György Bárdossy

Probabilistic Approaches for Handling Uncertainties

Mathematical methods are increasingly applied in geology and the number of applications rises constantly. Actual problems and new results are presented in Mathematical Geology, the journal of the International Association for Mathematical Geology. A number of excellent textbooks discusses the different aspects of mathematical applications in geology, e.g. Davis [42], Rock [148] etc. We rely on this rich bibliography and limit ourselves to the mathematical treatment of uncertainties.

Review of Uncertainty Oriented Mathematical Methods

Until the late sixties probability theory and statistics were the only methods to quantify uncertainties. Since that time new mathematical theories have been developed to handle uncertainties and to model them. We call them uncertainty oriented methods when they can handle not only numbers but also uncertain inputs.

Review of the Main Uncertainties and Risks in Geology

The term of uncertainty is broadly used in science and technology, but it is difficult to define it properly. It is discussed even by theoretical mathematicians as a fundamental term and is defined by them as a lack of certainty in describing an object, a feature or a process.

Test Calculations and Other Applications

In this chapter uncertainty calculations, carried out by us will be discussed. We tried to cover different fields of geological investigations, both pure scientific and practical ones. Similar calculations, performed by other authors will also be presented in Sects. 5.5–5.7.