原地生成宇宙成因核素测年技术思考(四):核素浓度年份化数列累加方法探讨

原地生成宇宙成因核素测年技术中,计算核素浓度的传统通用等式假设了地表侵蚀速率(参数ε)及样品的位置在暴露期间保持不变,从而简化了计算过程。然而这种假设可能并不符合复杂地质背景的实际情况,从而造成计算结果误差较大,与其他测年方法结果也难以相互比较和匹配。本文利用将核素总浓度按年份分解为每年生成的浓度,经衰变和侵蚀的综合影响后至今剩余的浓度(称为年份净剩余浓度),组成数列累加的办法,分别推导了地表样品在高程以及侵蚀速率变化情况下的核素浓度计算等式。在此基础上,给出了地表生成速率和侵蚀速率逐年变化情况下的通用浓度年份化累加等式。最后讨论了传统浓度计算等式中的参数ε(侵蚀速率)的地质意义,明确了ε是一个积分中值,并不代表暴露期间的算术平均侵蚀速率,而是每年的侵蚀速率以自然指数加权的复杂方式(即T年前的那一年的生成浓度将乘以e-(λ+ρεΛ)(T-1))影响到样品的最终浓度值。

Consideration on in situ produced cosmogenic nuclide dating techniques (4):Discussion on the accumulation method of nuclide concentration annualized data

It is assumed that the surface erosion rate(ε)and position of samples are constant during exposure in traditional formula of in-situ cosmogenic nuclide dating technology,thus calculation is simplified.However,such a hypothesis may be inconsistent with actual complex geological background,which results in big errors and cannot be compared with dating results of other methods.To solve this problem,this work decomposes the total concentration of nuclides into the concentration generated each year and the remaining concentration by decay and erosion(called net residual concentration for the year),then these data are accumulated into a sequence.Equations of nuclide concentration under the change of sample elevation and erosion rate are derived,respectively.The accumulation equation of the concentration is given based on the varying surface production rate and erosion rate each year.The geological meaning of the parameterε(erosion rate)in the traditional concentration formula is discussed.It is clarified that the erosion rate for a given year affects the final concentration of the sample in a complex way by natural exponential weighting(the annual concentration of T years ago is multiplied by e-(λ+ρεΛ)(T-1)),which is integral mean value rather than the arithmetic mean erosion rate in the period of exposure.