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CN-122019954-A - Method suitable for uranium lead isotope dating and common lead deduction

CN122019954ACN 122019954 ACN122019954 ACN 122019954ACN-122019954-A

Abstract

The invention belongs to the field of isotope theory and application, and particularly relates to a method suitable for uranium lead isotope dating and common lead deduction, which comprises the steps of deducing a third-stage age t 2 calculation formula according to a U-Pb isotope three-stage age formula, and calculating t 2 and alpha 2 、β 2 by adopting uranium lead isochrone fitting; establishing a regression equation according to a three-stage age formula of the U-Pb isotope, calculating a regression equation coefficient, establishing an overrun equation according to the regression equation coefficient calculation formula, calculating t 1 、t 2 by adopting a Newton iteration method, calculating alpha 1 、β 1 、μ 1 according to t 1 、t 2 、α 2 , calculating an age error, carrying out contrast verification on t 2 , and discussing the reliability of the result. The result obtained by the method accords with the isotope theory, can accurately measure the isotope dating of the lead isotope composition, has better reliability and measurement accuracy, and can effectively avoid the problems that the common lead is unreliable, the open system is difficult to dating for multiple times, the common lead is deducted, and the like.

Inventors

  • HAN JUN
  • NIE JIANGTAO
  • GUO CHUNYING

Assignees

  • 核工业北京地质研究院

Dates

Publication Date
20260512
Application Date
20251230

Claims (10)

  1. 1. A method for uranium lead isotope dating and common lead deduction, comprising: step1, deducing a third-stage age t 2 calculation formula according to a U-Pb isotope three-stage age formula, and calculating a third-stage age t 2 and a common lead value alpha 2 、β 2 by adopting uranium-lead isochrone fitting; Step 2, establishing a regression equation according to a three-stage age formula of the U-Pb isotope, and calculating regression equation coefficients; Step 3, establishing an overrun equation according to a regression equation coefficient calculation formula, and calculating the second-stage age t 1 and the third-stage age t 2 by adopting a Newton iteration method; Step 4, calculating a common lead value alpha 1 、β 1 , 238 U/ 204 Pb atomic ratio mu 1 according to the second stage age t 1 , the third stage age t 2 and the common lead value alpha 2 ; And 5, calculating an age error, comparing and verifying the ages of t 2 obtained by calculation in the step 1 and the step 3, and discussing the reliability of the result.
  2. 2. The method for uranium lead isotope dating and common lead deduction according to claim 1, wherein in the step 1, a U-Pb three-stage age evolution formula is obtained according to a U-Pb three-stage age formula, and the U-Pb three-stage age evolution formula is as follows: α 1 ＝α 0 +μ 0 (e λ8t0 -e λ8t1 )...............................................(3) α 2 ＝α 1 +μ 1 (e λ8t1 -e λ8t2 )...............................................(4) α 3 ＝α＝α 2 +μ 2 (e λ8t2 -1)...............................................(5) β 1 ＝β 0 +μ 0 /137.88(e λ5t0 -e λ5t1 )......................................(6) β 2 ＝β 1 +μ 1 /137.88(e λ5t1 -e λ5t2 )......................................(7) β 3 ＝β＝β 2 +μ 2 /137.88(e λ5t2 -1).....................................(8) In the formulas (3) - (5), alpha=alpha 3 、α 0 、α 1 、α 2 corresponds to 206 Pb/ 204 Pb values at the moment t 0 、t 1 、t 2 at present, wherein t 0 is the earth formation time, t 1 is the second stage age, and t 2 is the third stage age, respectively, (6) - (8) wherein beta=beta 3 、β 0 、β 1 、β 2 corresponds to 207 Pb/ 204 Pb values at the moment t 0 、t 1 、t 2 at present, respectively, mu 0 、μ 1 、μ 2 corresponds to 238 U/ 204 Pb atomic ratio which is evolved until now under a closed condition at the moment t 0 、t 1 、t 2 and later, mu 2 is the current measured value, lambda 8 、λ 5 is the decay constant of 238 U、 235 U, and 1/137.88 is the atomic ratio of 235 U evolution until now to 238 U, namely the constant 1/137.88.
  3. 3. The method for uranium lead isotope fix year and common lead deduction according to claim 2, wherein in the step 1, the third stage age t 2 and the common lead value alpha 2 are calculated by uranium lead isochrone fitting, wherein alpha is Y-axis and mu 2 is X-axis, a uranium lead isochrone scattered point data set is constructed, a weighted least square linear regression is carried out on the equivalent time line scattered point data set, a linear equation is fitted, and a slope b, an intercept a and a linear correlation coefficient R are obtained, when the absolute value of the linear correlation coefficient R is greater than or equal to 0.99, an age t 2 is calculated by the slope b= (e λ8t2 -1), and the common lead isotope ratio alpha 2 is t 2 when the intersection point of the fitting line and the Y-axis is the intercept a; The method for calculating the common lead value beta 2 by adopting uranium-lead isochrone fitting comprises the steps of constructing a uranium-lead isochrone scatter data set by taking beta as a Y axis and mu 2 /137.88 as an X axis, carrying out weighted least square linear regression on the equivalent time line scatter data set, fitting a linear equation, obtaining an intercept a and a linear correlation coefficient R, and when the absolute value of the linear correlation coefficient R is greater than or equal to 0.99, determining that the intersection point of the fitted line and the Y axis is the intercept a, and determining that the common lead isotope ratio beta 2 is t 2 .
  4. 4. The method for uranium lead isotope dating and common lead deduction according to claim 2, wherein in the step 2, a regression equation and a regression equation coefficient formula are established as follows: β=b 1 ×α+b 2 ×μ 2 +a......................................................(I) Wherein, alpha and beta are respectively test values of 206 Pb/ 204 Pb、 207 Pb/ 204 Pb, b 1 、b 2 is a regression equation coefficient, and a is a constant term.
  5. 5. The method for uranium lead isotope dating and common lead deduction according to claim 4, wherein the step2 specifically includes using SPSS software to carry in measured U-Pb isotope data, using α and μ 2 as independent variables and β as dependent variables, establishing a regression equation, and calculating a coefficient b 1 、b 2 .
  6. 6. The method for uranium lead isotope dating and ordinary lead deduction according to claim 4, wherein in the step 3, an overrun equation is established as follows: 1+137.88×(b 2 -b 1 )+137.88×b 1 ×e λ8t2 ＝e λ5t2 .....................................(V)。
  7. 7. The method for uranium lead isotope dating and common lead deduction according to claim 6, wherein the step 4 specifically includes calculating an alpha 1 、μ 1 value according to a second stage age t 1 , a third stage age t 2 and a common lead value alpha 2 according to formula (3) and formula (4), wherein the alpha 1 value is obtained by superposing the radioactive lead of the stage on the alpha 0 in the t 0 ～t 1 stage, calculating the beta 1 value according to formula (6), wherein the beta 1 value is obtained by superposing the radioactive lead of the stage on the beta 0 in the t 0 ～t 1 stage, and calculating the 235 U/ 204 Pb value according to the present ratio of ( 238 U/ 204 Pb)/( 235 U/ 204 Pb) being 137.88.
  8. 8. The method for uranium lead isotope dating and common lead subtraction according to claim 6, wherein in step 5, the age error is calculated by the following method: ① When the original measurement data give experimental errors, the errors are brought into an age equation to be directly calculated to obtain age errors; ② Calculating standard deviation and mean square error of the fitting straight line and actual scattered point data by adopting a least square method, and carrying out calculation by using an age formula to obtain an age error; ③ When the age is fitted by the Newton iteration method through the overrun equation, the standard deviation and the mean square error are obtained through regression calculation according to the regression equation, and the standard deviation and the mean square error are brought into the age iteration software to obtain an age error result.
  9. 9. The method for uranium lead isotope dating and common lead deduction according to claim 6, wherein in the step 5, the comparison and verification are performed on the ages of t 2 calculated in the steps 1 and 3, and the specific steps include: The age of t 2 obtained by combining the binary linear regression with the iteration method in the step 3 is compared with the age of t 2 calculated by fitting the isochrone according to the step 1, the age is a credible value when the ages are consistent within an error range, the age result is discussed according to specific conditions when the obtained ages are inconsistent, and the ages obtained by the two methods are mathematically consistent and also need to be compared according to geological conditions and the existing ages, so that the reliability of the ages is ensured.
  10. 10. The method for uranium lead isotope dating and common lead subtraction according to claim 6, wherein in step 5, reliability of results is discussed according to calculated age results, specifically as follows: ①t 1 >t 2 The iterative calculation results are consistent in the error range according to the combination of the isochrone and the binary linear regression, the age is reliable, and the method belongs to a three-stage or more than three-stage evolution system; ②t 1 <t 2 The age is nonsensical or is a U-Pb two-stage evolution system, t 1 is taken as the second stage age, and t 1 calculated by the isochrone method is required to be consistent with t 1 calculated by the iterative method; ③t 1 ＝t 2 The calculated t 1 of the isochrone method is consistent with the calculated t 1 of the iterative method, which is a U-Pb two-stage evolution system.

Description

Method suitable for uranium lead isotope dating and common lead deduction Technical Field The invention belongs to the field of isotope theory and application, and particularly relates to a method suitable for uranium-lead isotope dating and common lead deduction. Background Uranium-lead isotopes are commonly used for rock and mineral formation and hydrothermal activity age calculation in definite years, and are commonly obtained by methods (LA-ICP-MS, SHRIMP, SIMS and the like) such as full-rock and single-mineral thermoelectricity mass spectrometry (TIMS) and laser ablation of micro-area in-situ scale, ion probes and the like. The TIMS method adopts a double-diluent method to measure 204Pb、206Pb、207Pb、208 Pb abundance through mass spectrometry, obtains U, pb content data through inductively coupled plasma mass spectrometry (ICP-MS) measurement, and obtains corresponding ages according to the U-Pb isotope theory by fitting calculation through computer software, wherein 232 Th and 208 Pb (the same applies below) of decay daughter are not considered. The in-situ method is to obtain single-point U, pb content, 207Pb/206Pb、207Pb/235 U (corrected common lead) and 206Pb/238 U (corrected common lead) values by using methods such as laser, ion excitation, secondary ion and the like on the premise of not damaging a sample, using a method of interpolating a standard sample, measuring 204 Pb atoms based on a common lead content reference standard sample, and obtaining the values of the single-point U, pb content, the 207Pb/206Pb、207Pb/235 U (corrected common lead) and the 206Pb/238 U (corrected common lead) according to an isotope evolution mode and the standard sample comparison, so as to fit and calculate isotope ages. There are several basic definitions of ① homogenization at the time of U-Pb isotope dating. The isotope composition of lead at the initial stage of earth formation is consistent and identical to that of lead of merle iron, and is called original lead. The subsequent change in the isotopic composition of lead is a result of adding different amounts of radioactive lead to the original lead, ② common lead (original lead). The result is that the original lead plus the radioactive causative lead at the time of separation of the radioactive parent and daughter lead, and thereafter the number of lead atoms does not change. In order to solve the problem of years of multi-stage open systems, a U-Pb system 'curtain-stage' mode is defined, wherein the U-Pb system is opened only in the transient process of some serious geological events, the geological change event of the transient is called as 'curtain', and the time interval between the two curtains is called as 'stage', and uranium and lead are in a closed system. Based on this pattern, the expression can be made in a U-Pb three-stage pattern: 206Pb/204Pb＝206Pb/204Pb0+μ0(eλ8t0-eλ8t1)+μ1(eλ8t1-eλ8t2)+μ2(eλ8t2-1)…(1) 207Pb/204Pb＝207Pb/204Pb0+(μ0/137.88)×(eλ5t0-eλ5t1)+(μ1/137.88)×(eλ5t1-eλ5t2)+(μ2/137.88)×(eλ5t2-1)…(2) 206Pb/204Pb0、207Pb/204Pb0 Respectively 206Pb/204Pb、207Pb/204 Pb atomic ratio at the time of earth formation (t 0), mu 0、μ1、μ2 respectively 238U/204 Pb atomic ratio at the time of corresponding t 0、t1、t2 and thereafter evolving under closed conditions, mu 2 as the current measurement value, lambda 8、λ5 respectively 238U、235 U decay constant, e λ8t0、eλ8t1、eλ8t2 respectively 238 U decay factor from t 0、t1、t2 to date, e λ5t0、eλ5t1、eλ5t2 respectively 235 U decay factor from t 0、t1、t2 to date, mu 0/137.88、μ1/137.88、μ2/137.88 respectively representing 235U/204 Pb value evolving under closed conditions from t 0、t1、t2 to date. Since the isotopic composition change of the common lead is limited by the radionuclide and the age of the radioactive parent, the apparent age and the consistent line age are both deducted when the isotopic analysis data are directly used for calculating the apparent age and the consistent line age. In general, normal lead can be tested for the lead isotopic composition of a single mineral, such as galena, from which the radioactive parent and daughter are separated at that time, but in such single minerals, it is problematic if found whether such single mineral represents the isotopic system of the test target. The common lead can also be determined by adopting a single-stage mode method, most of geologic bodies in the nature belong to a U-Pb multi-stage evolution system, and the method obviously has a great problem. The method of obtaining age by using standard substance and using 204 Pb correction data to fit inconsistent line in the micro-area in-situ method is not completely in accordance with isotope principle. In addition, in the micro-area in-situ test, since the measurement point scale is limited, even if the minerals are selected, whether the test target point contains lead caused by mixed minerals or minerals affected by multi-stage isotope opening events cannot be ensured, and the lead isotope composition of the point ma