ANALYSIS OF THE EXOGENOUS GEOLOGICAL PROCESS DEVELOPMENT BASED ON THE MODELS OF THE MATHEMATICAL MORPHOLOGY OF LANDSCAPES

Abstract

The paper aims to show the efficiency of applying the approaches used in the mathematical morphology of landscapes to the analysis of exogenous geological process development. Taking thermokarst plains with fluvial erosion as an example, it is shown that the approaches of the mathematical morphology of landscapes permit analyzing the terrain development under complex conditions of several interacting exogenous geological processes. Thermokarst areas develop under the impact of two interacting processes, i.e., thermokarst and fluvial thermoerosion. They include the following stages: constant generation of new thermokarst foci, constant decrease in the number of the thermokarst foci, when lakes are drained by thermoerosion, constant change in the conditions for the development of new thermokarst foci due to the transformation of the main surface into the khasyrei surface. The approaches of the mathematical morphology of landscapes revealed that each of the two types of surface within the thermokarst plains with fluvial erosion reached a dynamic balance upon the emergence, growth, and drainage of thermokarst lakes. Taking the formation and development of thermal cirques on abrasion shores within the permafrost zone as an example, it is shown that the approaches of the mathematical morphology of landscapes make it possible to analyze a set of processes for thermal cirques development under complex interaction of their foci. Based on the analysis of the mathematical model of the formation and development of thermal cirques, it is shown that in conditions of an abrasion slope that is relatively homogeneous in terms of geological and geocryological conditions, a dynamic balance is reached. It is characterized by stabilizing two parameters: the average density of thermal cirques and the probabilistic distribution of the thermal cirque size along the slope strike. An analytical relationship was obtained between the probabilistic distributions of chord sizes of the forming young landslides and all presented landslides, including partly erased ones by the later landslides; and the relationship between the average statistical forms of landslides along the coastline and the distribution parameters of the chord sizes of the forming young landslides. The obtained regularities were tested at several sites based on remote sensing data.