Problem of describing the function of a GPR source

Abstract

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 ).