The method of integral equations and fourier transforms for the problems of modeling the electrical monitoring of dams and barriers

Abstract

Design of electrical monitoring of dams and barriersis an actual task in geophysics. A primary purpose is an exposure of change of structure, erosion, cracks and losses of weir on the early stages. Then it is important to remove and repair a weir and prevent destructions of dike overall. For mathematical modeling of electrical monitoring of dams and barriers, the authors consider the method of ERT. The paper shows a mathematical model of the electrical survey of dams and barriers based on the method of integral equations and the Fourier transform. Numerical calculations for this model are performed. The simulation results for studying the influence of the location of the water-dam boundary with respect to the sounding array are presented. For the purposes of mathematical modeling, two extreme cases were considered: a) a fluid is assumed to be infinitely conductive, b) a fluid is not conductive, i.e. distilled. The effect of a change in the position of the supply electrode at a fixed water level was also studied. The simulation results are presented in the form of apparent resistivity curves, as it is customary in geophysical practice. Distribution of density of secondary charges is also shown for the cases of infinitely conducting and distilledwater.