Paper No. 10-9
Presentation Time: 10:40 AM
FUTURE AND CURRENT APPROACHES FOR MODELING THE DISTRIBUTION OF MINERALS ON EARTH AND OTHER PLANETS (Invited Presentation)
HYSTAD, Grethe, Department of Mathematics, Statistics, and Computer Science, Purdue University Northwest, Hammond, IN 46323, ELEISH, Ahmed, Tetherless World Constellation, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, HAZEN, Robert M., Geophysical Laboratory, Carnegie Institution, 5251 Broad Branch Road NW, Washington, DC 20015, MORRISON, Shaunna M., Geophysical Laboratory, Carnegie Institution for Science, Washington, DC 20015 and DOWNS, Robert T., Department of Geosciences, University of Arizona, Tucson, AZ 85721
Previous research has showed that the mineral species coupled with their localities is a Large Number of Rare Events (LNRE) distribution since most of Earth’s mineral species are rare, known from only a few localities. An alternative approach to species estimation is the Bayesian approach that allows the estimation of Earth’s undiscovered, mineralogical diversity. In Bayesian statistics, the parameters are not considered fixed as they are in classical statistics but assumed to have their own probability distribution such that prior information about the parameters can be built into the model. Markov chain Monte Carlo (MCMC) simulations are used to generate samples of the model parameters such that estimates and inference are directly obtained.
Subsequently, the idea of a composite LNRE model is introduced that takes into account the different subgroups of minerals and adds up the contribution from each subgroup. As a result of new and improved high-resolution sampling techniques, new mineral species are discovered more frequently than in the past. The numbers of new minerals being discovered are influenced by the mineralogical techniques employed. For example, an ongoing program at Caltech conducted by Ma et al. (2014) has identified a number of nanometer-scale minerals that could not have been identified by the light microscope techniques of earlier decades. The minerals are first divided into groups determined by their maximum grain sizes and a composite LNRE model is fitted to these groups. As increasingly smaller maximum grain sizes of minerals are discovered, an estimate of the total number minerals of that size can be added to the model. The talk concludes with a discussion regarding on how to best group the minerals for a composite LNRE model.
Ma, C.; Beckett, J.R.; Rossman, G. R. (2014) Monipite, MoNiP, a new phosphide mineral in a Ca-Al-rich inclusion from the Allende meteorite. Am Mineral 99(1):198–205
![[Visit Client Website]](/img/gsa/banner.jpg)