2D subsidence trough approximation by experimental points

Abstract

The article discusses algorithms for plotting an analytical function of a preset shape to describe a subsidence trough using the vertical displacements measured at a set of points situated on ground surface at a random fashion. For building and improving calculation algorithms, a one-dimensional problem is examined first, using actual data from base points on ground surface; then, the problem is extended and generalized to a 2D subsidence trough. The shape of the trough is approximated by the preset function in the form of a combination of the Gaussian integrals with three (or five in 2D case) constitutive parameters. The applicability of a random search algorithm in funding parameters of an unknown function is considered. For testing the proposed algorithm applicability, a simulation model is built for a possible subsidence trough formed by means of combination of 1D troughs in the main sections of the model 2D trough. With the help of this model trough, a set of points is generated on ground surface to model a possible real-life ensemble of points. The in situ ensemble of points will be determined using appropriate measurement instrumentation and algorithms being developed these days. Inserted in the algorithm, these points make it possible to find parameters of the approximating functions for the 2D case and to build a relevant analytical expression for ground surface subsidences. This approach can be effective using the satellite technologies and randomly spread natural reflectors in the ground area.