Quantifying the age peaks,age ranges and weights of detrital ages based on the EM algorithm

Detrital geochronology fundamentally involves the quantification of major age ranges and their weights winthin an age distribution.This study presents a streamlined approach,modeling the age distribution of detrital zircons using a normal mixture model,and employs the Expectation-Maximization(EM)algorithm for precise estimations.A method is introduced to automatically select appropriate initial mean values for EM algorithm,enhancing its efficacy in detrital geochronology.This process entails multiple trials with varying numbers of age components leading to diverse k-component models.The model with the lowest Bayesian Information Criterion(BIC)is identified as the most suitable.For accurate component number and weight determination,a substantial sample size(n>200)is advisable. Our findings based on both synthetic and empirical datasets confirm that the normal mixture model,refined by the EM algorithm,reliably identifies key age parameters with minimal error.As a kind of probability density estimator,the normal mixture model offers a novel visualization tool for detrital data and an alternative foundation for KDE in calculating existing similarity metrics.Another focus of this study is the critical examination of quantitative metrics for comparing detrital zircon age patterns.Through a case study,this study demonstrates that metrics based on empirical cumulative probability distribution(such as K-S and Kuiper statistics)may lead to erroneous conclusions.The employment of the Kullback-Leibler(KL)divergence,a metric grounded in probability density estimation,is proposed.Reference critical values,simulated via the Monte Carlo method,provide more objective benchmarks for these quantitative metrics. All methodologies discussed are encapsulated in a series of MATLAB scripts,available as open-source code and a standalone application,facilitating wider adoption and application in the field.