the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 Jan 2025
Rapid dose rate estimation for trapped charge dating using pXRF measurements of potassium concentration
Abstract. Quantifying environmental radiation dose rates is an essential step in age calculation using trapped charge dating methods. A means of rapid dose rate estimation would therefore be useful for a variety of reasons, especially in contexts where rapid equivalent dose estimates are available. For instance, for informing sampling strategy, providing initial age estimates, or supporting portable luminescence studies. However, high-precision methods often used for calculating dose rates are typically time consuming and expensive and are impractical for such ‘range-finder’ applications. Portable X-ray fluorescence (pXRF) offers a rapid means of measuring the Potassium (K) concentration of sediment, although the other radionuclides typically used to calculate dose rates (Uranium (U) and Thorium (Th)) fall beneath its detection limits at the quantities at which they are usually present in sediments. In this study, we investigate whether pXRF measurements of K concentration alone can be used to accurately estimate total environmental dose rates. A large, global training dataset of 1473 radionuclide samples is used to generate a set of linear relationships between (1) K concentration and external beta dose rate; (2) external beta and gamma dose rates; and (3) external gamma and alpha dose rates. We test the utility of these relationships by measuring the K contents of 67 sediment samples with independent high-precision radionuclide data from a variety of contexts using pXRF. The resulting K concentrations are then converted to external dose rate estimates using the training equations. A simplified set of attenuation parameters are used to correct infinite matrix dose rate estimates, and these are combined with cosmic ray and internal contributions to rapidly calculate total environmental dose rates for a range of theoretical, common luminescence dating scenarios (such as 180–250 μm quartz that has undergone etching). Results show that pXRF can accurately measure K concentrations in a laboratory setting. The training equations can predict external beta dose rates accurately based on K content alone, whilst external alpha dose rates are predicted less accurately. In combination, total estimated dose rates show good agreement with their counterparts calculated from high-precision methods, with 68–98 % of our results lying within ±20 % of unity depending on the scenario. We report better agreement for scenarios where alpha contributions are assumed to be negligible (e.g., in the case of etched, coarse-grained quartz or potassium feldspar). The use of simplified attenuation factors to correct estimated infinite matrix dose rates does not contribute significantly to resulting scatter, with uncertainties mostly resulting from the training equations. This study serves as a proof of concept that pXRF measurements, along with a set of linear equations and a simplified correction procedure, can be used to rapidly calculate range-finder environmental dose rates.
Competing interests: Some authors are members of the editorial board of Geochronology.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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RC1: 'Comment on egusphere-2025-55', Anonymous Referee #1, 16 Feb 2025
The manuscript presents a fast dose rate estimation method for trapped charge dating using potassium measurements. The manuscript is well written, but I do have several remarks.
First, the interpretation and data analysis are somewhat too optimistic. Correlations might not be that high in a real-world scenario. Second, I was wondering if the term "training" is related to machine learning methods; if not, I would not use it. Third, was the data analyzed using a weighted least squares method, and was the weighting applied to the y or x data axis? The errors on the x-axis are much larger in most of the plots.
L37 "in Gy per time unit, e.g.," Gy is energy per mass, so "Gy per time" is somewhat misleading. Please remove "Gy per time".
L58-59 "all of which influence radiation emission and absorption." This is not true. For example, radiation emission cannot be changed by grain size. Please remove the fragment "all of which influence radiation emission and absorption."
L87 "De" subscript is missing.
Figure 1 could be replaced by a plot showing dose rates arising from K vs U and Th. This would (or would not) better support the claims.
L214-228 This interpretation is somewhat too optimistic. From the perspective of this article, we are only measuring K%, so I was wondering if on all plots in Fig. 4, the x-axis should be K% instead.
Figure 5 Would it be possible to add x-error bars? Usually, values that are measured with higher precision should be on the x-axis. This is related to weighting in the least squares method.
Figures 6 and 7 The same comment as above.
L103-104 The sentence structure is unclear. Consider rephrasing for better readability.
L145 Check consistency in terminology when referring to potassium measurement techniques.
Citation: https://doi.org/10.5194/egusphere-2025-55-RC1 -
RC2: 'Comment on egusphere-2025-55', Loïc Martin, 18 Mar 2025
Dose rate determination is necessary for most luminescence dating method, and developing tools and method for its determination is essential. This research presents the use of portable XRF, an instrument that is widely available, affordable and precise, for determining K content in sediments, one of the main contributor to dose rate. While this has already been investigated, this study goes further by proposing to estimate the beta dose rate, gamma dose rate and alpha dose rate based on these K measurement and a training relationship obtained thanks to an extended dataset. While the correlation between K content and dose rates seems logical, there is very few attempts to quantify it and even fewer to propose a practical method to do so. Even if some uncertainties on the results are larges (and this is discussed in the paper), this method provide a way to quickly estimate dose rates, with potentially a high spatial resolution and on site. This has the potential to bring very relevant information for targeting samples of interest and a better understanding of the chrono-stratigraphy of sites, in the same way than portable OSL method already brought (its complementary with the presented method is highlighted in the study).
The manuscript is well constructed, the method and reasoning are well explained. The dataset used for the training relationship is large enough for such a study. Most of the relevant topic are discussed and most of the data are provided. Data about the portable XRF calibration are missing but will hopefully be added.
My main concern is about the use and meaning of some of the statistical tools used for characterizing the goodness of fitting of the training relashionship and of the dose rate obtained by applying it to K measurement with portable XRF. This is developed below with reference to the concerned line and figures. I believe that the methods used are not the right one and I suggest to either switch to a different one that makes more sense, or to justify and discuss of the reasoning behind the application of the current one. It is essential for the study to resolve this point because it has major consequences concerning the uncertainty and precision of the method developed.
Beyond this major correction, I only have some minor comments detailed below.
Detailed comments:
Fig.1 some graph of U/Th and K/U ratios in the same sediments would also provide very useful information to interpret the relationship between K and beta, alpha and gamma dose rate.
L116: Be careful here: positive correlation does not imply proportionality (which is the meaning of the ∝ symbol). It only mean that the two parameters are moving in the same direction, not that there is a proportionality between them. Please clarify if the reference quoted are demonstrating the proportionality or the only the positive correlation of beta dose rate and K content, and if you are looking for demonstrating their proportionality in the paper.
L117 and L121: same issue, positive correlation is different than proportionality. Please clarify which one apply here.
L130: This is a nice sampling set. Could you provide some database (spreadsheet, table,…) as supplementary date with their identification, sampling location, radio-element content, type of geology and reference (if published before)? Is there any sample that you rejected for some reason? Are you planning to update your results with additional samples?
L191: Is this water content value from an average of measurement over samples, from a published value, or simply a standard value from experience? Please specify it.
Fig.4: Please be aware that the standard errors of a linear regression represent the uncertainties on the fitting parameters, i.e the range within which these parameters will still represent a good fit of the data. They are not an estimate of well the data point fit to the regression line. Here is a little reasoning to understand what is wrong here: if you were to measure some over datapoints for these graphs, and you managed to measure them with a negligible error, then you would not expect them to align with the regression line within the standard error of its parameters. You would rather expect them to show scatter like the rest of the datapoints, because of the natural variations of radioactive elements (and therefore of dose rates) in the different geological material worldwide.
This mean that if you estimate the uncertainty of your model by using the standard errors of the slope and intercept, you implicitly imply that all measurement should be on the regression line within these errors, and that the data scattering represents the measurement error (in a wide range, including error on sampling, preparation, calibration, measure, etc…). This is difficult to justify considering that the dataset includes samples from very different geological context, and we know that these ratios (beta dose rate / K, beta dose rate / gamma dose rate, gamma dose rate / alpha dose rate) naturally fluctuate from a place to another without being the results of measurement error.
At the opposite (for example), on your fig.5, the standard errors are the right way to estimate the uncertainty, because it is expected that all the data points should align and that the scattering is only due to measurement errors, and not to a natural dispersion.
So, if you want to characterize the variability of the value around the regression, you need to use a metric that indicates how much the data point can scatter around the regression line. The ideal metric for this would be the Root Mean Square Error (RMSE). Please use the RMSE value instead of the standard errors for calculating the uncertainty on the training relationship, or please justify and discuss the use of standard error to characterize the uncertaintyon the training relationship.
L231: What about the quantification limit rather than the detection limit? If you are using the content of K for estimating the other variables, the quantification limit seems more adapted.
L235: It is noticeable that even if the K of a sample fell below the detection limit or the quantification limit, that will still allow to infer on the beta dose rate intensity, as well as on the gamma and alpha dose rates (by giving maximum dose rates, that will provide minimum ages) considering the results showed on fig. 4 . So even a non-detection of K in a sample provides useful information.
L236 to L245: the 9% of difference between the trend line and the unity line seems typical of a calibration issue. It is unlikely that this could come from the high-precision measurements because you used two different techniques for these measurements. Could you provide more information about the standards used for the pXRF calibration? In particular the K concentration and the type of matrix. For example, if the high K standards have a matrix composition significantly different from the sample you measure, then it can cause a calibration bias. This could help to determine if there is an issue from the calibration, or to exclude this as the source of the observed bias. Please also provide the uncertainty on the pXRF calibration, this is necessary for discussing of the accuracy of the measurements.
Fig.5: Change the Y axis title KHR to KHP.
Please provide the uncertainty bars on the pXRF measurement, including the uncertainty on the calibration.
On the frequency graph, it is unclear what the 74% and 91% values are referring too. Please either add a comment in the figure description or simply delete them (as I don’t think they are necessary to understand the frequency graph, and they are already given in the main text).
I am surprised to see that some of the uncertainty on the high-precision K measurements are quite high (up to 10%). Could you provide some information about that? Please also indicate if the uncertainties are provided at 1 or 2 sigma.
L262: As explained for fig.4, in this case the standard errors of the regression are not a good estimate of the uncertainty of the observed relationships in the training data set. This is because the data scattering is not due to measurement errors but to the natural variability of sediments. You should use RMSE as uncertainty.
Could you also specify if the uncertainty on the pXRF measurement of table S2 includes the pXRF calibration uncertainty? If not, please add this uncertainty to your calculations.
L264: “the standard deviation of these mean uncertainties is <0.001 Gy/ka in all cases”. It is unclear what you mean by this, and what does it mean for your results. Could you elaborate this further?
L269: Could you actually present some quantitative value of these correlation, for example by calculating their Pearson correlation coefficient (PCC)? That will allow the reader to evaluate how significant are the correlations. In the case of the alpha dose rate, I am not so sure that this can be called a good correlation (but the PCC may tell overwise).
L269 to L282: Here there is a wrong use of statistics, or a misunderstanding of their meaning: if you want to quantify the agreement between the rapid estimate and the high precision estimate of the dose rates, then you should to calculate the R² of your datapoints relative to the unity line, not the one relative to the datapoint trendline. Here is an absurd reasoning: imagine all your datapoints are perfectly aligned (negligible scattering) around a trendline with a slope of 0.33 (like you have for the alpha dose trendline). Then your R² relative to the trendline would be 1 (perfect match), however there would be a very poor agreement between rapid estimates of dose rate and high precision estimates.
L280 to L282: considering the high scattering beyond uncertainties and low R², the most likely conclusion would rather be that a linear trend is simply not representative of your datapoints. But this may change once you recalculate the uncertainties on your fast measurement and training relationship according to the previous comments.
Besides, if you look at the red trendline of fig. 6a compared to the unity line, you can see that the supposed relationship actually underestimates the dose rate when it is below 5 Gy/ka.
L284 to L290: Could you actually calculate the standard errors on parameters of the regression lines, and check if there are compatible with the unity line (i.e that the slope is within 2 standard error value of the value 1 and that the intercept is within 2 standard error value of 0). If it is, that would simply mean that the differences between trendline and unity line can be explained by the scattering of the datapoints.
L291 to L300: This makes sense, and that could allow you to calculate the reliability of the method depending on the measured K content (using the data from the training set for example). This would be a very useful information for the method you developed.
L316 to L320: same than for L269 to L282, you cannot test the agreement by calculating the R² between the datapoints and their trendline. For that, you need to calculate the R² between the datapoints and the unity line. However, you can test if the trendline parameters are compatible with the unity line within their standard error (see comment for L284 to line 290).
L335: same comment than for L316 to L320 and for L269 to L282
L343 to L349 and fig.7: It is not always an overestimation because for lower dose rate you have an underestimation (the red trendline is above the unity line).
It would be useful to test if the trendline parameters are compatible with the unity line within their standard error (see comment for L284 to line 290). That will help to see if their difference can be explained by the uncertainty on the linear regression.
You seem to forget an important source of error here: the sampling bias. Every dating laboratory have regional areas of predilection, depending on the focus of their studies and the projects they have (for example, some laboratories have a high focus on South Africa, while other would have high focus on North America). This could be a factor significant enough for creating a bias between the dataset available at your lab and the more worldwide dataset used to build the training relationship. I invite you to generate training relationship for the different parts of the world for the which you have data, to see if significant difference in trends can be observed. Of course, this represent some work that may be beyond the focus of your current manuscript, but you should at least discuss of this potential sampling bias.
L354: same comment about the calculation of R² than for L269 to L282, although this will not change significantly your result here.
L337: do not forget the measurement error part in the uncertainty.
L375: I would say that “very well” is a little overstated and should be removed. From fig. 5 there seems to be a bias that resemble to a calibration issue and should be tested or discussed further.
L384 to L394: This point occurred in my mind while reading about your lab setting. It is indeed very important and I am please to see it discussed. You could add that the in-lab testing that you did is a necessary step before undergoing any field study on the subject.
L399: please provide (in supplementary data) data about your calibration (type of standard certification, their matrix, their K content) and the uncertainty associated with the calibration.
L427 to L433: You should add that the differences between the observed fitting parameter could be likely explained by the size of the different datasets and the sampling bias related to the nature or origin of the samples in each dataset.
L444 to L449: It is likely that, once you based your uncertainty on the RMSE instead of the standard error of the parameters like recommended, these negative intercepts will be compatible with the 0 value within uncertainty. I believe they are simply an artifact of the natural dispersion of radioactive elements and dose rate in geological samples around the world.
L451: You should also quote Nathan R. Jankowski, Zenobia Jacobs (2018): Beta dose variability and its spatial contextualisation in samples used for optical dating: An empirical approach to examining beta microdosimetry, Quaternary Geochronology 44, https://doi.org/10.1016/j.quageo.2017.08.005. They used pXRF for K spatially resolved K measurement in geological sample, with even an attempt to quantify U and Th with this instrument.
L467: negligible contribution will be more correct than “no contribution”
L478 to L485: You seem to forget that in the case of exposure surface dating, there is no need for dose rate calculation (the dose rate is not a part of the dating equation. It will only be useful in the case of burial surface dating, when the bleached surface is buried again and start re-accumulating charges under the effect of radiation.
Citation: https://doi.org/10.5194/egusphere-2025-55-RC2 -
RC3: 'Comment on egusphere-2025-55', Martin Autzen, 24 Mar 2025
The paper addresses an important part of luminescence dating: rapid determination of dose rates, potentially on-site screening use. The paper is well written and I think it contributes an important tool to the luminescence dating community, however I have a few remarks.
I am guessing that the "training" referred to in the paper is machine learning, but this is never specified. The pXRF is operated in two beam mode, but no explanation is given for what this means, nor is any data on the instrument or its settings provided.
One part which I feel is missing, is how the model works in the extremes. Based on the training set I assume that there are samples with low K but higher concentrations of Th and U. It would support the overall application of basing everything on measurements K content to show how the predictions fit in such cases. For now I feel that there is strong reliance on R2 values to determine how the method works with most of the datapoints clustered in a very narrow range. This is obviously not something the authors can control, but given the extensive dataset used for the training, some investigation over a broader dose rate range would help strengthen the paper.
Equations 3, 4, 5: ∝ does not directly imply a positive correlation, rather it is used to show proportionality between two or more variables. I'd suggest adjusting the text accordingly.
Figure 4: Did you compare the K beta dose rates when using the conversion factors of Creswell et al. (2018) as well, since this should be more accurate? It should increase the K beta dose rate about 7%, which is rather substantial. It would also affect later figures.
Figure 5: Any ideas why the pXRF underestimates K? Was it the same for reference materials?
Figure 6: It would be nice to see comparison of higher IM gamma dose rates as the data shown is still in the region where Fig. 4b appears to be described by a linear function. It would also show how suitable the choice of linear vs second order is for the training.
L432: Here I disagree that the linear fit should be used in lieu of a physical explanation as Figure 4b clearly shows that the relationship between IM beta dose rate and IM gamma dose rate is not linear, especially at higher IM beta dose rates. Assuming that you always have the same proportions of K, Th, and U and only the absolute activities are changing, then it would be linear, but that seems like an overly ideal situation. Since most of the datapoints are appear to be clustered between 0-3 Gy/ka, the R2 likely wouldn't change much if you use a second order polynomial, but at higher IM beta dose rates I'm guessing your fit would be a lot better.
Citation: https://doi.org/10.5194/egusphere-2025-55-RC3
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