Chromium geochemical background value quantitative characterization method

Through multivariate regression analysis based on abundance data, a new quantitative characterization method for chromium geochemical background value was proposed, which solved the problems of limited data volume and large calculation errors in the existing technology, and realized the objective and accurate characterization of chromium background value, providing a reliable basis for environmental quality evaluation and mineral resource exploration.

CN119541679APending Publication Date: 2025-02-28CHINA UNIV OF GEOSCIENCES (BEIJING)
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Patent Information

Application Number
CN202411595816.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-11
Publication Date
2025-02-28

AI Technical Summary

Technical Problem

In determining the geochemical background value of chromium, the data volume is limited, the unsuitable for samples of different weathering degrees, and the calculation error is large, and the background value of chromium content in the rock-soil-seed system cannot objectively reflect the background value of chromium content in the rock-soil-seed system.

Method used

Based on the abundance data of rock-soil-seed system samples, a new quantitative characterization method for chromium geochemical background value is proposed through parameter construction and multivariate regression analysis. This method does not require a large amount of sample data and can be suitable for samples of different weathering degrees. The reliability of error control within the content logarithmic difference of ±0.2 can reach 95%.

Benefits of technology

This method can objectively and accurately characterize the geochemical background value of chromium, make up for the shortcomings of traditional methods, provide a more reliable geochemical background value, and provide an important basis for environmental quality assessment and mineral resource exploration.

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Abstract

The invention provides a chromium geochemical background value quantitative characterization method, and belongs to the technical field of environmental quality evaluation. S1, determining source data of a fitting equation; based on abundance data of rocks, soil and sediments, selecting data which can be regarded as a background area sample and contains main oxides and chromium content, and recording 791 records in total; s2, on the basis of the 791 pieces of abundance data, calculating a weathering index WIG and a newly constructed element ratio parameter, and fitting an equation representing a chromium geochemical background value by adopting a piecewise function and a nonlinear multiple regression technology; during equation fitting, the error standard is set to be within the content logarithmic difference + / -0.2, and the sample within the error is required to be about 95% or above; and S3, fitting the obtained chromium geochemical background value quantitative characterization equation. According to the method, the defects of a traditional method and a current empirical equation method can be overcome, and an objective and reliable geochemical background value is provided for environment quality evaluation of chromium and mineral resource exploration.
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Description

Technical Field

[0001] The invention provides a method for quantitatively characterizing chromium geochemical background values, and belongs to the technical field of environmental quality assessment. Background Art

[0002] Chromium is not only a typical heavy metal element, but also an essential dietary trace nutrient for humans, and also an important metal mineral resource. Therefore, chromium is an important focus in the fields of soil environmental quality assessment and mineral resource exploration. In the rock-soil-sediment system, the geochemical background value of chromium is not only an important basis for conducting environmental quality assessment and pollution source tracing, but also an important reference for discovering and evaluating anomalies in the field of mineral resource exploration. At present, the method of determining the geochemical background value of element content is usually characterized by data statistical parameters, such as calculating the average value (or geometric mean) or median value based on the approximate normal (or lognormal) distribution, fractal (or multi-fractal) distribution, multi-mode distribution, etc. to characterize its geochemical background value. This type of method not only requires a large amount of data, but also the background value obtained is a relative expression, and cannot objectively express the geochemical background value of environmental samples or geological samples. For example, it is impossible to determine the geochemical background value of chromium for a rock, soil or sediment sample; even if multiple chromium content data are analyzed and tested for samples of different lithologies or different degrees of weathering, the determined background value is only relative and cannot objectively reflect the background value of chromium content in environmental samples or geological samples in the rock-soil-sediment system.

[0003] In view of the defects of the above-mentioned traditional determination of the geochemical background value of chromium, the applicant's scientific research team has proposed an idea that the geochemical background value of chromium in the sample can be calculated based on the main oxide content data of the sample (Journal of Geochemical Exploratin, 2015, Vol. 152, P110-117). Subsequently, based on this idea, the applicant's scientific research team also proposed an empirical equation for quantitatively characterizing the geochemical background value of selenium (Se) (Modern Geology, Vol. 32, No. 5, 2018, P1031-1041). For the quantitative characterization of the geochemical background value of chromium, the empirical equation proposed by the applicant's scientific research team in 2015 is still used (Journal of Geochemical Exploratin, 2015, Vol. 152, P110-117). The equation has the following defects: ① The amount of data used to fit the equation is limited, which is only 163 case data from 13 weathering profiles, which is not representative; ② The fitted equation is not applicable to the case where the weathering index WIG>120; ③ For the rock-soil-sediment abundance data, the calculated background value error is large (the error is within ±0.2 of the logarithmic difference of the content in only 40% of the cases). Summary of the invention

[0004] The present invention proposes a new method for quantitatively characterizing the geochemical background value of chromium, which can make up for the above-mentioned defects of the traditional method and the current empirical equation method, and provide objective and reliable geochemical background values ​​for environmental quality evaluation and mineral resource exploration of chromium.

[0005] The present invention is based on the abundance data of rock-soil-sediment system samples, namely the major oxide content and chromium content data, and regards the virtual samples represented by the abundance data as background area samples, and proposes a new method for quantitative characterization of chromium geochemical background values.

[0006] The new method proposed in the present invention can overcome the shortcomings of traditional data statistical parameter methods. For example, the background value determined by the traditional statistical parameter method is relative and needs to be determined based on a large amount of sample data, while the new method does not require a large amount of sample data to determine the background value, and the background value of one sample can also be determined, and the background value determined by the new method is objective.

[0007] Compared with the background value equation proposed by the applicant's research team in 2015, ① the original equation was obtained based on limited case data and had poor representativeness, while the new method is an equation based on a large amount of abundance data fitting and has strong representativeness. ② The new equation can be applied to samples with different degrees of weathering, which makes up for the deficiency that the original equation is not applicable to weathering index WIG>120. ③ The new equation has high accuracy in quantitative characterization of chromium background value in samples, and the error within ±0.2 of the logarithm difference of the content can reach 95% for the abundance data.

[0008] In summary, the present invention proposes a new method for quantitative characterization of chromium geochemical background values, which can make up for the deficiencies and defects of traditional methods and current empirical equation methods, and provide objective and reliable geochemical background values ​​for chromium environmental quality evaluation and mineral resource exploration.

[0009] The specific technical solutions are:

[0010] A quantitative characterization method for the geochemical background value of chromium is proposed. Based on the element abundance data of rocks, soils, and stream sediments in China, namely the major oxide content and chromium content data (a total of 791 records), an equation for calculating the geochemical background value of chromium samples in the rock-soil-sediment system is proposed through parameter construction and multivariate regression analysis.

[0011] The specific steps are as follows:

[0012] S1. Determine the source data for the fitting equation. Based on the rock, soil, and sediment abundance data, select data that can be regarded as background samples and contain major oxides and chromium content, totaling 791 records.

[0013] In the embodiment, the data used can come from: "Handbook of Applied Geochemical Element Abundance Data" compiled by Chi Qinghua and Yan Mingcai in 2007, published by Geological Publishing House; "China Soil Geochemical Parameters (Volumes 1, 2 and 3)" written by Hou Qingye et al. in 2020, published by Geological Publishing House; "Application Research of Geochemical Exploration Data for National Mineral Resources Potential Evaluation" written by Xiang Yunchuan et al. in 2018, published by Geological Publishing House.

[0014] S2. Based on the above 791 abundance data, the weathering index WIG and the newly constructed element ratio parameters were calculated, and the equation representing the geochemical background value of chromium was fitted using piecewise function and nonlinear multiple regression technology. When fitting the equation, the error standard was set to within ±0.2 of the logarithmic difference of the content, and more than 95% of the samples were required to be within the error.

[0015] S3. The equation for quantitative characterization of the chromium geochemical background value obtained by fitting is as follows.

[0016] The source data n of the fitting equation is 791 (i.e., a total of 791 abundance data records), the unit of oxide content is mass percentage (%), and the unit of chromium (Cr), titanium (Ti), and manganese (Mn) content is mass parts per million (ppm or μg / g).

[0017] a) According to SiO2<33, 29 data were screened. After removing one record, lgCr and Ti, Al2O3 contents were linearly fitted, and the error values ​​were within ±0.2 of the logarithmic difference of the contents. The calculation equation is:

[0018] lgCr=0.0634Al2O3+0.000308Ti+0.67n=28,r=0.921Equation 1a

[0019] At this time, the Al2O3 content is between 0.66 and 4.81, the Ti content is between 185 and 1510, the Cr content is between 4.7 and 26, and the calculated Cr background value is between 5.9 and 27.1. It is recommended that the equation prediction value be limited to the logarithmic extreme value of the original data and the calculated data within ±0.1, that is, the calculated Cr background value can be limited to between 3.7 and 34.1.

[0020] b) A total of 54 data were screened based on MgO>3.9. After removing 3 records, lgCr, lgMgO and lgNa2O were nonlinearly fitted, and the error values ​​were within ±0.2 of the logarithmic difference of the content. The calculation equation is:

[0021] lgCr=0.4818lgMgOlgNa2O+0.8408lgMgO-1.128lgNa2O+1.89n=51, r=0.980 Formula 1b

[0022] At this time, lgMgO is between 0.60 and 1.62, lgNa2O is between -0.49 and 0.70, Cr content is between 76 and 2500, and the calculated Cr background value is between 82.2 and 2648. It is recommended that the equation prediction value be limited to the logarithmic extreme value of the original data and the calculated data within ±0.1, that is, the calculated Cr background value can be limited to between 60.4 and 3334.

[0023] c) A total of 342 data were screened out based on the weathering index WIG≤65. After excluding 15 records, lgCr and lgFe2O3, Al2O3 / Ti were linearly fitted, and the error values ​​were all within ±0.2 of the logarithmic difference of the content (5 of the 15 records excluded had a logarithmic difference of the content within the ±0.2 error limit). The calculation equation is:

[0024] lgCr=0.8753lgFe2O3-91.15Al2O3 / Ti+1.47n=327, r=0.904 Formula 1c

[0025] At this time, lgFe2O3 is between -0.01 and 0.92, Al2O3 / Ti is between 0.0015 and 0.0050, Cr content is between 11 and 128, and the calculated Cr background value is between 12.5 and 128. It is recommended that the equation prediction value be limited to the logarithmic extreme value of the original data and the calculated data within ±0.1, that is, the calculated Cr background value can be limited to between 8.7 and 161.

[0026] The calculation formula of the weathering index WIG is as follows (Gong et al., Journal of Geochemical Exploration, 2013, Vol. 128, P14-24):

[0027] WIG=100[Na2O+K2O+(CaO-10 / 3P2O5)] / (Al2O3+Fe2O3+TiO2)

[0028] In the WIG calculation formula, the oxide represents its molar number in 100 g of sample, and when the (CaO-10 / 3P2O5) value is less than 0, it is taken as 0.

[0029] d) A total of 229 data were screened based on Na2O≤3. After eliminating 11 records, lgCr and Al2O3 / Ti, lg((CaO+MgO) / (Na2O+K2O)), and lgFe2O3 were linearly fitted, and the error values ​​were within ±0.2 of the logarithmic difference of the content. The calculation equation is:

[0030] lgCr=-150.2Al2O3 / Ti+0.1928lg((CaO+MgO) / (Na2O+K2O))+0.3987lgFe2O3+1.99

[0031] n=218,r=0.946Equation 1d

[0032] At this time, Al2O3 / Ti is between 0.0020 and 0.0086, lg((CaO+MgO) / (Na2O+K2O)) is between -0.75 and 0.98, lgFe2O3 is between -0.04 and 0.85, Cr content is between 4.5 and 96.9, and the calculated Cr background value is between 5.0 and 100. It is recommended that the equation prediction value be limited to the logarithmic extreme value of the original data and the calculated data within ±0.1, that is, the calculated Cr background value can be limited to between 3.6 and 126.

[0033] e) There are 137 other remaining data. After removing 17 records, lgCr and lgMn, lg(Al2O3 / MgO), and lg(Na2O / Fe2O3) show nonlinear fitting, and the error values ​​are within ±0.2 of the logarithmic difference of the content. The calculation equation is:

[0034] lgCr=-4.567lgMnlg(Al2O3 / MgO)lg(Na2O / Fe2O3)+6.612lgMnlg(Na2O / Fe2O3)

[0035] +12.99lg(Al2O3 / MgO)lg(Na2O / Fe2O3)-1.117lg(Al2O3 / MgO)-19.71lg(Na2O / Fe2O3)+2.47

[0036] n=120,r=0.987Equation 1e

[0037] At this time, lgMn is between 2.75 and 3.90, lg(Al2O3 / MgO) is between 0.60 and 1.98, lg(Na2O / Fe2O3) is between -0.44 and 0.52, Cr content is between 1.8 and 100, and the calculated Cr background value is between 1.8 and 100. It is recommended that the equation prediction value be limited to the logarithmic extreme value of the original data and the calculated data within ±0.1, that is, the calculated Cr background value can be limited to between 1.4 and 126.

[0038] Based on the idea that the content of major oxides in a sample can determine the background value of trace elements, the invention adopts rock-soil-sediment abundance data and piecewise nonlinear functions to fit and obtain a new equation for characterizing the geochemical background value of chromium.

[0039] ① A new equation for calculating the geochemical background value of chromium is proposed. This equation can be used to calculate the geochemical background value of chromium based on the major oxide content of samples in the rock-soil-sediment system.

[0040] ② The logarithmic difference between the calculated and measured chromium content values ​​of ±0.2 is proposed as a criterion for judging whether a sample is a background area sample. That is, when the logarithmic difference between the measured and calculated chromium content values ​​of the sample is within ±0.2, the sample can be regarded as a background area sample.

[0041] ③ It is proposed that virtual samples represented by the geochemical abundance values ​​of Chinese rocks, soils, and sediments can be regarded as background area samples, which are more representative than individual samples in traditional background areas, and the fitted equation is more objective and accurate in representing the geochemical background values ​​of the samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a fitting effect diagram for 791 abundance data of the present invention;

[0043] Figure 2 This is a graph showing the relationship between the measured value and the background value of the sample in Example 2. DETAILED DESCRIPTION

[0044] The specific implementation methods of the present invention are described here in conjunction with specific implementation cases.

[0045] Example 1

[0046] For rock / soil / stream sediment samples:

[0047] (1) The geochemical composition of the sample is tested, and at least the 11 major oxides or elements SiO2, Al2O3, TFe2O3, K2O, Na2O, CaO, MgO, Ti, P, Mn, and Cr required for the calculation of the present invention are contained (Table 1).

[0048] Table 1 Element content of samples

[0049]

[0050] Note: The unit of oxide content is %, and the unit of other elements content is μg / g.

[0051] (2) Based on the data in Table 1, the weathering index WIG of the sample was calculated (Table 2).

[0052] Table 2 Element content and weathering index WIG of samples

[0053]

[0054] Note: The unit of oxide content is %, and the unit of other elements content is μg / g.

[0055] (3) Based on the data in Table 2, the chromium geochemical background value of the sample was calculated (Table 3).

[0056] Table 3 Chromium content of samples and chromium geochemical background values ​​calculated by the present invention

[0057]

[0058] Note: The unit of oxide content is %, the unit of other elements content is μg / g, △lgCr=lgCr-lgCr 背景值 .

[0059] The samples in Table 3 above are calculated using different piecewise functions according to their respective major oxide contents and WIG values. For example, sample No. 77 uses formula 1b of the present invention to calculate the geochemical background value. The calculated geochemical background values ​​and their respective content logarithmic differences △lgCr are also listed in Table 3.

[0060] The logarithmic differences of the chromium content in this implementation case are all within ±0.2. Based on the criterion in key point 2 of the present invention, it is inferred that the samples in this case should all be background area samples.

[0061] At this point, the calculation of the chromium geochemical background value proposed by the present invention and the determination of whether the sample belongs to the background area sample have been completed.

[0062] The piecewise function equation proposed in the present invention contains 5 sub-equations; for 791 abundance data, there are 42 records with error values ​​outside the logarithmic difference of the content ±0.2, that is, there are 749 records with error values ​​within the logarithmic difference of the content ±0.2, accounting for 95% of the total number of records; the Cr background value calculated by the fitting equation can be limited to between 1.4 and 3334 μg / g. The fitting effect for 791 abundance data is as follows Figure 1 shown.

[0063] Example 2

[0064] Based on the content data of 11 oxides or elements (SiO2, Al2O3, TFe2O3, K2O, Na2O, CaO, MgO, Ti, P, Mn, Cr) in 8 soil samples from Pinggu area of ​​Beijing (Table 4), the chromium geochemical background value of each sample was calculated.

[0065] Table 4 Element contents and chromium geochemical background values ​​of samples

[0066]

[0067] Note: The unit of oxide content is %, the unit of other elements content is μg / g, △lgCr=lgCr-lgCr 背景值 .

[0068] Each sample in Table 4 is calculated using different piecewise functions according to its main oxide content and WIG value. For example, sample No. 1 uses formula 1c of the present invention to calculate the geochemical background value. The calculated geochemical background values ​​and their respective content logarithmic differences △lgCr are also listed in Table 4.

[0069] The correspondence between the measured values ​​of the eight samples and the calculated geochemical background values ​​in this implementation case is shown in the following figure: Figure 2 shown.

[0070] from Figure 2 Combined with Table 4, it can be seen that: ① In this case, the △lgCr of samples No. 1 to 5 are all within ±0.2, which shows that these 5 samples belong to the samples of the chromium geochemical background area; ② The measured values ​​of chromium content of samples No. 6 and No. 8 are slightly larger than the background error range defined by △lgCr=±0.2, indicating that the chromium content of these two samples is slightly higher than their geochemical background value; ③ The measured value of chromium content of sample No. 7 is obviously larger than the background error range defined by △lgCr=±0.2, so this sample should not belong to the chromium background area sample, and it can be considered as a sample with abnormal chromium content.

[0071] The traditional statistical parameter method for determining the geochemical background value of chromium not only requires a large amount of measured data, but also the background value obtained is only a relative expression and cannot objectively express the geochemical background value of the sample. The method proposed in the present invention does not require a large amount of sample data, and the background value of a sample can be determined, and the background value determined by the new method is objective.

[0072] Compared with the original background value equation proposed by the applicant's scientific research team in 2015, the original equation was a conceptual equation obtained based on limited case data, which was not only poorly representative, but also not applicable to the calculation of samples with a weathering index WIG>120. The new equation proposed in the present invention is obtained based on a large amount of abundance data fitting, which is not only highly representative, but also applicable to samples with different degrees of weathering, and has high accuracy in calculating the geochemical background value of chromium (the confidence level can reach 95% when the error range is controlled within ±0.2 of the logarithmic difference of the content).

[0073] Usually, the difference in lithology and weathering degree of samples can lead to a difference of more than 2 orders of magnitude in the chromium geochemical background value, while the traditional statistical method only relies on the parameter statistics of a large amount of chromium content data to determine the chromium geochemical background value, which has obvious defects due to ignoring the differences in lithology and weathering degree of the samples themselves. The new equation proposed in the present invention calculates the chromium geochemical background value based on the properties of the samples themselves, that is, it is calculated based on the data of the major oxide content of the samples, which can eliminate the influence of the lithology and weathering degree of the samples, and is therefore an objective representation.

[0074] The chromium geochemical background value calculated according to the present invention can provide an important basis for conducting environmental quality assessment of heavy metal chromium in soil and tracing pollution sources, and can also provide an important reference for discovering and evaluating anomalies in chromium mineral resource exploration.

Claims

1. A method for quantitatively characterizing chromium geochemical background values, characterized in that: The following steps are involved: S1, determine the source data of the fitting equation; Based on the rock, soil, and sediment abundance data, we selected data that can be considered as background samples and contain major oxides and chromium content, totaling 791 records; S2. Based on the above 791 abundance data, the weathering index WIG and the newly constructed element ratio parameters were calculated, and the equation characterizing the geochemical background value of chromium was fitted using piecewise function and nonlinear multivariate regression technology; when fitting the equation, the error standard was set to within ±0.2 of the logarithmic difference of the content, and it was required that more than 95% of the samples were within the error range; S3. Equation for quantitative characterization of chromium geochemical background value obtained by fitting.

2. A method for quantitatively characterizing chromium geochemical background values ​​according to claim 1, characterized in that: The equation for quantitative characterization of the chromium geochemical background value obtained by fitting in S3 is as follows: The source data n of the fitting equation is 791, that is, a total of 791 abundance data records, the unit of oxide content is mass percentage, %; the unit of chromium Cr, titanium Ti, and manganese Mn content is mass parts per million, ppm or μg / g; a) According to SiO2<33, a total of 29 data were screened out; after removing one record, lgCr and Ti, Al2O3 contents were linearly fitted, and the error values ​​were within ±0.2 of the logarithmic difference of the contents; the calculation equation was: lgCr=0.0634Al2O3+0.000308Ti+0.67n=28,r=0.921Formula 1a At this time, the Al2O3 content is between 0.66 and 4.81, the Ti content is between 185 and 1510, the Cr content is between 4.7 and 26, and the calculated Cr background value is between 5.9 and 27.1; b) A total of 54 data were screened based on MgO>3.9; after removing 3 records, lgCr, lgMgO, and lgNa2O were nonlinearly fitted, and the error values ​​were within ±0.2 of the logarithmic difference of the content; the calculation equation was: lgCr=0.4818lgMgOlgNa2O+0.8408lgMgO-1.128lgNa2O+1.89n=51, r=0.980 Formula 1b At this time, lgMgO is between 0.60 and 1.62, lgNa2O is between -0.49 and 0.70, Cr content is between 76 and 2500, and the calculated Cr background value is between 82.2 and 2648; c) A total of 342 data were screened out based on the weathering index WIG≤65; after eliminating 15 records, lgCr was linearly fitted with lgFe2O3 and Al2O3 / Ti, and the error values ​​were within ±0.2 of the logarithmic difference of the content; the calculation equation was: lgCr=0.8753lgFe2O3-91.15Al2O3 / Ti+1.47n=327, r=0.904 Formula 1c At this time, lgFe2O3 is between -0.01 and 0.92, Al2O3 / Ti is between 0.0015 and 0.0050, Cr content is between 11 and 128, and the calculated Cr background value is between 12.5 and 128; The calculation formula of the weathering index WIG is as follows: WIG=100[Na2O+K2O+(CaO-10 / 3P2O5)] / (Al2O3+Fe2O3+TiO2) In the WIG calculation formula, the oxide represents its molar number in 100 g of sample, and when the (CaO-10 / 3P2O5) value is less than 0, it is taken as 0; d) A total of 229 data were screened out based on Na2O≤3; after eliminating 11 records, lgCr and Al2O3 / Ti, lg((CaO+MgO) / (Na2O+K2O)), lgFe2O3 were linearly fitted, and the error values ​​were within ±0.2 of the logarithmic difference of the content; the calculation equation was: lgCr=-150.2Al2O3 / Ti+0.1928lg((CaO+MgO) / (Na2O+K2O))+0.3987lgFe2O3+1.99 n=218,r=0.946Equation 1d At this time, Al2O3 / Ti is between 0.0020 and 0.0086, lg((CaO+MgO) / (Na2O+K2O)) is between -0.75 and 0.98, lgFe2O3 is between -0.04 and 0.85, Cr content is between 4.5 and 96.9, and the calculated Cr background value is between 5.0 and 100; e) There are 137 other remaining data in total. After removing 17 records, lgCr and lgMn, lg(Al2O3 / MgO), and lg(Na2O / Fe2O3) show nonlinear fitting, and the error values ​​are all within ±0.2 of the logarithmic difference of the content. The calculation equation is: lgCr=-4.567lgMnlg(Al2O3 / MgO)lg(Na2O / Fe2O3)+6.612lgMnlg(Na2O / Fe2O3)+12.9 9lg(Al2O3 / MgO)lg(Na2O / Fe2O3)-1.117lg(Al2O3 / MgO)-19.71lg(Na2O / Fe2O3)+2.47 n=120,r=0.987Equation 1e At this time, lgMn is between 2.75 and 3.90, lg(Al2O3 / MgO) is between 0.60 and 1.98, lg(Na2O / Fe2O3) is between -0.44 and 0.52, the Cr content is between 1.8 and 100, and the calculated Cr background value is between 1.8 and 100.

3. A method for quantitatively characterizing chromium geochemical background values ​​according to claim 2, characterized in that: The predicted value of equation 1a is limited to within ±0.1 of the logarithmic extreme value of the original data and the calculated data, that is, the calculated Cr background value is limited to between 3.7 and 34.1; The predicted value of equation 1b is limited to within ±0.1 of the logarithmic extreme value of the original data and the calculated data, that is, the calculated Cr background value is limited to between 60.4 and 3334; The predicted value of equation 1c is limited to within ±0.1 of the logarithmic extreme value of the original data and the calculated data, that is, the calculated Cr background value is limited to between 8.7 and 161; The predicted value of equation 1d is limited to within ±0.1 of the logarithmic extreme value of the original data and the calculated data, that is, the calculated Cr background value is limited to between 3.6 and 126; The predicted value of equation 1e is limited to within ±0.1 of the logarithmic extreme value of the original data and the calculated data, that is, the calculated Cr background value is limited to between 1.4 and 126.

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