Mathematical methods of seismic risk assessment

The mathematical technology of evaluation of sites of probable occurrence of geodynamic disasters, specifically earthquakes, based on an analysis of geodynamic instability indirect indicators, namely, horizontal gradients of gravity anomalies in isostatic reduction is presented in this paper. A set of deterministic mathematical models which form the groundwork of the seismic risk assessment technology is outlined herein. Special attention is paid to the probability mathematical model of assessment of seismic risks, the core of which is the representation of probable geodynamic states of geologic environment as a simplest event flow, followed by the construction of the Kolmogorov differential equations system to estimate probabilities of finding the geologic environment in these states. The principal results of the practical application of the mathematical models developed by the authors to assess seismic risks exemplified by way of the examples of the Baikal region and the north-western territory in Turkey are given and considered herein.