Research output: Contribution to journal › Article › peer-review
Problem of describing the function of a GPR source. / Kabanikhin, S. I.; Iskakov, K. T.; Tokseit, D. K. et al.
In: Bulletin of the Karaganda University-Mathematics, Vol. 100, No. 4, 7, 2020, p. 71-80.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Problem of describing the function of a GPR source
AU - Kabanikhin, S. I.
AU - Iskakov, K. T.
AU - Tokseit, D. K.
AU - Shishlenin, M. A.
AU - Toibekov, A.
N1 - The work was supported by a grant from the Ministry of education and science of the Republic of Kazakhstan under contract No. 132 dated 12.03.2018 under the project AR05133922 and KPFI SB RAS project No. 26.
PY - 2020
Y1 - 2020
N2 - In this paper, we consider the problem of determining the source h(t)delta(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 delta(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(tau), is defined as the solution of the Volterra integral equation of the first kind, f(t) = integral(t)(0) r(t - tau)h(tau)d tau 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(T) consists in numerically solving the inverse problem, in which the function of the source h(tau) is unknown, and the electromagnetic parameters of the medium are known: the permittivity epsilon; the conductivity sigma; the magnetic permeability mu and the response of the medium to a given excitation h(tau).
AB - In this paper, we consider the problem of determining the source h(t)delta(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 delta(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(tau), is defined as the solution of the Volterra integral equation of the first kind, f(t) = integral(t)(0) r(t - tau)h(tau)d tau 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(T) consists in numerically solving the inverse problem, in which the function of the source h(tau) is unknown, and the electromagnetic parameters of the medium are known: the permittivity epsilon; the conductivity sigma; the magnetic permeability mu and the response of the medium to a given excitation h(tau).
KW - radargram processing
KW - source recovery
KW - mathematical simulation
KW - calculation results
KW - HYPERBOLIC PROBLEM
KW - FREQUENCY-DOMAIN
KW - EQUATIONS
KW - TERMS
UR - https://www.elibrary.ru/item.asp?id=44699418
U2 - 10.31489/2020M4/71-80
DO - 10.31489/2020M4/71-80
M3 - Article
VL - 100
SP - 71
EP - 80
JO - Вестник Карагандинского университета. Серия Математика
JF - Вестник Карагандинского университета. Серия Математика
SN - 2518-7929
IS - 4
M1 - 7
ER -
ID: 28015138