U-Pb dating method for common lead accessory minerals based on LA-ICPMS surface scanning technology

Abstract

This invention discloses a U-Pb dating method for common lead by-product minerals based on LA-ICPMS surface scanning technology, comprising: 1. using LA-ICPMS to perform surface scanning on common lead-containing mineral samples and age standards to obtain and measure data; 2. calculating the expected value of the standard sample measurement data; 3. calculating the fractionation coefficient; 4. performing fractionation correction on the samples; 5. initializing the iterative age; 6. calculating the iterative age; 7. rearranging and grouping the sample data according to the iterative age; 8. calculating virtual points and their errors and correlation coefficients; 9. calculating the intersection age to update the iterative age. This invention can quickly obtain data with different U-Pb ratios and small errors, while avoiding the interference of deep fractionation faced by point analysis techniques, thus enabling accurate common lead correction and regression analysis to obtain mineral ages.

Description

Technical Field

[0001] This invention relates to the field of isotope geochronology, and more particularly to a U-Pb dating method for common lead accessory minerals based on LA-ICPMS surface scanning technology. Background Technology

[0002] Isotope geochronology is a fundamental discipline for exploring the spatiotemporal evolution and dynamic processes of the Earth. Among its dating methods, U-Pb dating of accessory minerals using LA-ICPMS is the most widely applied. Compared to methods such as ID-TIMS and SIMS, it has advantages such as high efficiency and low cost. The minerals studied have gradually expanded from zircon to rutile, vesuvianite, apatite, monazite, garnet, sphene, scheelite, wolframite, epidote, calcite, cassiterite, and others. Currently, LA-ICPMS accessory mineral dating mainly uses point analysis techniques. For accessory minerals containing common lead, point analysis techniques are less efficient, difficult to design, and involve complex data processing, with a high risk of analytical failure.

[0003] LA-ICPMS spot analysis of common lead minerals has the following problems:

[0004] 1. As the depth of single-point ablation increases, the mass spectrometry signal decreases rapidly, and the isotope ratios undergo deep fractionation, making them difficult to correct.

[0005] 2. Due to the presence of common lead and its non-uniformity in the direction perpendicular to the depth of the mineral sample surface, the isotope ratio of a single point in the sample may vary with depth. It is difficult to distinguish whether this is due to depth fractionation or the influence of common lead. This requires manual editing and screening of the measurement data of each single point, which is labor-intensive and inefficient.

[0006] 3. Multiple single-point data points with different uranium-lead parent-child ratios are required to accurately calculate the regression equation. Therefore, it is generally necessary to combine other analytical methods to determine the analytical points before the experiment, which increases the difficulty and cost of the analysis.

[0007] 4. If the point location is not selected properly during point analysis, the measurement data may not be dispersed in the TW map, but concentrated in a certain place in the TW. This may lead to the failure of the regression equation calculation or high uncertainty. In this case, it is necessary to introduce an ordinary lead evolution model of the earth to limit the intercept of the regression equation and introduce other error terms.

[0008] While LA-ICPMS surface scanning can quickly obtain isotope ratio information of mineral surfaces, it suffers from poor accuracy in a single measurement and the inability to directly perform dating analysis on the measurement data. Summary of the Invention

[0009] To address the aforementioned technical problems, the present invention aims to provide a U-Pb dating method for common lead by-product minerals based on LA-ICPMS surface scanning technology. This method aims to rapidly obtain measurement data of different uranium-lead parent-child ratios with smaller errors, while avoiding the interference of deep fractionation faced by point analysis techniques. This allows for accurate common lead correction and regression analysis to obtain mineral ages.

[0010] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0011] The present invention provides a U-Pb dating method for common lead accessory minerals based on LA-ICPMS planar scanning technology, characterized by the following steps:

[0012] Step S1: Set the mass spectrometer to measure isotopes including 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 U isotopes were used, and the same laser parameters were applied to age standards and samples containing common lead for LA-ICPMS surface or line scanning analysis, respectively, to obtain the corresponding values ​​of the age standards for U isotopes. 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 Several measurements of U isotopes, and the results of tests on samples containing common lead. 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 Several measurements of U isotopes;

[0013] Background values ​​were removed from several measurements of age standard samples and samples containing common lead, and the measured data after background removal were filtered to obtain the filtered measured data.

[0014] Based on the filtered N S Calculate N for each age standard based on measurement data. S Isotope ratio measurements, including: age standard samples The i-th measurement value Age standard The i-th measurement value Age standard The i-th measurement value The value of i ranges from 1 to N. S ;

[0015] Based on the N of the screened samples containing common lead for testing M The measurement data were used to calculate the isotope ratios of the sample containing common lead, including: the measurement data of the sample containing common lead. The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value j ranges from 1 to N M ;

[0016] Step S2: Calculate the age standard using formula (1). The expected value of the measurement x S Age standard Expected value of measurement y S and age standard The expected value of the measurement u S :

[0017]

[0018] Step S3: Obtain age standard samples Recommended value Age standard Recommended value Age standard Recommended value And calculate using equation (2) fractionation coefficient β x , fractionation coefficient β y , fractionation coefficient β u :

[0019]

[0020] Step S4: Use formula (3) to test the sample containing common lead. The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value Fractionation correction was performed separately to obtain the test sample containing common lead. The j-th correction value Samples containing common lead The j-th correction value Samples containing common lead The j-th correction value

[0021]

[0022] Step S5: Define the current iteration number as w and initialize w = 0; define the age of the sample containing ordinary lead in the wth iteration as t. w and initialize t w =0; Set the grouping parameter to N;

[0023] Step S6, the sample containing common lead to be tested 208 Pb isotopes contain elements from before mineral formation. 208 Pb isotopes and those derived from 232 The products formed by the radioactive decay of Th isotopes 208 Pb isotopes, and the mineral formation process 208 Pb isotopes are denoted as 208 Pb c ; Use equation (4) to calculate the content of lead in the sample to be tested. Grouping index of the j-th virtual point in the w-th iteration Thus, the sample containing common lead was obtained. N in the wth iteration M Grouping indicators for virtual points;

[0024]

[0025] In equation (4), λ2 is 232 The decay constants of Th isotopes;

[0026] Step S7: For the sample containing common lead to be tested... N in the wth iteration M Virtual point grouping indicators Sort the data, and then, based on the sorting results, perform the following steps: and The samples are also sorted to obtain the sample containing common lead in the w-th iteration. The sorted set of correction values And the sample containing common lead in the wth iteration Correction value set in, This indicates the sample containing common lead in the w-th iteration. The j-th correction value after sorting. This indicates the sample containing common lead in the w-th iteration. The j-th correction value after sorting;

[0027] Step S8, for and Divide the samples into K groups, such that each group has N data points. Let the sample containing common lead be the data in the w-th iteration. The v-th data in the k-th group is denoted as and Let the sample containing common lead in the w-th iteration be... The v-th data in the k-th group is denoted as and

[0028] Step S9: Calculate the kth virtual point in the TW graph under the wth iteration using equation (5).

[0029]

[0030] Step S10: Calculate the k-th virtual point in the w-th iteration using equation (6). Statistical error

[0031]

[0032] Step S11: Calculate the correlation coefficient of the k-th group of data in the w-th iteration using equation (7).

[0033]

[0034] Step S12: Fit the K virtual points and their statistical errors and correlation coefficients using the two-error variable linear regression method to obtain the regression equation: Y = aX + b; where a represents the slope of the regression equation, b represents the intercept of the regression equation, and X represents the x-axis variable in the TW plot. The value of Y represents the y-axis variable in the TW plot. The possible values ​​of ;

[0035] Step S13: Construct the parametric equation system of the harmonic curve using equation (8):

[0036]

[0037] In equation (8), t represents the age parameter of the mineral, and X(t) represents the x-axis variable in the TW plot. The value of Y(t) represents the y-axis variable in the TW plot. The value of λ8 is 238 The decay constant of U isotopes, λ⁵ is 235 The decay constant of U isotopes, where α is the Earth average.

[0038] Step S14: Calculate the mineral age parameter t corresponding to the intersection point of the regression equation and the harmonic curve in the TW diagram, and use it as the age t of the (w + 1)-th iteration. w+1 ;

[0039] Step S15: After assigning w + 1 to w, if |t w -t w-1 |< limit, stop the iteration and obtain the final age T = t of the mineral w , otherwise, return to step S6 and execute sequentially. limit represents the error threshold.

[0040] An electronic device according to the present invention includes a memory and a processor, characterized in that the memory is used to store a program for supporting the processor to execute the U-Pb dating method, and the processor is configured to execute the program stored in the memory.

[0041] A computer-readable storage medium according to the present invention, characterized in that a computer program stored on the computer-readable storage medium executes the steps of the U-Pb dating method when run by a processor.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] 1. By adopting the LA-ICPMS surface scanning technology for the dating analysis of common lead-bearing accessory minerals, the present invention quickly scans the entire mineral surface at a relatively shallow erosion depth to obtain isotope data with different uranium-lead ratios. Through iterative correction data rearrangement and grouping, virtual points with smaller errors are constructed, linear equation regression and common lead correction are achieved, accurate mineral ages are obtained, and the difficulties of the traditional LA-ICPMS point analysis technology in designing experiments, such as the low success rate and low efficiency of manually selecting mineral surface points with different uranium-lead ratios, the difficulty of correcting severe depth fractionation caused by long-term erosion in point analysis, and the influence of fluctuations in uranium-lead ratios caused by common lead due to uneven composition of minerals in depth, are overcome. The problem that it is difficult to correctly estimate the error size of the isotope ratio data measured by LA-ICPMS surface scanning and is related to the isotope ratio, resulting in inaccurate dating, is solved.

[0044] 2. This invention employs LA-ICPMS surface scanning technology instead of the traditional LA-ICPMS point analysis technology for experiments. Surface scanning achieves an ablation depth of approximately 1 μm on the mineral surface, while point analysis typically achieves an ablation depth of approximately 28-30 μm. As the laser ablation pit deepens over time, the ratio of pit depth to pit diameter changes, leading to a continuous variation in depth fractionation over time. Therefore, the depth fractionation effect caused by using surface scanning technology is far less than that of point analysis technology, greatly overcoming the difficulties in depth fractionation correction in point analysis technology.

[0045] 3. This invention uses LA-ICPMS surface scanning technology to quickly scan the entire mineral surface, while traditional LA-ICPMS point analysis technology requires manual selection of several points on the mineral surface for analysis experiments. Therefore, surface scanning technology has a higher success rate in obtaining isotopic data of different uranium-lead parent-child ratios, which helps to reduce the uncertainty of the regression equation and thus improves the accuracy of dating.

[0046] 4. This invention improves data processing efficiency by directly processing all data obtained from LA-ICPMS area scanning technology, whereas traditional LA-ICPMS point analysis technology requires manual editing and processing of data obtained from each point analysis separately.

[0047] 5. This invention uses the geometric mean instead of the arithmetic mean to calculate the expected value of the isotope ratio, which solves the problem that the arithmetic mean of the ratio of isotope A to isotope B is inconsistent with the reciprocal of the arithmetic mean of the ratio of isotope B to isotope A caused by the isotope ratio data not following a normal distribution.

[0048] 6. This invention utilizes calculations As a grouping criterion, the measurement correction data are rearranged, grouping data that theoretically fall at the same point in the TW diagram into a group. A virtual point is constructed using N pairs of measurement data within each group, and the measurement errors and correlation coefficients for different isotope ratios are reasonably estimated. Theoretically, the error of the virtual point can be suppressed to the level of the error of a single measurement relative to the error of a single measurement.

[0049] 7. This invention utilizes a linear regression method with two error variables, while simultaneously considering virtual points. and The measurement error is used to calculate the regression equation, which is more efficient than using the least squares linear regression method, and does not consider... Using the error of the measurement correction value to calculate the regression equation has higher accuracy.

[0050] 8. This invention uses an iterative method to calculate mineral ages, ensuring the consistency between the mineral ages used in data correction and processing and the final mineral ages.

[0051] 9. This invention does not require the introduction of an additional model of the evolution of lead on Earth. The parameters are used as the anchor points of the regression equation intercept for ordinary lead correction, thus avoiding the introduction of additional errors.

[0052] 10. The present invention is in The calculation has already taken into account 232 The effects of radioactive decay of Th isotopes are therefore also applicable to those containing... 232 Dating analysis of common lead-containing accessory minerals in Th. Attached Figure Description

[0053] Figure 1 This is a flowchart of U-Pb dating data processing for common lead-containing accessory minerals using LA-ICPMS surface scanning technology, provided in Embodiment 1 of the present invention.

[0054] Figure 2 The distribution of calibration data obtained by surface scanning of sample ZK803-97 provided in Embodiment 1 of the present invention in the TW plot;

[0055] Figure 3 The distribution of virtual points in the TW diagram obtained by grouping and calculating the sample surface scanning data provided in Embodiment 1 of the present invention;

[0056] Figure 4 The age distribution map of intersection points is obtained by multiple bootstrap sampling as provided in Embodiment 1 of the present invention. Detailed Implementation

[0057] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings:

[0058] like Figure 1 As shown, a U-Pb dating method for common lead accessory minerals based on LA-ICPMS planar scanning technology includes the following steps:

[0059] Step S1: Using 91500 as the age standard and garnet ZK803-97 as the test sample, perform a surface scan experiment. The surface scan is performed with the age standard inserted before and after the test sample, i.e., 91500, ZK803-97, 91500. Set the mass spectrometer to measure isotopes including... 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238U isotopes were used. The same laser parameters were employed for LA-ICPMS surface scanning or line scanning analysis of age standards and samples containing common lead. In Example 1, the laser beam diameter was 30 μm, the line scanning ablation rate for both standards and experimental samples was 20 μm / s, and the repetition rate was 7 Hz. Background gas signal acquisition was performed for 20 s before ablation of each sample, followed by a 20 s purge. After the experiment, signal matching was performed using laser switch recording and mass spectrometry recording. Background segment mass spectrometry data was extracted based on the laser switch closing time to calculate the experimental environment. 206 Pb, 207 Pb, 208 Pb, 232 Th、 238 Background value of U. Based on the laser activation time and sample labeling records, mass spectrometry records of the age standard and the sample to be tested were extracted respectively. 206 Pb, 207 Pb, 208 Pb, 232 Th、 238 U data, thereby obtaining the corresponding age samples for each 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 Several measurements of U isotopes, and the results of tests on samples containing common lead. 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 Several measurements of U isotope were collected; background values ​​were removed from the measurements of age standard samples and samples containing common lead, and the measured data after removing background values ​​were filtered to retain only data where all isotopes are positive, while data containing values ​​less than or equal to 0 were removed, resulting in the filtered measured data.

[0060] Based on the filtered N S Calculate N for each age standard based on measurement data. S Isotope ratio measurements, including: age standard samples The i-th measurement value Age standard The i-th measurement value Age standard The i-th measurement value The value of i ranges from 1 to N. S ;

[0061] Based on the N of the screened samples containing common lead for testing MThe measurement data were used to calculate the isotope ratios of the sample containing common lead, including: the measurement data of the sample containing common lead. The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value j ranges from 1 to N M ;

[0062] Step S2: Calculate the age standard using formula (1). The expected value of the measurement x S Age standard Expected value of measurement y S and age standard The expected value of the measurement u S :

[0063]

[0064] Step S3: Obtain age standard samples Recommended value Age standard Recommended value Age standard Recommended value And calculate using equation (2) fractionation coefficient β x , fractionation coefficient β y , fractionation coefficient β u :

[0065]

[0066] The fractionation coefficients calculated in Example 1 are as follows:

[0067] β x =0.780

[0068] β y =1.014

[0069] β u =0.975

[0070] Step S4: Use formula (3) to test the sample containing common lead. The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value Fractionation correction was performed separately to obtain the test sample containing common lead. The j-th correction value Samples containing common lead The j-th correction value Samples containing common lead The j-th correction value

[0071]

[0072] Step S5: Define the current iteration number as w and initialize w = 0; define the age of the sample containing ordinary lead in the wth iteration as t. w and initialize t w =0; Set the grouping parameter to N. Generally, the value of N can be between 40 and 90. In this example, the value of N is 40.

[0073] Step S6, the sample containing common lead to be tested 208 Pb isotopes contain elements from before mineral formation. 208 Pb isotopes and those derived from 232 The products formed by the radioactive decay of Th isotopes 208 Pb isotopes, and the mineral formation process 208 Pb isotopes are denoted as 208 Pb c ; Use equation (4) to calculate the content of lead in the sample to be tested. Grouping index of the j-th virtual point in the w-th iteration Thus, the sample containing common lead was obtained. N in the wth iteration M Grouping indicators for virtual points;

[0074]

[0075] In equation (4), λ2 is 232 The decay constant of Th isotopes, λ² = 4.940 × 10⁻⁶. -11 yr -1 ;

[0076] Step S7: For the sample containing common lead to be tested... N in the wth iteration M Virtual point grouping indicators Sort the data, and then, based on the sorting results, perform the following steps: and The samples are also sorted to obtain the sample containing common lead in the w-th iteration. The sorted set of correction values And the sample containing common lead in the wth iteration Correction value set in, This indicates the sample containing common lead in the w-th iteration. The j-th correction value after sorting. This indicates the sample containing common lead in the w-th iteration. The j-th correction value after sorting.

[0077] In Example 1, the corrected The position in the TW diagram is as follows Figure 2 As shown in the scatter plot, each point corresponds to The value is represented in grayscale.

[0078] Step S8, and for and Divide the samples into K groups, such that each group has N data points. Let the sample containing common lead be the data in the w-th iteration. The v-th data in the k-th group is denoted as and Let the sample containing common lead in the w-th iteration be... The v-th data in the k-th group is denoted as and K through N M / N is obtained by taking the positive value downwards. In Example 1, K = 126.

[0079] Step S9: Calculate the kth virtual point in the TW graph under the wth iteration using equation (5).

[0080]

[0081] Step S10: Calculate the k-th virtual point in the w-th iteration using equation (6). Statistical error

[0082]

[0083] Step S11: Calculate the correlation coefficient of the k-th group of data in the w-th iteration using equation (7).

[0084]

[0085] In Example 1, as Figure 3As shown, the distribution of K = 126 virtual points obtained by measuring sample ZK803 - 97 in the TW diagram is represented by error ellipses. The center coordinates of the k-th error ellipse in the w-th iteration are The size and tilt angle of the error ellipse are affected by control.

[0086] Step S12: Use the linear regression method with double error variables to fit the K virtual points, their statistical errors, and correlation coefficients to obtain the regression equation: Y = aX + b; a represents the slope of the regression equation, b represents the intercept of the regression equation, X represents the magnitude of the x-axis variable in the TW diagram and Y represents the magnitude of the y-axis variable in the TW diagram . In Example 1, the regression equation Y = -0.0172X + 0.8306 is obtained, and the line corresponding to the regression equation is shown by a [[ID=十二]] Figure 3 dashed line.

[0087] Step S13: Use Equation (8) to construct the parameter equations of the concordia curve:

[0088]

[0089] In Equation (8), t represents the age parameter of the mineral, X(t) represents the magnitude of the x-axis variable in the TW diagram and Y(t) represents the magnitude of the y-axis variable in the TW diagram . λ8 is 238 the decay constant of the U isotope, λ5 is 235 the decay constant of the U isotope, and α is the average of the Earth's In Example 1, λ8 = 1.55125×10 -10 yr -1 , λ5 = 9.8485×10 -10 yr -1 , and α = 137.818. The concordia curve is shown by the Figure 3 black curve in.

[0090] Calculate the mineral age parameter t corresponding to the intersection point of the regression equation and the concordia curve in the TW diagram, and use it as the age t in the (w + 1)-th iteration w+1 ;

[0091] Step S14: After assigning w + 1 to w, if |t w - t w-1 | < limit, stop the iteration and obtain the final age T of the mineral = t w , otherwise, return to Step S6 and execute sequentially. limit represents the error threshold. In Example 1, limit is taken as 1 Ma, and the iteration stops when w = 2, and finally the mineral age T = 140.2 Ma is obtained.

[0092] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0093] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0094] The following is an evaluation of the experimental results and the rationality of the grouping parameters in Example 1:

[0095] The regression equation is fitted using K virtual points, containing two undetermined parameters, so the degrees of freedom F is K-2. In this example, F = 124. Looking up the table, the 95% confidence interval for MSWD with F = 124 degrees of freedom is [0.7667, 1.238].

[0096] Calculate the MSWD (Mean Study Data Evaluation Metric) for experimental data.

[0097]

[0098] In Example 1, MSWD = 0.91. This indicates that the experimental data conforms to the chi-square statistical distribution, and the grouping parameter N = 40 is reasonable.

[0099] The confidence intervals for mineral ages obtained in Example 1 are estimated below:

[0100] Using the bootstrap sampling method, the set of measurements of the age standard obtained in step S1 is processed. The set of measured values ​​for samples containing common lead. A total of 1000 samplings with replacement were performed; the data set after the first sampling was analyzed in the order of steps 2 to 14 to obtain the mineral age T. l The age statistics histogram obtained from 1000 Bootstrap samplings is as follows: Figure 4 As shown, the 95% confidence interval for the age of the mineral to be tested in this experiment is 140.5 ± 2.7 Ma.

[0101] Analysis of the surface scanning results of garnet ZK803-97, which contains common lead accessory minerals, shows that the MSWD value is reasonable, indicating that the experimental data conforms to the statistical distribution law. The 95% age confidence interval is consistent with the deposit age of 130-140 Ma obtained by other data and methods, indicating that the method proposed in Example 1 is effective.

[0102] In summary, the U-Pb dating method for common lead accessory minerals based on LA-ICPMS surface scanning technology provided by this invention is an improvement upon the traditional LA-ICPMS point analysis method for dating common lead accessory minerals. As a grouping indicator, virtual points were constructed to successfully estimate and suppress measurement errors. A linear regression analysis with two error variables was performed, and the mineral age was obtained through iteration. The rationality of the experimental data and processing was evaluated by MSWD, and the confidence interval of the age was estimated by bootstrap sampling. This method overcomes the difficulty of point selection in LA-ICPMS point analysis, avoids the complicated data processing and depth fractionation correction problems of each single point measurement data, and helps to quickly obtain data with different common lead content. This not only improves the efficiency of analysis, but also helps to reduce the uncertainty of the linear regression equation and improve the accuracy of common lead correction and age.

Claims

1. A U-Pb dating method for common lead accessory minerals based on LA-ICPMS planar scanning technology, characterized in that, Includes the following steps: Step S1: Set the mass spectrometer to measure isotopes including 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 U isotopes were used, and the same laser parameters were applied to age standards and samples containing common lead for LA-ICPMS surface or line scanning analysis, respectively, to obtain the corresponding values ​​of the age standards for U isotopes. 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 Several measurements of U isotopes, and the results of tests on samples containing common lead. 206 Pb isotopes, 207 Pb isotopes, 208 Pb isotopes, 232 Th isotopes, 238 Several measurements of U isotopes; Background values ​​were removed from several measurements of age standard samples and samples containing common lead, and the measured data after background removal were filtered to obtain the filtered measured data. Based on the filtered N S Calculate N for each age standard based on measurement data. S Isotope ratio measurements, including: age standard samples The i-th measurement value Age standard The i-th measurement value Age standard The i-th measurement value The value of i ranges from 1 to N. S ; Based on the N of the screened samples containing common lead for testing M The measurement data were used to calculate the isotope ratios of the sample containing common lead, including: the measurement data of the sample containing common lead. The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value j ranges from 1 to N M ; Step S2: Calculate the age standard using formula (1). The expected value of the measurement x S Age standard Expected value of measurement y S and age standard The expected value of the measurement u S : Step S3: Obtain age standard samples Recommended value Age standard Recommended value Age standard Recommended value And calculate using equation (2) fractionation coefficient β x , fractionation coefficient β y , fractionation coefficient β u : Step S4: Use formula (3) to test the sample containing common lead. The j-th measurement value Samples containing common lead The j-th measurement value Samples containing common lead The j-th measurement value Fractionation correction was performed separately to obtain the test sample containing common lead. The j-th correction value Samples containing common lead The j-th correction value Samples containing common lead The j-th correction value Step S5: Define the current iteration number as w and initialize w = 0; define the age of the sample containing ordinary lead in the wth iteration as t. w and initialize t w =0; Set the grouping parameter to N; Step S6, the sample containing common lead to be tested 208 Pb isotopes contain elements from before mineral formation. 208 Pb isotopes and those derived from 232 The products formed by the radioactive decay of Th isotopes 208 Pb isotopes, and the mineral formation process 208 Pb isotopes are denoted as 208 Pb c ; Use equation (4) to calculate the content of lead in the sample to be tested. Grouping index of the j-th virtual point in the w-th iteration Thus, the sample containing common lead was obtained. N in the wth iteration M Grouping indicators for virtual points; In equation (4), λ2 is 232 The decay constant of Th isotopes; Step S7: For the sample containing common lead to be tested... N in the wth iteration M Virtual point grouping indicators Sort the data, and then, based on the sorting results, perform the following steps: and The samples are also sorted to obtain the sample containing common lead in the w-th iteration. The sorted set of correction values And the sample containing common lead in the wth iteration Correction value set in, This indicates the sample containing common lead in the w-th iteration. The j-th correction value after sorting. This indicates the sample containing common lead in the w-th iteration. The j-th correction value after sorting; Step S8, for and Divide the samples into K groups, such that each group has N data points. Let the sample containing common lead be the data in the w-th iteration. The v-th data in the k-th group is denoted as and Let the sample containing common lead in the w-th iteration be... The v-th data in the k-th group is denoted as and Step S9: Calculate the kth virtual point in the TW graph under the wth iteration using equation (5). Step S10: Calculate the k-th virtual point in the w-th iteration using equation (6). Statistical error Step S11: Calculate the correlation coefficient of the k-th group of data in the w-th iteration using equation (7). Step S12: Fit the K virtual points and their statistical errors and correlation coefficients using the two-error variable linear regression method to obtain the regression equation: Y = aX + b; where a represents the slope of the regression equation, b represents the intercept of the regression equation, and X represents the x-axis variable in the TW plot. The value of Y represents the y-axis variable in the TW plot. The value of ; Step S13: Construct the parametric equation system of the harmonic curve using equation (8): In equation (8), t represents the age parameter of the mineral, and X(t) represents the x-axis variable in the TW plot. The value of Y(t) represents the y-axis variable in the TW plot. The value of λ8 is 238 The decay constant of U isotopes, λ⁵ is 235 The decay constant of U isotopes, where α is the Earth average. Step S14: Calculate the mineral age parameter t corresponding to the intersection of the regression equation and the concordance curve in the TW plot, and use it as the age t for the (w+1)th iteration. w+1 ; Step S15, after assigning w + 1 to w, if |t w - t w-1 | < limit, stop the iteration and obtain the final age T = t of the mineral w , otherwise, return to step S6 and execute sequentially, where limit represents the error threshold.

2. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the U-Pb dating method of claim 1, and the processor is configured to execute the program stored in the memory.

3. A computer-readable storage medium storing a computer program, characterized in that, The computer program is executed by the processor to perform the steps of the U-Pb dating method of claim 1.

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