Development of a mathematical model for signal processing using laboratory data

Abstract

In this paper, we consider a mathematical model for the interpretation of the radarograms which obtained by GPR systems. As noted in [1–3], in addition to testing the algorithms, it is necessary to compare the calculated data of the mathematical model with the real data obtained from the GPR. One of the reasons preventing the spread of GPR technologies is the complexity of data interpretation, which requires the involvement of highly qualified specialists. In connection with this research as a mathematical model and a comparison with the real data of the GPR in an ideal layered medium, will provide a method for interpreting radarograms. We have conducted a series of experimental studies using the Loza – A georadar at the newly created laboratory ground. A distinctive feature of these studies is the choice of several localized objects in the form of iron sheets placed in an ideal layered medium, namely in clean dry sand. The choice of such an environment is necessary for testing the algorithms, the mathematical models developed by us for determining the depth of localized several objects. A series of experimental studies were conducted using georadar and a number of radarograms were obtained to study the depth of objects. A cycle of calculations was carried out to verify the conformity of the results of mathematical modeling with real georadar data. Key words: electrodynamics equation, magnetic permeability, dobeshi wavelets, medium conductivity, dielectric permeability, Maxwell equation.