Risk Assessment based on the Mathematical Model of Diffuse Exogenous Geological Processes

The estimation of the risk caused by hazardous geological processes is a common problem. The aim of this paper is to present a method for solving problems involving a wide spectrum of diffuse exogenous geological processes, based on the mathematical morphology of landscapes. Diffuse processes develop as random rounded sites within certain areas and include karstification, subsidence, thermo-karstification and aeolian processes. Model assumptions take into consideration spatial and temporal randomness of occurrence, independent growth under occasional conditions, and cessation of growth given a ‘stop factor’, with transformation into degenerate sites. Based on these model assumptions, the following probabilities of impact by diffuse exogenous geological processes are solved for analytically. Firstly, the probability of impact on engineering constructions of round shape given the size of the diffuse processes and the known average impact risk; secondly, the probability of impact on small engineering constructions (points); and lastly, the probability of impact on linear engineering constructions of specified length. The computed impact probabilities are verified in various areas within Western Siberia.