ISSN 10693513, Izvestiya, Physics of the Solid Earth, 2010, Vol. 46, No. 9, pp. 735–738. © Pleiades Publishing, Ltd., 2010. Original Russian Text © V.K. Khmelevskoy, B.P. Petrukhin, P.Yu. Pushkarev, 2010, published in Fizika Zemli, 2010, No. 9, pp. 11–14.
Magnetotellurics and RadioWave Interference Sounding V. K. Khmelevskoy, B. P. Petrukhin, and P. Yu. Pushkarev Faculty of Geology, Moscow State University, Moscow, Russia Email:
[email protected] Received February 26, 2010
Abstract—The plane harmonic electromagnetic fields are considered in the theory of magnetotelluric meth ods in the range of frequencies from 0.0001 Hz to 20 kHz. These fields are natural by their origin and contain information on the depths from tens of meters up to 100 km and more. The magnetotelluric soundings, which use the fields of radio stations, expand the frequency band almost up to 1 MHz and make it possible to study the depths from the first few meters. The method of radiowave interference sounding supplements geoelec tric prospecting on plane waves into the range of even higher frequencies (up to 100 MHz). In this case, the conduction and displacement currents become comparable, which makes it possible to distinguish objects both by their electrical conductivity and by their dielectric permittivity. For the twolayered model of a medium, there exist simple kinematic methods of data interpretation of a radiointerferometry sounding. Within multilayer, and especially horizontally heterogeneous, media, methods for solving equations of elec trodynamics and inverse problems of geophysics are required. In the present paper, the foundations of the theory of radiointerferometry sounding, the methodology, its role in geoelectric prospecting, and the oppor tunities for the solution of geological problems are discussed. DOI: 10.1134/S1069351310090028
INTRODUCTION Magnetotellurics is based on the study of the natu ral variable electromagnetic field of the Earth. Varia tions with a frequency below 1 Hz are mainly con nected with the interaction of solar wind with the magnetosphere and ionosphere of the Earth, and at higher frequencies, up to 20 kHz (audiorange), they are caused to the maximum extent by thunderstorms. Such a broad frequency spectrum makes it possible to solve a variety of problems connected with the study of the deep horizons of the Earth’s crust and the upper mantle of the Earth, with the searching and prospect ing of mineral deposits, and various geological engi neering, hydrogeological, and other problems. On frequencies higher than 0.0001 Hz, with some reservations, the field source can be considered suffi ciently removed from the Earth’s surface, and the Earth’s sphericity can be neglected [Khmelevskoy and Petrukhin, 2010]. This makes it possible to use a model of a plane wave, whose front is parallel to the Earth’s surface. Strictly speaking, within the frequency range mentioned above, an electromagnetic wave as an object existing independently of its source, owing to internal energy transformations, does not exist in the Earth. The field propagation has a diffusive nature and the oscillation process exists due to the changes in the current in the source. However, the planewave model is feasible and convenient from the point of view of the consistency of the theory of electromagnetic prospecting. The method of radiomagnetotelluric sounding works within the frequency range from 10 kHz to 1 MHz, [Bastani and Pedersen, 200l; Tezkan and Saraev, 2008].
The fields of remote radio stations, which can be consid ered as planewave fields, are used in the method. The interpretation of the data of the method of radiomagne totelluric sounding is based on the principles developed in magnetotellurics [Berdichevskii and Dmitriev, 2009]. On frequencies that depend on the electrical con ductivity of the Earth but, most frequently of the order of 1 MHz, the density of the displacement current in the Earth becomes comparable with the density of the conductivity current. The electromagnetic field struc ture is substantially complicated; however, now, it depends not only on the resistivity of the rocks, but also on their dielectric permittivity. This increases the information potential of electromagnetic prospecting; however, due to the strong skin effect its depth of pen etration is limited by several tens of meters. THE METHOD OF RADIO INTERFEROMETRY SOUNDING The method of radiowave interference sounding is based on the excitation and recording of the field of radiowaves within the range from 100 kHz to 100 MHz for obtaining the data on the resistivity and the dielec tric permittivity of rocks [Krylov, 1953; Khmelevskoy, 1980]. It is possible to say that it originates from the ondometric method, which was proposed as early as in 1910 by the German scientists Lowry and Leimbach; and, in our country, A.A. Petrovskii began to develop it in the twenties. The method can be considered as a phase version of a groundpenetrating radar. Another type of radar, the amplitude or pulse modulated radar (better known as a georadar), utilizes
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frequencies higher than 100 MHz for the boundary identification in the upper part of the section on which the dielectric permittivity of rocks changes [Vladov and Starovoitov, 2005]. The depth of penetration of georadar research depends substantially on electrical resistivity: when loose watersaturated rocks are stud ied, it does not exceed the first few meters; in frozen or hard rocks, it can exceed 10 m; and in glaciers it can exceed 100 m. In the method of radiointerferometry sounding, a signal is recorded that is obtained as a result of the interference of the incident and reflected harmonic radiowaves. Reflections are observed on the bound aries of geological layers or bodies with different values of electrical resistivity and dielectric permittivity. As a result of radiointerferometry sounding, the interfer ence curves (the frequency dependence diagrams of a signal) are plotted in a linear scale. For the simplest twolayered model of a medium, the maximuma, caused by the phase synchronism of the incident and reflected signals, and the minimuma, which correspond to the frequencies on which they vary in phase opposition, can be observed in the inter ference pattern. There is a simple kinematic method of interpretation of such curves. In this case, it is possible to estimate the parameters of the model from the dif ference in the frequencies between adjacent maxi muma or minimuma [Bulgakov and Rysakov, 1962]. It should be noted that the kinematic interpreta tion, based on the raypath theory of wave propaga tion, is applied in the georadar and in the seismic sur vey. The possibility of the application of this approach is connected with the relatively short wavelengths uti lized in these methods. In the method of radiointer ferometry sounding, where the wavelengths are com parable with the depth of prospecting, the raypath theory should be used with caution. For interpretation of the data of radiowave inter ference sounding that correspond to the multilayer and horizontally heterogeneous models, it is necessary to use a more complex methodology of interpretation, which is similar to the one used in magnetotellurics. It is based on the solution of the Maxwell equations of electrodynamics and Tikhonov’s theory of the solution of inverse problems. However, in this case, it is neces sary to take into account the displacement currents in the Earth and in air; i.e., it turns out that the quasista tionary approximation cannot be used [Petrukhin, 2001]. Furthermore, the number of parameters of geo electric model increases (the field depends both on the electrical resistivity and on the dielectric permittivity). RADIOWAVE INTERFERENCE SOUNDING IN THE FIELD OF PLANE WAVES Traditionally, the method of radiowave interfer ence soundings was adapted in the dipole version (radiointerferometry sounding, the dipole version, RWISD); i.e., measurements were conducted near
the transmitter (transmitting dipole) whose field had a sufficiently complex structure. The theory and meth odology of the field works are substantially simplified if we pass to the study of the fields from remote broad casting or special radio stations whose field can be considered as a plane one (radiowave interference sounding with a plane field, RWISP). The methodol ogy of the field works becomes similar to those utilized in the case of profiling by the radiointerferometry method [Tarkhov, 1961] and in the case of sounding by the radiokip (radio comparator and bearing) method [Simakov et al., 2007]. At present, radioether within the range from 100 kHz to 100 MHz is filled sufficiently tightly, and in the future, the number of utilized frequencies appar ently, will only increase. Certainly, the presence of radio signals substantially depends on the region of works and, in this question, additional studies are necessary. For the time being, we will restrict ourselves to the theoretical analysis of the possibilities of the RWISP method. From the results of measuring of the two horizontal mutually orthogonal components of the electric field Ex and the magnetic field Hy, the calculation of impedance Z = Ex/Hy is possible. In the horizontally layered media, its value is robustly determined and does not depend on the orientation of axes x and y (although in practice, depending on the field polariza tion, the values of the field components depend on the measurement azimuths). In the horizontally heterogeneous media, the com ponents of a planewave electromagnetic field are interrelated by the following linear relationships: Ex = Zxx Hx + Zxy Hy, Ey = Zyx Hx + Zyy Hy, Hz = Wzx Hx + Wzy Hy, where Zxx, Zxy, Zyx and Zyy are the impedance tensor components and Wzx and Wzy are the Wiese–Parkin son matrix components [Berdichevskii and Dmitriev, 2009]. For their determination, it is necessary to use at least two field polarizations. In this case, as in the method of radiomagnetotelluric sounding, it is possi ble to use the fields of two radio stations located at a particular distance from each other and broadcasting on two close frequencies. THE INTERFERENCE CURVES FOR THE TWOLAYERED MODEL In the simplest twolayered model, a plane wave falling on the Earth’s surface penetrates the upper layer and is reflected at a depth h1 from the roof of the second layer, whose electrical resistivity and/or dielec tric permittivity differ from the parameters of the first layer. Calculation of the interference curves in the method of radiowave interference sounding for the twolayered model is carried out by the following for mula:
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MAGNETOTELLURICS AND RADIOWAVE INTERFERENCE SOUNDING arg(Z), deg 20
arg(Z), deg 0
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Fig. 2. Frequency dependence of the phase and modulus of impedance for the twolayered model with the following parameters: ρ1 = 30 Ω m, ρ2 = 30 Ω m, ε1 = 50, ε = 20, h1 = 30 m.
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Fig. 1. Frequency dependence of the phase and modulus of impedance for the twolayered model with the following parameters: ρ1 = 2400 Ω m, ρ2 = 30 Ω m, ε1 = 10, ε2 = 20, h1 = 30 m.
k ωμ Z ( ω ) = – 0 coth ⎛ ik 1 h 1 + arccoth 1⎞ , ⎝ k1 k 2⎠ where Z is the electrical impedance on the medium surface, ω is the angular frequency of the field oscilla tions, μ0 is the magnetic permeability of vacuum (the rocks are considered nonmagnetic), and k1 and k2 are the wave numbers of the first and second layers. The wave number of a layer with a number j is calculated by the following formula: kj =
2
iωμ 0 /ρ j + ω μ 0 ε 0 ε j ,
where ρj and εj are the electrical resistivity and the dielectric permittivity (relative) of the layer, ε0 is the dielectric permittivity of vacuum. The interference pattern of the radiowave interfer ence sounding represents the frequency dependence of the scalar impedance |Z| in the linear scale. We will supplement this pattern with the frequency depen IZVESTIYA, PHYSICS OF THE SOLID EARTH
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dence of the impedance phase arg(Z). Recall that if the scalar impedance reflects the ratio of the amplitudes of electrical and magnetic components, then the imped ance phase is the phase difference of the oscillations of these components. The interference curves that correspond to a method favorable to a radiowave interference sound ing section with a strong reflecting boundary due to the high value of ρ1 (2400 Ω m) and owing to the con trast of electrical resistivity (ρ1 ρ2) are presented in Fig. 1. As a result, the interference curves are obtained with pronounced oscillations. Similar patterns corre spond to the following types of sections: (1) At the top (ρ1, ε1), a rock mass of the dry sand gravel species is found; underneath (ρ2, ε2) it, the same rocks are found; however, below the groundwater level of h1 = 30 m; (2) Under the thickness of frozen rocks (ρ1, ε1), thawed rocks are located (ρ2, ε2); however, the base of the frozen ground is located at a depth of h1 = 30 m. Oscillations in the curves of radiowave interfer ence sounding scan be absent. Such an example is given in Fig. 2. Here, although the dielectric permit tivity of the layers are different, the electric impedance varies smoothly with frequency. The kinematic inter pretation (based on the difference in the frequencies between the extrema) of such a curve is not possible, No. 9
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but its dynamic interpretation is possible, just as any other curve of electromagnetic sounding. CONCLUSIONS 1. Plane waves are used both in the theory of magne totellurics (including the audiofrequency and radiofre quency ranges) and in the theory of radiowave interfer ence sounding with a plane field (RWISP). 2. The merit of the RWISP method consists in the fact that it provides data both on the electrical resistiv ity and on the dielectric permittivity of rocks. In the solution of the direct problem, both the displacement currents and the conduction currents are considered. 3. Some parameters of the model can be estimated based on the specific features of the RWISP curves. More comprehensive data will provide the classical solution of the inverse problem of electromagnetic sounding. 4. For the practical implementation of the RWIS P method, which uses the fields of broadcasting and special radio stations, it is necessary to investigate the signal intensity within the frequency range from 100 kHz to 100 MHz, and, also, to adapt the sensors and measuring devices of the field components. 5. The RWISP method in unmounted and truck mounted modifications is promising in the study of depths up to several tens of meters, especially in the case of a high electrical resistivity of the upper part of the section (dry, hard rock, and frozen rocks). 6. The range and variety of tasks that can be solved by this method includes searching and prospecting of solid mineral deposits; the estimation of the thickness of cover deposits; the search for waterbearing zones and tectonic fault zones in the rock massif; the track ing of the level of ground water; the mapping of frozen and thawed rocks; and the study of chemical pollu tions of soils.
REFERENCES 1. M. Bastani and L. Pedersen, “Estimation of Magneto telluric Transfer Functions from Radio Transmitters,” Geophys. 66 4, 1038–1051 (2001). 2. M. N. Berdichevskii and V. I. Dmitriev, Interpretation Models and Methods of Magnetotellurics (Nauchnyi Mir, Moscow, 2009), pp. 1–680 [in Russian]. 3. A. K. Bulgakov and V. M. Rysakov, “About the Possibil ity of Applying the Electromagnetic HighFrequency Oscillations in the Exploration Geophysics,” in The Problems of Diffraction and Propagation of Waves. Vol. 1 (Publishing House of LGU, Leningrad, 1962), pp. 143–150 [in Russian]. 4. V. K. Khmelevskoy, The Basic Course of Electromagnetic Prospecting. Part 2 (Publishing House of Moscow State University, Moscow, 1980), pp. 1–267 [in Russian]. 5. V. K. Khmelevskoy and B. P. Petrukhin, “The Possibil ities of RadioWave Interference Soundings According to the Data of the Dynamic Modeling of TwoLayered Geoelectric Media,” Vestn. Mosk. Gos. Univ., (Geol.) 4 No. 1, 48−52 (2010). 6. M. K. Krylov, “Geophysical Prospecting by the High Frequency Alternating Field (Interference Sounding,” estn. Mosk. Gos. Univ., (Geol.) 4 (3), 46–52 (1953). 7. B. P. Petrukhin, Peculiarities of Calculation of the Curves of HighFrequency Electromagnetic Soundings, Avail able from VINITI, No. 1490V01 (Moscow, 2001) [in Russian]. 8. A. E. Simakov, M. I. Pertel, A. K. Saraev, Kh. M. Jime nez, K. Torre, and P. Martin, “Possibilities of Radio Magnetotelluric Method for the Solution of Ecological Problems,” in Problems of Geophysics. Vyp. 40 (Publish ing House of St. Petersburg State University, St. Peters burg, 2007), pp. 101–109 [in Russian]. 9. A. G. Tarkhov, Fundamentals of Geophysical Prospecting by the Radiokip Method (Gosgeoltekhizdat, Moscow, 1961), pp. 1–216 [in Russian]. 10. A. Tezkan and A.Saraev, “A New Broadband Radiom agnetotelluric Instrument: Applications to Near Sur face Investigations,” Near Surf. Geophys. 6 (4), 245– 252 (2008). 11. M. L. Vladov and A. V. Starovoitov, Introduction in the Georadiolocation (Publishing House of MSU, Moscow, 2005), pp. 1–153 [in Russian].
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