V.I. Sakhterov1, I.V. Prokopovich2, A.V. Popov3

1−3 Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN) (Troitsk, Russia)

The paper considers a simple method of adapting well-proven GPR resistively-loaded dipole antennas for ground penetrating radar application to the problems of borehole radar logging. One of the main problems in the design of the antennas for borehole applications is providing their azimuthal directivity, together with strictly limited system diameter. To achieve this goal, it has been proposed to use an electrically conducting shield coupled with a transmitting dipole antenna. In order to reduce parasitic resonant re-emissions, the free ends of the dipole have been grounded to the metal shield. On specially made stands, the radiation patterns of such a radiating system were measured when placing the radiating system on the earth surface, as well as inside a barrel with wet soil, simulating the radar operation in a well. The influence of the distance between the shield and the dipole on the formation of the radiation pattern was experimentally studied. It turned out that at distances comparable to the shield width, one has to make a compromise choice between higher radiation power and better antenna directivity. A realistic field measurement of the azimuthal radiation pattern between two drilled wells in wet soil was also carried out. All directional diagrams were plotted as the values of the first maximum of the probing pulse passed through the ground layer and registered by the receiver. In order to confirm the observed regularities, an approximate analytical solution was written to the diffraction problem of a plane wave impinging at an infinitely long conducting strip. As it is well known, the transition to the complex variables, followed by the conformal Zhukovsky transform, allows one to transform the strip into a circle of unit radius. In such a geometry, the Helmholtz equation allows for separation of variables in polar coordinates, which makes it possible to write down an analytical solution for the azimuthal variable in form of Mathieu functions. The long-wavelength approximation allows one to solve the radial equation in terms of Hankel functions. The ratio of the wave field amplitude at the receiver point in the middle of the illuminated area to the field strength in the opposite point in the shadow zone allows us to estimate the shielded dipole receiver directivity. Further analysis of the studied antenna system included a three-dimensional simulation of the radiation pattern by numerical solution of the EM wave propagation problem by the method of finite differences in the time domain (FDTD). Such simulations were carried out for several different values of the distance between the dipole and the shield and for different cases of the surrounding material medium. It was shown that large values of the dielectric constant leads to the growing of the radiation pattern main lobe. The results of numerical simulation and analytical solution are consistent with each other and correspond to the directivity patterns observed in the laboratory experiment. All three approaches (analytical approximate solution, numerical simulation, experiment) confirmed the pronounced radiation pattern of the proposed shielded dipole radiating system, which can be effectively used for practical solution of the radar logging problem.

Sakhterov V.I., Prokopovich I.V., Popov A.V. Shielded dipole antenna for borehole GPR applications. Radiotekhnika. 2022. V. 86.
№ 8. P. 103−112. DOI: https://doi.org/10.18127/j00338486-202208-11 (In Russian)

1. Popov A.V., Prokopovich I.V., Edemskij D.E., Morozov P.A., Berkut A.I. Glubinnyj georadar: principy i primenenie. Jelektromagnitnye volny i jelektronnye sistemy. 2018. T. 23. № 4. S. 28−36 (In Russian).
2. Volkomirskaja L.B., Gulevich O.A., Varenkov V.V., Reznikov A.E., Sahterov V.I. Sovremennye georadary serii «Grot» dlja jekologicheskogo monitoringa. Jekologicheskie sistemy i pribory. 2012. № 5. S. 3−5 (In Russian).
3. Wu T.T., King R.W.P. The cylindrical antenna with nonreflecting resistive loading. IEEE Trans. Antennas Propag. 1965. V. 13.
   № 3. P. 369−373.
4. Engheta N., Papas C.H., Elachi C. Interface extinction and subsurface peaking of the radiation pattern of a line source. Applied Physics B. 1981. V. 26. № 4. P. 231−238.
5. Patent 2117368 (Rossija). Antenna dlja georadara. O En Den, A.E. Reznikov (In Russian).
6. Patent 142226 (Rossija) Jekranirovannaja antenna georadara. O En Den (In Russian).
7. O En Den. Legkij, kompaktnyj shatrovyj jekran dlja antenn georadarov. Special'naja tehnika. 2006. №5. S. 32−35 (In Russian).
8. Garbacevich V.A., Morozov P.A., Morozov F.P., Prokopovich I.V., Popov A.V. Raschet i modelirovanie cilindricheskoj shhelevoj antenny dlja zadach radiolokacionnogo karotazha. Trudy XXVI Vseross. otkrytoj nauch. konf. «Rasprostranenie radiovoln». Kazan'. 2019. T. 2. S. 443-446 (In Russian).
9. Patent 2753250 (Rossija). Napravlennaja antenna dlja podzemnogo izluchenija. Sahterov V.I. (In Russian).
10. Garbacevich V.A. Issledovanie izluchatelej i signalov ionozonda i georadara dlja diagnostiki geofizicheskih sred. Avtoref. diss. … kand. fiz.-mat. nauk. Institut zemnogo magnetizma, ionosfery i rasprostranenija radiovoln. 2008 (In Russian).
11. Rothammel' K. Antenny: Per. s nem. Izd. 3-e, dop. M.: Jenergija. 1979. 320 s. (In Russian).
12. Uitteker Je.T., Vatson Dzh.N. Kurs sovremennogo analiza. Chast' II. Transcendentnye funkcii. M.: Fizmatgiz. 1963. 516 s. (In Russian).
13. Giannopoulos A. Modelling ground penetrating radar by GprMax. Construction and Building Materials. 2005. V. 19. P. 755−762.
14. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas Propagat. 1966. V. 14. № 3. P. 302−307.