Fifty years' experience with hidden errors in applying classical mathematical geology

Abstract

Classical mathematical geology is a branch of mathematical geosciences in which mathematical methods and models-not specifically developed for and not exclusive to specific geosciences-are applied to describe, to model and to analyse quantitatively geoscientific subjects and processes. It was the dominant approach in the 1960s to 1980s and it is still used today to solve numerous, mostly limited and less complex problems. The methods have been implemented in the form of algorithms in commercial software packages that are widely used in geological practice. Their application frequently assumes specific pre-conditions, which are often difficult, if not impossible, to verify. This situation can result in significantly spurious output and errors that are often not recognised (hidden errors). In this paper five case studies are used to demonstrate these errors. In particular, they demonstrate that small mistakes can lead to serious, but often unrecognised, misinterpretations. The main conclusion is that there is a need to improve education and training in classical mathematical geology especially for engineering sections of consulting firms, governmental agencies and individual consultants.