Problem of describing the function of a GPR source

In this paper, we consider the problem of determining the source h(t)δ(x) of electromagnetic waves from GPR data. The task of electromagnetic sensing is to find the pulse characteristic of the medium r(t) and consists in calculating the response of the medium to the pulse source of excitation δ(t) (Dirac Delta function). To determine the analytical expression of the impulse response of a homogeneous medium r(t), we use the method proposed in [1-2]. To determine h(t), the inverse problem is reduced to a system of Volterra integral equations. The source function h(τ ), is defined as the solution of the Volterra integral equation of the first kind, f(t) = ∫t0 r(t − τ )h(τ )dτ in which f(t) is the data obtained by the GPR at the observation points. The problem of calculating the function of the GPR source h(τ ) consists in numerically solving the inverse problem, in which the function of the source h(τ ) is unknown, and the electromagnetic parameters of the medium are known: the permittivity ε; the conductivity σ; the magnetic permeability µ and the response of the medium to a given excitation h(τ )

Development of a mathematical model for signal processing using laboratory data

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

An inverse hyperpolic integrodifferential problem arising in Geophysics II

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