swiss National Foundation
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(#PZ00P2_148191 for P.GV).
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Rhodes, E.J., 2013. Effective closure temperature in leaky and/or saturating thermochronometers. Earth Planet Sc Lett 384, 209-218.
Guralnik, B., Li, B., Jain, M., Chen, R., Paris, R.B., Murray, A.S., Li, S.H., Pagonis, V., Valla, P. G., Herman, F.. Radiation-induced growth and isothermal decay of infrared-stimulated
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luminescence from feldspar. Radiat Meas, In Press.
Herman, F., Braun, J., Dunlap, W., 2007. Tectonomorphic scenarios in the Southern alps of New Zealand. J. Geophys. Res. 112. B04201. doi:10.1029/2004JB003472
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Herman, F., Rhodes, E.J., Jean, B.C., Heiniger, L., 2010. Uniform erosion rates and relief
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amplitude during glacial cycles in the Southern Alps of New Zealand, as revealed from OSL-thermochronology. Earth Planet Sc Lett 297, 183-189.
Herman F., Seward D., Valla P.G, Carter A., Kohn B., Willett S.D., Ehlers T.A., 2013. Worldwide acceleration of mountain erosion under a cooling climate. Nature, 504, 423-426.
Huntley, D.J., 2006. An explanation of the power-law decay of luminescence. J Phys-Condens Mat 18, 1359-1365. Huntley, D.J., Lian, O.B., 2006. Some observations on tunnelling of trapped electrons in
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ACCEPTED MANUSCRIPT feldspars and their implications for optical dating. Quaternary Sci Rev 25, 2503-2512. Jain, M., Guralnik, B., Andersen, M.T., 2012. Stimulated luminescence emission from localized recombination in randomly distributed defects. J Phys-Condens Mat 24.
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Kallmann, H., Spruch, G. M., 1956. Number of Traps and Behavior of Excited Electrons in Luminescent Materials. Phys. Rev. 103, 94 – 102.
Kars, R.H., Wallinga, J., 2009. IRSL dating of K-feldspars: Modelling natural dose response
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curves to deal with anomalous fading and trap competition. Radiat Meas 44, 594-599.
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Li, B., Li, S.H., 2011. Luminescence dating of K-feldspar from sediments: A protocol without anomalous fading correction. Quat Geochronol 6, 468-479.
Li, B., Li, S.H., 2012. Determining the cooling age using luminescence-thermochronology. Tectonophysics 580, 242-248.
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Li, B., Li, S.H., 2013. The effect of band-tail states on the thermal stability of the infrared stimulated luminescence from K-feldspar. J Lumin 136, 5-10. Li, S.H., Chen, G., 2001. Studies of thermal stability of trapped charges associated with OSL
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from quartz. J Phys D Appl Phys 34, 493-498.
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Li, S.H., Tso, M.Y.W., Wong, N.W.L., 1997. Parameters of OSL traps determined with various linear heating rates. Radiat Meas 27, 43-47.
Murray, A.S., Wintle, A.G., 1999. Isothermal decay of optically stimulated luminescence in quartz. Radiat Meas 30, 119-125.
Prokein, J., Wagner, G. A., 1994. Analysis of thermoluminescent glow peaks in quartz derived from the KTB-drill hole. Radiat. Meas. 23, 85 – 94. Randall, J.T., Wilkins, M.H.F., 1945. Phosphorescence and Electron Traps .1. The Study of
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ACCEPTED MANUSCRIPT Trap Distributions. Proc R Soc Lon Ser-A 184, 366-389. Reiners, P.W., Brandon, M.T., 2006. Using thermochronology to understand orogenic erosion. Annu Rev Earth Pl Sc 34, 419-466.
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Sarkar, S.D., Mathew, G., Pande, K., Chauhan, N., Singhvi, A.K., 2013. Rapid denudation of Higher Himalaya during late Pleistocence, evidence from OSL thermochronology. Geochronometria, 40, 304 – 310.
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Singarayer, J.S., Bailey, R.M., 2003. Further investigations of the quartz optically stimulated
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luminescence components using linear modulation. Radiat Meas 37, 451-458. Spooner, N.A., Questiaux, D.G., 2000. Kinetics of red, blue and UV thermoluminescence and optically-stimulated luminescence from quartz. Radiat Meas 32, 659-666. Thiel, C., Buylaert, J. P., Murray, A., Terhorst, B., Hofer, I., Tsukamoto, S., and Frechen, M.,
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2011a. Luminescence dating of the Stratzing loess profile (Austria) - Testing the potential of an elevated temperature post-IR IRSL protocol. Quaternary International 234, 23-31. Thomsen, K.J., Murray, A.S., Jain, M., 2011. Stability of Irsl Signals from Sedimentary K-
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Feldspar Samples. Geochronometria 38, 1-13.
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Valla, P.G., Herman, F., van der Beek, P.A., Braun, J., 2010. Inversion of thermochronological age-elevation profiles to extract independent estimates of denudation and relief history - I: Theory and conceptual model. Earth Planet Sc Lett 295, 511-522.
Wintle, A. G., 2008. Luminescence dating: where it has been and where it is going. Boreas 37, 471-482. Wu, T. S., Kunz, A., Jaiswal, M. K., Chen, Y. G., 2012. A feasibility study on the application of luminescence dating for quartz from different rock types as a thermochronometer. Quat.
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ACCEPTED MANUSCRIPT Geochronol. 10, 340 – 344. Ypma, P.J., Hochman, M., 1991. Thermoluminescence geothermometry - a case study of Owtay basin. Australian Petroleum Exploration Association 31, 312 - 324.
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Zhou, L. P., and Shackleton, N. J., 2001. Photon-stimulated luminescence of quartz from loess and effects of sensitivity change on palaeodose determination. Quaternary Science Reviews
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20, 853-857.
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Figure 1. Evolution of saturation ratios (n/N) for a) 1.55 eV and b) 1.70 eV traps under different cooling rates (0.01 to 2 °C.ka-1, see legend for details). The n/N values with Tp=30oC (vertical lines in a and b) are used for generating values in panel (c); c) Synthetic “observed” n/N of different trap depths under different scenarios (see legend for details) when cooling from 200 oC to 30 oC; d) Relationship between n/N of two luminescence traps during cooling (iso-cooling-rate plots). Two groups of traps are investigated: 1) 1.55 and 1.70 eV (thick and black); 2) 1.55 and 1.60 eV (thin and red). The shaded area is the forbidden zone where the deep trap is saturated (n/N > 0.86) or the shallow trap is empty (n/N < 0.05). For both cases, x-axis refers to 1.55-eV trap, while the y-axis refers to the 1.60- or 1.70- eV trap (The reader is referred to the web version for colorful plot).
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Figure 2. Solution spaces for the initial temperature (T0), cooling rate (β), and present-day temperature (Tp) obtained by the SLT-1.55 (a, e, h), SLT-1.70 (b, f, i), DLT (c, g, j) and FLT (d, h, l) approaches. The constrained cooling rates are shown by color-coding (the color bar applies to all four panels below it). The input T0 and Tp parameters are 200 oC and 30 oC for all scenarios, respectively. The input β values are 0.01, 0.1 and 1.0 oC.ka-1 for the left (a-d), middle (e-h) and right (i-l) columns, respectively. Note the logarithmic scale for the color map.
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Figure 3. a) Relationships between the trap depth of relatively stable trap (dS), difference in trap depth (δE) and minimum cooling rates (βmin, shown by different colors) that can be constrained by applying the MLT approach; b) The variation of βmin with the dS for a given δE of 0.21 eV, which was extracted along the profile AA’ in (a).
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Modeled by DLT2
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Table 1. Summary of the input cooling scenarios, associated synthetic saturation ratios, and output parameter ranges from MLT based forward modeling.
Modeled by FLT2
Synthetic observed n/N1
Given β ( oC.ka-1)
lowest T0 ( oC)
Tp ( oC)
β ( C.ka-1)
0.738-0.949-0.992-0.999 0.600-0.855-0.959-0.990 0.499-0.736-0.874-0.943 0.343-0.512-0.646-0.744 0.236-0.348-0.447-0.531 0.192-0.275-0.351-0.420
0.01 0.1 0.2 0.5 1.0 1.5
30 40 40 40 45 45
8.9-31.2 22.8-33.6 25.4-35.8 26.0-38.4 24.2-41.2 21.6-42.8
0.005-0.325 0.02-0.24 0.02-0.30 0.02-0.60 0.08-1.18 0.06-1.76
lowest T0 ( oC)
Tp ( oC)
β ( C.ka-1)
30 40 50 65 70 75
19.3-31.224.8-33.6 26.0-32.7 26.0-31.8 24.2-31.6 21.6-29.6
0.005-0.175 0.02-0.20 0.12-0.28 0.40-0.60 0.8-1.18 1.26-1.76
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1. The n/N values are shown for the different trap depths in the following order: 1.55, 1.60, 1.65 and 1.70 eV; 2. DLT refers to using 1.55- and 1.70-eV traps together, while FLT refers to using 1.55-, 1.60-, 1.65- and 1.70-eV traps together for forward modeling.
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Highlights -Investigation of a Multi-Luminescence-Thermochronometer (MLT) approach -Numerical experiments to constrain rock cooling rates and present-day temperatures -Resolution and limitation of the MLT approach are discussed.
S1350-4487(15)30025-1
DOI:
10.1016/j.radmeas.2015.05.002
Reference:
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To appear in:
Radiation Measurements
Received Date: 15 October 2014 Revised Date:
5 April 2015
Accepted Date: 10 May 2015
Please cite this article as: Qin, J., Chen, J., Valla, P.G., Herman, F., Li, K., Estimating rock cooling rates by using multiple luminescence thermochronometers, Radiation Measurements (2015), doi: 10.1016/ j.radmeas.2015.05.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Estimating rock cooling rates by using multiple luminescence thermochronometers
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Jintang Qin1, Jie Chen1*, Pierre G. Valla2, Frédéric Herman2, Kechang Li3
State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing, China
Institute of Earth Surface Dynamics, University of Lausanne, Lausanne, Switzerland
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Qinghai Earthquake Administration, Xi’ning, Qinghai Province, China
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*Corresponding author: [email protected], phone number: +86-10-62009093; Postal address: Prof. Jie Chen
Institute of Geology, China Earthquake Administration 903,
P.O.Box 9803,
Huayanlijia
No.1,
Beitucheng
West
Street
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Room
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Chaoyang District, Beijing 100029,China
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ACCEPTED MANUSCRIPT Abstract The potential of luminescence thermochronology is characterized by diverse luminescence signals with different thermal stabilities available for a single rock sample. These signals may
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be exploited together to constrain rock cooling rates. In this study, we performed numerical synthetic experiments to assess the advantages and limitations of using multiple luminescence thermochronometers (MLT) of a hypothetical single rock sample to constrain its cooling rate.
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A series of luminescence traps with typical depths of quartz mineral are investigated (i.e. 1.55
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to 1.70 eV). We use synthetic luminescence saturation ratios predicted from imposed cooling scenarios to assess the benefits of MLT-based forward modeling on constraining rock cooling rates. Our results show that the prescribed cooling rates can be constrained by applying the MLT approach to a single sample, without the requirement of a priori knowledge on the
luminescence
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present-day temperature, which is mandatory for the approach only using a single thermochronometer.
Due
to
the saturation
effect
of luminescence
thermochronometers, the minimum cooling rates that can be constrained with given trap
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depths are also investigated for the MLT approach.
Keywords: Thermochronology; multiple luminescence thermochronometers; cooling rate; numerical sensitivity analysis; present-day temperature
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ACCEPTED MANUSCRIPT 1. Introduction Rocks cool as they travel towards the Earth’s surface in response to exhumation. Their cooling histories can be inferred by measuring radiogenic isotopes or lattice damages in
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mineral crystals (e.g. Braun et al., 2006; Reiners and Brandon, 2006 for reviews). The net accumulation of such radiogenic products is determined by the balance between their production and loss, the latter generally following an Arrhenius relationship (e.g. Dodson,
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1973). The ultimate concentration of radiogenic products can be converted into an apparent
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age, which corresponds to the time since the rock temperature cooled through its closure temperature (Dodson, 1973). Given the geothermal gradient is known, one can then convert apparent ages into an exhumation rate (e.g. Braun et al. 2006). However, this heavily depends on a good knowledge of the thermal conditions of the Earth’s crust. To reduce such a
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dependence, age-elevation profiles or using several thermochronometric systems are possible ways (e.g. Herman et al., 2013).
While most thermochronometric techniques rely on radiogenic isotopes, it has been
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proposed to use luminescence signal as a thermochronometer (e.g. Prokein and Wagner 1994;
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Herman et al. 2010; Li and Li 2012). In particular, optically stimulated luminescence (OSL) thermochronometry is featured by its potential low closure temperature (~40 oC, Guralnik et al. 2013), providing high sensitivity to change in surface topography and potential applicability to constrain recent and/or high-temporal-resolution geological events (Herman et al., 2010). OSL and thermoluminescence (TL) signals of quartz have already been used for exploring basin geothermal evolution or retrieving mountain long-term erosion and relief history (Ypma and Hochman, 1991; Prokein and Wagner, 1994; Herman et al., 2010; Wu et
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ACCEPTED MANUSCRIPT al., 2012; Sarkar et al., 2013). In this study, we exploit the fact that various luminescence signals have different thermal stabilities (Murray and Wintle, 1999; Spooner and Questiaux, 2000; Bailey, 2001; Li and Chen, 2001) to introduce a multi-thermochronometric approach
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based on luminescence dating, as proposed in Li and Li (2012). Here we assess the advantages and limitations of using multiple luminescence thermochronometers (MLT) together to constrain rock cooling rates through numerical synthetic experiments. We test the
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possibility of incorporating two or more thermochronometers to avoid the requirement of
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closure or present-day temperatures estimates, since they are not easy to be precisely constrained (Grün et al., 1999; Li and Li, 2012; Guralnik et al., 2013).
2. Methods
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2.1 Theory
The theoretical framework of dynamics of charges’ responsible for quartz luminescence signals has already been established for first-order kinetics by the following
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equation (Randall and Wilkins, 1945; Kallmann and Spruch, 1956; Christodoulides et al., 1971; Li and Li, 2012; Guralnik et al., 2013):
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( ⁄ )
1 = − + , = 1,2 … (1)
where i denotes the type of electron traps, Ni is the total number of traps, ni is the number of trapped charges at time t (ka), ni/Ni is the saturation ratio of traps, (Gy.ka-1) is the ionizing dose rate, Doi (Gy) is the characteristic saturation dose, and τi (ka) is the lifetime of trapped charges, which is defined by the Arrhenius relationship (Christodoulides et al., 1971): =
!(")
(2) 4
ACCEPTED MANUSCRIPT where si (ka-1) is the frequency factor of trapped charges, Ei (eV) is the trap depth, kB is the Boltzmann constant (8.617*10-5 eV.K-1) and T(t) is the rock temperature (K) at time t (ka). A long-term linear and constant cooling scenario is assumed in this study, in which the
#() = # − $ (3)
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temperature evolution is described as follows:
where T0 (°C) is the initial temperature at the beginning of the rock cooling and β (oC.ka-1) is
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the constant cooling rate.
In the equations shown above, D0i can be obtained experimentally by fitting the
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luminescence dose response curve with a saturating exponential equation, while can be calculated based on the concentration of radioactive elements in the rock and grain sizes considered (e.g. Aitken, 1985). Ei and si are usually determined by pulse annealing or
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isothermal decay experiments (Li et al., 1997; Murray and Wintle, 1999; Li and Li, 2013). The saturation ratio ni/Ni can be determined experimentally by dividing the natural luminescence intensity by the maximum saturation intensity of the regenerated dose response
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curve (e.g. Guralnik et al., 2013). The cooling rate β, cooling period t and initial temperature
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T0 are the unknown geological parameters, which are expected to be derived from inverting the saturation ratios (ni/Ni). Clearly, it is a non-unique problem.
2.2 Forward modeling
The numerical forward modeling approach (e.g., Herman et al. 2007; Valla et al., 2010; Braun et al. 2012) is employed to find all possible combinations of T0, β and t in a given parameter space that generate the synthetic “observed” n/N,. In practice, we first
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ACCEPTED MANUSCRIPT numerically integrate equation (1) with respect to t under an imposed cooling scenario (given T0 and β) to generate the “observed” n/N values as our synthetic data for each trap. Then, the equation (1) is numerically integrated with prescribed T0 and β, and the integration interval
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(tint) is determined by the ratio of (T0 + 60) to the assigned cooling rate β, since the possible lowest present-day temperature is rarely lower than -60 oC at the Earth’s surface. The integration time-step is 2 ka, and thereafter the synthetic saturation ratios are correspondingly
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recorded in an interval of 2 ka. An exhaustive search is then performed to compare these
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saturation ratios with the “observed” n/N values. If the difference between the modeled and “observed” n/N values is less than 5%, the corresponding assigned T0, β as well as the present-day temperature Tp (Tp= T0-β*t) are recorded. Subsequently, this iterative process is repeated with all possible combinations of T0 and β within the given parameter space. All
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combinations of T0, β and Tp that generate n/N values being consistent with the synthetic “observed” saturation ratios are clustered to construct a solution space for each single luminescence thermochronometer (SLT). For the MLT approach, only the combination of T0,
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β and Tp, which generate n/N values that are consistent with the synthetic “observed” values
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for two or more kinds of traps, are clustered as the solution space for our MLT approach. In this study, we test two strategies for the MLT approach by adopting either two or four traps. We specify them as the “double luminescence thermochronometers” (DLT) and “four luminescence thermochronometers” (FLT) method, respectively. Finally, the solution space is compared with the prescribed cooling scenarios to evaluate the performance of corresponding approach in quantitatively retrieving the prescribed cooling rate.
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ACCEPTED MANUSCRIPT 2.3 Parameters for the numerical calculation Here, we employed a set of trap depths (1.55, 1.60, 1.65 and 1.70 eV) as potential candidates for our MLT approach, which are typical values for the quartz mineral (Bailey,
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2001; Li and Li, 2012). The 1.55-eV trap may correspond to the 230 oC TL peak while the 1.70-eV trap may correspond to the fast component OSL signal, which is usually assumed to correspond to the 325 oC TL peak (Bailey, 2001). The frequency factor (si) is assumed to be
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1013 s-1(Murray and Wintle, 1999; Bailey, 2001; Li and Li, 2012). The dose rate ( ) is
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assumed to be 3.3 Gy.ka-1, which is estimated based upon the typical environmental radioactive elements concentrations (U~3 ppm, Th~11 ppm and K~1.8%) with a grain size of 90-125 µm. The characteristic doses (D0i) are assumed as 200 Gy for all traps, although they can vary in practice (Zhou and Shackleton, 2001; Li and Li, 2012; Guralnik et al., 2015). All
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numerical calculations shown thereafter are implemented using MATLAB ©.
3. Results and discussion
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3.1 Evolution of saturation ratios during the rock cooling
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Firstly, we integrate equation (1) numerically for the different traps mentioned in section 2.3 under different imposed cooling scenarios with an initial temperature T0 of 200 oC and cooling rates β ranging from 0.01 to 2 oC.ka-1. Fig. 1a, b show the evolution of saturation ratios for the 1.55-eV and 1.70-eV traps under various cooling rates β, respectively. Electrons started to accumulate at ambient temperatures of ~70 oC and ~100 oC for the 1.55-eV and 1.70-eV traps, respectively. It is expected that the saturation ratios would differ for different traps during rock cooling before they all reach saturation, and such a difference is depending
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ACCEPTED MANUSCRIPT on the cooling rate. To visualize it, we extracted snapshots at Tp = 30 oC in Fig. 1a, b as well as for similar evolutions using the 1.60- and 1.65-eV traps (not shown) and combine these snapshots together to generate Fig. 1c, which shows the saturation ratios of these four traps at
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Tp = 30 oC under different cooling scenarios. Fig. 1c shows the different traps have various resolutions in resolving cooling rates. It is clear from this result that the uncertainty of the constrained β could be potentially diminished by incorporating more than one trap into
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Fig. 1
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analysis, therefore further justifying the use of our MLT approach.
The co-evolution of n/N values of two traps under different cooling rates is shown by the contours of cooling rate (iso-β curves) in Fig. 1d. Two types of combination are shown: 1.55-1.60 eV (thin and red lines) and 1.55-1.70 eV (thick and black lines). The n/N values of
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relatively shallow (1.55 eV) and relatively deep (1.60 or 1.70 eV) traps are shown on x-axis and y-axis, respectively. The shaded area is the forbidden zone where the deep trap is saturated (n/N > 0.86, Wintle, 2008) or the shallow trap is empty (n/N < 0.05). The 1.55 - 1.70
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combination is applicable when β is higher than 0.2 oC.ka-1, while the 1.55 - 1.60 combination
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is applicable to all investigated scenarios. However, β is better resolved by the former combination since the intervals between iso-β curves are larger. For real rock samples, since we do not know a priori the cooling rate, it seems reasonable to incorporate a range of traps to allow the MLT approach being compatible with a larger range of cooling scenarios. Besides improving the resolution, and more importantly, Fig. 1d seems to show that no priori knowledge about Tp is needed to constrain the cooling rate once we get n/N values of two different traps. In the following, we employed the forward modeling to demonstrate the
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3.2 Constraining rock cooling rates using the MLT approach
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Suppose a rock cooled from 200 to 30 oC, the synthetic saturation ratios (Fig. 1c) modeled under a range of cooling scenarios (β = 0.01, 0.1, 0.2, 0.5, 1.0 and 1.5 oC.ka-1) were used as input observables for forward modeling to assess the potential of the MLT approach in
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constraining cooling rates. For the parameter space of forward modeling, T0 ranged from 30 to
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250 oC in steps of 5 oC; β ranged from 0.005 to 3 oC.ka-1 in steps of 0.005 oC.ka-1 when applying the forward modeling to the n/N values predicted with β = 0.01 oC.ka-1, while it ranged from 0.02 to 3 oC•ka-1 in steps of 0.02 oC•ka-1 for n/N values predicted with higher β values to reduce the computational cost. It should be emphasized that in the current numerical
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study, we only want to demonstrate the performance of the MLT approach, for which the coarse sampling interval does not matter, but a narrow sampling interval of β is preferred
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when applied to real rock samples.
Fig. 2
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The solution spaces (T0, Tp and β) are shown in Fig. 2. The prescribed β are 0.01 (slow cooling), 0.1 (medium cooling) and 1.0 (fast cooling) oC.ka-1 for the left, middle and right columns. From the first to the fourth row, the solution spaces are for SLT (1.55 eV), SLT (1.70 eV), DLT (1.55 and 1.70 eV) and FLT (1.55, 1.60, 1.65 and 1.70 eV) approaches, respectively. Since the choice of T0 does not affect constraint of β when T0 is high enough (well above the closure temperature, i.e. >100 oC), we only show the solution space with T0 bounded between 30 and 120 oC in Fig. 2.
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ACCEPTED MANUSCRIPT The solution space is wide if only the 1.55- or 1.70-eV trap is employed. The information of Tp helps greatly narrowing the solution space. Although the 1.70-eV trap helps better constraining the cooling rate β than 1.55-eV trap for the slow (Fig. 2b) and medium
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(Fig. 2f) cooling scenarios, its solution spaces are complicated by the saturation effects (n/N > 0.86, Fig. 1c). In fact, the saturation of 1.70-eV trap sets an upper limit for β. Under the fast cooling scenario, these two traps perform similarly on constraining β, however, the range of
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permitted Tp is much narrower for the 1.55-eV trap than that for the 1.70-eV trap (Fig. 2i and
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2j). Tp constrained by the 1.55-eV trap can be effectively regarded as the boundary Tp for the 1.70-eV trap. Therefore, the uncertainties in β are expected to be reduced by using these two or more traps together in a MLT approach. It is somewhat similar to the SLT approach of Li and Li (2012), but here we do not need external information on Tp anymore.
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For the slow and medium cooling scenarios (Fig. 1c, prescribed β = 0.01 and 0.1 o
C.ka-1), the DLT-constrained β range from 0.005 to 0.325 oC.ka-1 and from 0.02 to 0.24 oC.ka-
1
, respectively. Correspondingly, the permitted Tp are constrained in the range of 9 to 31 oC
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and 23 to 34 oC (Fig. 2c and 2g). For the fast cooling scenario (prescribed β = 1.0 oC.ka-1), the
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permitted β and Tp are bounded in the range of 0.08 to 1.18 oC.ka-1 and 24 to 41 oC with the DLT method (Fig. 2j). Two more traps (1.60 and 1.65 eV) are incorporated for the FLT method. For slow and fast cooling scenarios, the permitted β and Tp are substantially narrowed. The β values are constrained in the range of 0.005 to 0.175 oC.ka-1 and 0.8 to 1.18 o
C.ka-1, while the permitted Tp values are in the range of 19.3 to 31.2 oC and 24.2 to 31.6
o
C.ka-1, for slow and fast cooling scenarios, respectively (Fig. 2d and 2l). However, for the
medium cooling rate, the constraints on the permitted β and Tp are not significantly improved
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for almost all cooling scenarios except the case with prescribed β = 0.1 oC.ka-1. The FLT method improves the potential overestimation of DLT constrained β values for the scenarios with prescribed β = 0.01 and 0.1 oC.ka-1, while it improves a potential underestimation of the
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DLT constrained β values if the prescribed β is higher than 0.1 oC.ka-1. For the former two
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scenarios, the improvement is due to the incorporating traps suffering less from the saturation effect (Fig. 1d). However, for other scenarios, the improvement is due to the narrower bound of the permitted lowest initial temperature T0 (Table 1).
We mentioned earlier that the choice of T0 does not affect the constrained β, if T0 is
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high enough (i.e. > 100 oC). However, the lowest permitted T0 is constrained by the DLT and FLT methods, and the increase of this lower limit eliminates the low cooling rates for the FLT method (Fig. 2 and Table 1). If the initial temperature T0 is higher than 75 oC, then the DLT
C.ka-1 (Table 1).
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3.3 Minimum cooling rate constrained by MLT approach Thermochronometers with different thermal stabilities are required for the MLT approach. However, it is possible that the relatively stable traps are getting saturated while the most unstable traps are still empty at low cooling rate. Therefore, the dose saturation of
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ACCEPTED MANUSCRIPT luminescence signal sets a lower limit for cooling rate that can be effectively constrained by the MLT approach, which was therefore investigated numerically with a range of difference in traps’ thermal stabilities.
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The difference in thermal stabilities was depicted by different trap depths. For a specified β, the equation (1) was numerically integrated for the relatively stable trap with a given depth of dS and the relatively unstable trap with a depth of dS - δE. Then, we examined
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whether the n/N value of the unstable trap was < 0.05 (taken as the criteria for an empty trap)
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when the n/N value of the stable trap was just > 0.86 (criteria for trap saturation). We increased δE from 0.01 eV to 1.00 eV in steps of 0.01 eV. The minimum δE predicting the n/N value just <0.05, as well as the corresponding β and dS, were recorded. The above iterative process was repeated with dS varing from 1.5 to 2.5 eV in steps of 0.05 eV, and β
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ranging from 0 to 2 oC•ka-1 in steps of 0.01 oC.ka-1, respectively. The integration interval was also taken as the ratio of (T0 + 60) to the assigned cooling rate β, and other parameters were
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taken as following: T0 = 250 oC, D0 = 200 Gy, = 3.3 Gy•ka-1 and s = 1013 s-1. Fig. 3
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Fig. 3 shows the relationship among all recorded δE, β and dS. Different colors indicates the minimum cooling rate (βmin) that can be constrained by the traps with depth of dS and dS – δE, e.g., in the case of trap depths of 1.8 and 1.6 eV, the minimum cooling rate that can be effectively constrained is ~ 0.2 oC.ka-1. Clearly, βmin increases significantly with the δE for any dS. For a given δE, the βmin decreases with the depth of relatively stable trap (dS). For instance, we took a profile across the color map of Fig 3a at δE = 0.21 eV (AA’). As shown in Fig.3b, βmin decreases from 0.25 to 0.01 oC.ka-1 with dS increasing from 1.5 to 2.5 eV. Such a
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3.4 Advantages and limitations of the MLT approach
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applying the MLT approach.
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different thermal stabilities based on a priori estimate of the expected cooling rates, before
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In this study, we tested the potential of the MLT approach to constrain rock cooling rates using a numerical investigation. To apply the MLT approach to natural samples, the natural intensities of multiple luminescence signals could be converted into either 1) De values, and thereafter apparent closure ages (i.e. De/ ) or 2) saturation ratios (n/N) (Guralnik
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et al., 2013). For both cases, the thermal kinetic parameters (E and s) of the multiple luminescence signals have to be determined experimentally for each individual sample (Chen and Pagonis, 2011; Guralnik et al., in press). Combining these data all together, the thermal
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history of the sample can be constrained in two ways correspondingly: 1) by confronting the
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apparent closure ages against the associated closure temperature (Braun et al., 2006; Guralnik et al., 2013); or 2) by numerical forward modeling approach exploiting MLT as we proceeded for the synthetic data in section 3.2. Indeed, by incorporating the experimentally derived parameters (D0, E, s and ) into equations (1) – (3), forward modeling allows to compute modeled n/N values with every combination of T0, β in the given parameter space [T0, β] for each luminescence trap. One can then search numerically in the parameter space for the bestfit combinations generating modeled n/N values consistent with the observed n/N values for
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ACCEPTED MANUSCRIPT all investigated traps. The ensemble of such T0, β, the corresponding cooling period t and the resulting Tp cover all possible cooling history generating the observed n/N. In that framework, any knowledge/assumption on both the apparent closure temperature and present-day
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temperature Tp is not required. Further, our approach also enables to estimate the Tp as a model output. Finally, if T0 is high enough, a rough cooling rate can also be read out directly from a plot similar to Fig. 1d based on DLT method. The next step will be to test our MLT
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approach on natural samples to fully infer its potential in constraining rock cooling histories.
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For the MLT approach, different methods can be adopted considering the available number of traps as well as the trap depths. For the quartz system, if the initial temperature T0 is high enough (> 100 oC), the constrained cooling rates are independent of the choice of T0, therefore, the unknown parameters in equations (1) – (3) reduce to two (only the cooling rate
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and the cooling period). In this case, the DLT method constrains the cooling rate satisfactorily. However, more than two thermochronometers are preferred if we are not sure whether or not the T0 is possibly low (e.g. reheating thermal event). The FLT method exploited here could
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eliminate such possibilities for the cooling scenarios with prescribed cooling rate being higher
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than 0.1 oC.ka-1 (Fig. 2 and Table 1). When the cooling rate is lower than 0.1 oC.ka-1, we should be cautious about the saturation effect, which would limit the application of the MLT approach. For the slow cooling scenarios, a small difference in the traps thermal stability is preferred (Fig. 3), although the associated resolution in the output cooling rate will get worse (Fig. 1d). For application to real rock samples, more than two thermochronometers are recommended with consideration of balancing the potential saturation and resolution of the multiple thermochronometers. An expected cooling rate could provide guidance to optimize
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ACCEPTED MANUSCRIPT the experimental parameters to isolate multiple luminescence signals with appropriate differences in their thermal stabilities. TL signals and different components of the OSL signal for quartz are suitable
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candidates for the MLT approach, since luminescence signals with different thermal stabilities can be isolated during a single measurement sequence (e.g. Aitken, 1985; Singarayer and Bailey, 2003). However, Guralnik et al. (2015) demonstrated the complexities of using
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bedrock quartz OSL signal as a potential thermochronometer through a comprehensive
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investigation on its basic luminescence characteristics, which may also be applied to the TL signals of bedrock quartz. The development of non-fading post-infrared infrared stimulated luminescence (pIR IRSL, Thiel et al., 2011) and multiple elevated temperature (MET)-pIR IRSL (Li and Li, 2011) signals of potassium feldspars (K-feldspars) are of great potential for
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the MLT approach, since signals with different thermal stabilities can be simply isolated by changing the IR stimulation temperature (Thomsen et al, 2011; Li and Li, 2013). The conventional low temperature IRSL signal is generally less thermally stable than the post-IR
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IRSL signals, and it may play an important role for the MLT approach of K-feldspars. Since
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new generic models have been developed to describe the trapping and anomalous fading processes of the IRSL signal (Huntley, 2006; Kars and Wallinga, 2009; Jain et al., 2012), they may enable the use of IRSL signals without fading correction. By using the IRSL and pIR IRSL signals together, we will have more candidates for the MLT approach. Li and Li (2012) investigated the effects of the dose rate ( ) and characteristic saturation dose (D0) on resolving rock cooling rates using luminescence thermochronometers. Such effects also hold for each single thermochronometer of the MLT. In fact, the ratio of to 15
ACCEPTED MANUSCRIPT D0, which is the “probability per unit time of an empty trap being filled by the radiation”, is the ultimate controlling factor (Huntley and Lian, 2006). It implies that the luminescence signal with a smaller /D0 is preferred to serve as a relatively stable thermochronometer for
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the MLT approach.
4. Conclusions
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In this study, the applicability and advantage of the multiple luminescence
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thermochronometers (MLT) approach to constrain rock cooling rates from a single sample is demonstrated through numerical forward modeling with different electron trap depths typical for the quartz mineral. The rock cooling rates are independently constrained by MLT saturation ratios without a priori knowledge on the present-day temperature. If we
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independently know that the initial temperature has been high enough (i.e. > 100 oC), two thermochronometers with sufficient difference in their thermal stabilities can constrain the cooling rate satisfactorily. Otherwise, more thermochronometers may help reducing the
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uncertainty in cooling rate predictions. Due to the saturation effect of luminescence signals,
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the minimum cooling rate that can be constrained should be evaluated before applying the MLT approach to natural rock samples.
Acknowledgments
We are thankful to an anonymous reviewer for his/her constructive comments, which greatly help us clarifying our manuscript. We also thank Dr. Shenghua Li for his inspirational suggestions during revisions. This work was supported by the National Science Foundation of
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ACCEPTED MANUSCRIPT China (41272195), SKLED grant (No. LED2010A04), IGCEA grant (No. 1417), China Postdoctoral Science Foundation (2013M540997), and the Swiss National Foundation
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(#PZ00P2_148191 for P.GV).
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Figure 1. Evolution of saturation ratios (n/N) for a) 1.55 eV and b) 1.70 eV traps under different cooling rates (0.01 to 2 °C.ka-1, see legend for details). The n/N values with Tp=30oC (vertical lines in a and b) are used for generating values in panel (c); c) Synthetic “observed” n/N of different trap depths under different scenarios (see legend for details) when cooling from 200 oC to 30 oC; d) Relationship between n/N of two luminescence traps during cooling (iso-cooling-rate plots). Two groups of traps are investigated: 1) 1.55 and 1.70 eV (thick and black); 2) 1.55 and 1.60 eV (thin and red). The shaded area is the forbidden zone where the deep trap is saturated (n/N > 0.86) or the shallow trap is empty (n/N < 0.05). For both cases, x-axis refers to 1.55-eV trap, while the y-axis refers to the 1.60- or 1.70- eV trap (The reader is referred to the web version for colorful plot).
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Figure 2. Solution spaces for the initial temperature (T0), cooling rate (β), and present-day temperature (Tp) obtained by the SLT-1.55 (a, e, h), SLT-1.70 (b, f, i), DLT (c, g, j) and FLT (d, h, l) approaches. The constrained cooling rates are shown by color-coding (the color bar applies to all four panels below it). The input T0 and Tp parameters are 200 oC and 30 oC for all scenarios, respectively. The input β values are 0.01, 0.1 and 1.0 oC.ka-1 for the left (a-d), middle (e-h) and right (i-l) columns, respectively. Note the logarithmic scale for the color map.
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Figure 3. a) Relationships between the trap depth of relatively stable trap (dS), difference in trap depth (δE) and minimum cooling rates (βmin, shown by different colors) that can be constrained by applying the MLT approach; b) The variation of βmin with the dS for a given δE of 0.21 eV, which was extracted along the profile AA’ in (a).
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Modeled by DLT2
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Table 1. Summary of the input cooling scenarios, associated synthetic saturation ratios, and output parameter ranges from MLT based forward modeling.
Modeled by FLT2
Synthetic observed n/N1
Given β ( oC.ka-1)
lowest T0 ( oC)
Tp ( oC)
β ( C.ka-1)
0.738-0.949-0.992-0.999 0.600-0.855-0.959-0.990 0.499-0.736-0.874-0.943 0.343-0.512-0.646-0.744 0.236-0.348-0.447-0.531 0.192-0.275-0.351-0.420
0.01 0.1 0.2 0.5 1.0 1.5
30 40 40 40 45 45
8.9-31.2 22.8-33.6 25.4-35.8 26.0-38.4 24.2-41.2 21.6-42.8
0.005-0.325 0.02-0.24 0.02-0.30 0.02-0.60 0.08-1.18 0.06-1.76
lowest T0 ( oC)
Tp ( oC)
β ( C.ka-1)
30 40 50 65 70 75
19.3-31.224.8-33.6 26.0-32.7 26.0-31.8 24.2-31.6 21.6-29.6
0.005-0.175 0.02-0.20 0.12-0.28 0.40-0.60 0.8-1.18 1.26-1.76
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1. The n/N values are shown for the different trap depths in the following order: 1.55, 1.60, 1.65 and 1.70 eV; 2. DLT refers to using 1.55- and 1.70-eV traps together, while FLT refers to using 1.55-, 1.60-, 1.65- and 1.70-eV traps together for forward modeling.
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Highlights -Investigation of a Multi-Luminescence-Thermochronometer (MLT) approach -Numerical experiments to constrain rock cooling rates and present-day temperatures -Resolution and limitation of the MLT approach are discussed.