{"title":"基于贝叶斯理论和高斯Copula的三种构造背景下辉长岩判别数学模型","authors":"Shuai Han, Mingchao Li, Qi Zhang, Heng Li","doi":"10.1086/705413","DOIUrl":null,"url":null,"abstract":"Discriminating among tectonic settings by the chemical composition of igneous rocks is a feasible method in geochemistry. In this study, the feasibility of using gabbroic rocks to discriminate among tectonic settings is analyzed, and a mathematical model based on Gaussian copula and Bayesian theory is set up to discriminate among three tectonic settings: island arc, ocean island, and mid-oceanic ridge. The derivation of the model includes three steps: (1) determine the probability density functions (PDFs) of the elements in different tectonic settings, (2) determine the joint PDFs of the geochemical components of the rocks from different tectonic settings using copula functions, and (3) determine the tectonic settings of rocks using Bayesian theory. The optimal parameters of the mathematical model are calculated using a genetic algorithm, and finally the definitive form of the model is determined with nine basic elements: TiO2, Al2O3, FeOT, CaO, MnO, K2O, Na2O, Ni, and Sr. An experiment shows that the success rates of the mathematical model on the three tectonic settings are 84.03%, 95.48%, and 91.84%, respectively. The average percent success rate is 92.13%, which is significantly higher than using discrimination diagrams and the naive Bayes algorithm. Such an ideal result indicates that using gabbroic rocks to determine the types of tectonic settings is feasible. Moreover, this study can provide support for the application of machine learning and mathematical methods in the field of geochemistry.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2019-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1086/705413","citationCount":"4","resultStr":"{\"title\":\"A Mathematical Model Based on Bayesian Theory and Gaussian Copula for the Discrimination of Gabbroic Rocks from Three Tectonic Settings\",\"authors\":\"Shuai Han, Mingchao Li, Qi Zhang, Heng Li\",\"doi\":\"10.1086/705413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Discriminating among tectonic settings by the chemical composition of igneous rocks is a feasible method in geochemistry. In this study, the feasibility of using gabbroic rocks to discriminate among tectonic settings is analyzed, and a mathematical model based on Gaussian copula and Bayesian theory is set up to discriminate among three tectonic settings: island arc, ocean island, and mid-oceanic ridge. The derivation of the model includes three steps: (1) determine the probability density functions (PDFs) of the elements in different tectonic settings, (2) determine the joint PDFs of the geochemical components of the rocks from different tectonic settings using copula functions, and (3) determine the tectonic settings of rocks using Bayesian theory. The optimal parameters of the mathematical model are calculated using a genetic algorithm, and finally the definitive form of the model is determined with nine basic elements: TiO2, Al2O3, FeOT, CaO, MnO, K2O, Na2O, Ni, and Sr. An experiment shows that the success rates of the mathematical model on the three tectonic settings are 84.03%, 95.48%, and 91.84%, respectively. The average percent success rate is 92.13%, which is significantly higher than using discrimination diagrams and the naive Bayes algorithm. Such an ideal result indicates that using gabbroic rocks to determine the types of tectonic settings is feasible. Moreover, this study can provide support for the application of machine learning and mathematical methods in the field of geochemistry.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2019-10-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1086/705413\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://doi.org/10.1086/705413\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1086/705413","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
A Mathematical Model Based on Bayesian Theory and Gaussian Copula for the Discrimination of Gabbroic Rocks from Three Tectonic Settings
Discriminating among tectonic settings by the chemical composition of igneous rocks is a feasible method in geochemistry. In this study, the feasibility of using gabbroic rocks to discriminate among tectonic settings is analyzed, and a mathematical model based on Gaussian copula and Bayesian theory is set up to discriminate among three tectonic settings: island arc, ocean island, and mid-oceanic ridge. The derivation of the model includes three steps: (1) determine the probability density functions (PDFs) of the elements in different tectonic settings, (2) determine the joint PDFs of the geochemical components of the rocks from different tectonic settings using copula functions, and (3) determine the tectonic settings of rocks using Bayesian theory. The optimal parameters of the mathematical model are calculated using a genetic algorithm, and finally the definitive form of the model is determined with nine basic elements: TiO2, Al2O3, FeOT, CaO, MnO, K2O, Na2O, Ni, and Sr. An experiment shows that the success rates of the mathematical model on the three tectonic settings are 84.03%, 95.48%, and 91.84%, respectively. The average percent success rate is 92.13%, which is significantly higher than using discrimination diagrams and the naive Bayes algorithm. Such an ideal result indicates that using gabbroic rocks to determine the types of tectonic settings is feasible. Moreover, this study can provide support for the application of machine learning and mathematical methods in the field of geochemistry.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.