Geomathematical Modeling of Magma Crystallization: Linking Mineral Formation to Geochemical Processes in Volcanic Environments

Abstract

Mathematically, rocks can be modeled using the parametric materials (Minerals) that constitute the rocks. These materials (Minerals) depend on the variability of temperature (T), under isobaric condition and the bulk composition(X), of the parent (Basalt) magma and then analysed it using certain mathematical parametres such as Matrix, set Notation and Geometry. Ten samples were collected at random at different points in Kassa Volcanic Field (KVF). These samples were examined under thin section in university of Jos geology laboratory, using Petrographic Microscope both plane and cross polarized light and the detailed minerals observed were, Olivine, Pyroxene, Plagioclase and magnetite. Two kilograms(2kg) of each of the samples were pulverized and subjected to chemical analysis using Inductively couple Plasma Mass spectrometer (ICPMS) in Canadian Geochemical Laboratory  and the chemical compositions analysed were SiO₂, Na₂O, K₂O, Fe₂O₃, FeO, MgO, CaO, TiO₂, etc. For trace elements, it includes Ba, Rb, Sr, Cs, Ni, Cr, V, U, Th, Nb, Li, Ga, Zr, Mn, etc.  In modeling of basalt and its equivalent, granite, mathematical computation, examination of minerals under thin section, chemical analysis of the basalt were the major objectives of this research After all these analyses using mathematical modeling approach, three novel empirical parametres: [Matrix, Set notation and Geometry] were developed and employed to study the essential rock forming minerals, the distribution of trace elements in rock as well as establishing a relationship between continuous and discontinuous reaction series.