TY - JOUR

T1 - A mathematical model based on Bayesian theory and Gaussian copula for the discrimination of gabbroic rocks from three tectonic settings

AU - Han, Shuai

AU - Li, Mingchao

AU - Zhang, Qi

AU - Li, Heng

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85074704360&partnerID=8YFLogxK

U2 - 10.1086/705413

DO - 10.1086/705413

M3 - Journal article

AN - SCOPUS:85074704360

SN - 0022-1376

VL - 127

SP - 611

EP - 626

JO - Journal of Geology

JF - Journal of Geology

IS - 6

ER -