water chemistry are new challenges possible from coda compositional data analysis point of view

John Aitchison died in December 2016 leaving behind an important inheritance: to continue to explore the fascinating world of compositional data. However, notwithstanding the progress that we have made in this field of investigation and the diffusion of the CoDA theory in different researches, a lot of work has still to be done, particularly in geochemistry. In fact most of the papers published in international journals that manage compositional data ignore their nature and their consequent peculiar statistical properties. On the other hand, when CoDA principles are applied, several efforts are often made to continue to consider the log-ratio transformed variables, for example the centered log-ratio ones, as the original ones, demonstrating a sort of resistance to thinking in relative terms. This appears to be a very strange behavior since geochemists are used to ratios and their analysis is the base of the experimental calibration when standards are evolved to set the instruments. In this chapter some challenges are presented by exploring water chemistry data with the aim to invite people to capture the essence of thinking in a relative and multivariate way since this is the path to obtain a description of natural processes as complete as possible

Geomathematics theoretical foundations, applications and future developments

This book provides a wealth of geomathematical case history studies performed by the author during his career at the Ministry of Natural Resources Canada, Geological Survey of Canada (NRCan-GSC). Several of the techniques newly developed by the author and colleagues that are described in this book have become widely adopted, not only for further research by geomathematical colleagues, but by government organizations and industry worldwide. These include Weights-of-Evidence modelling, mineral resource estimation technology, trend surface analysis, automatic stratigraphic correlation and nonlinear geochemical exploration methods. The author has developed maximum likelihood methodology and spline-fitting techniques for the construction of the international numerical geologic timescale. He has introduced the application of new theory of fractals and multifractals in the geostatistical evaluation of regional mineral resources and ore reserves and to study the spatial distribution of metals in rocks. The book also contains sections deemed important by the author but that have not been widely adopted because they require further research. These include the geometry of preferred orientations of contours and edge effects on maps, time series analysis of Quaternary retreating ice sheet related sedimentary data, estimation of first and last appearances of fossil taxa from frequency distributions of their observed first and last occurrences, tectonic reactivation along pre-existing schistosity planes in fold belts, use of the grouped jackknife method for bias reduction in geometrical extrapolations, and new applications of the theory of permanent, volume-independent frequency distributions

Modified Weights-of-Evidence Modeling with Example of Missing Geochemical Data

Weights of evidence (WofE) and logistic regression (LR) are two loglinear methods for mineral potential mapping. Both models are limited by their respective basic assumptions in application. Ideally, WofE indicator patterns have the property of conditional independence (CI) with respect to the point pattern of mineral deposits to be predicted; in LR, there supposedly are no interactions between the point pattern and two or more of the indicator patterns. If the CI assumption is satisfied, estimated LR coefficients become approximately equal to WofE contrasts and the two methods produce similar results; additionally, bias then is avoided in that the sum of all estimated posterior probabilities becomes approximately equal to the number of observed discrete events. WofE allows construction of input layers that have missing data as a separate category in addition to known presence-absence type input, while logistic regression as such is not capable of handling missing data. As an improved WofE model based on LR, modified weights of evidence (MWofE) inherit the advantages of both LR and WofE, i.e., eliminates bias due to lack of CI and can handle missing data as well. Pixel or unit area input for MWofE consists of positive and negative weights for presence and absence of a pattern plus zeros for missing data. MWofE first is illustrated by application to simple examples. Next, it is applied to a study area with 20 known gold occurrences in southwestern Nova Scotia in relation to four input layers based on geological and lake geochemical data. Assuming that geochemical data were missing for the northern part of the study area, MWofE, like WofE but unlike LR, provides posterior probabilities for the entire area