## RMT method. How it works?

###### Place of the RMT method in the geoelectric

The modern variant of the radiomagnetotellurics (RMT) is a frequency-domain electromagnetic soundings.  In the RMT method electromagnetic fields in the frequency range 10-1000 kHz are used. In the case of using the controlled source (CSRMT modification) the frequency range extends to 1-1000 kHz. Therefore, by frequency range and interval of depths of investigation, RMT method takes intermediate place between ground penetration radar and audiomagnetotellurics (Figure 1).

Figure 1. Frequency range and interval of depths of investigation of the RMT method.

###### Sources of the electromagnetic field

In the RMT method the signals of broadcast radio transmitters are used. It can be transmitters of the radio navigation systems like Alfa or Omega, BBC transmitters, exact time signals in Frakfurt (77.5 kHz) or Mayak in Russia (549, 576 kHz). Some of this radio transmitters can be foud on this map. The moste famoust and powerful VLF radio transmitters (10-30 kHz) with approximate broadcasting areas are shown in Figure 2.

Figure 2. The moste famoust and powerful VLF radio transmitters with approximate broadcasting areas by [McNeill and Labson 1991]

Most of radio transmitters are designed as vertical electric dipoles (Figure 3). In the primary field of VED there are only three components: the vertical component of the electric field Ez, the horizontal and radial component of the electric field Er directed toward the source, and the horizontal and azimuthal component of the magnetic field Hj, orthogonal to the Er. Moreover, only Er and Hj components contain information about the electrical conductivity of rocks and soils. Therefore we have the simple rule: for measuring the EM field of the radio transmitter we have to orient the receiving electric antenna towards the radio transmitter, and the magnetic antenna orthogonal to this direction. Of course, some deviation in the orientation of the receiving antennas from the direction to the radio transmitter is possible (usually ± 30°).

Figure 3. The picture of the antenna of the radio transmitter of the VLF navigation system, Tsushima, Japan.

In reality, measurements are usually made at a significant distance from radio transmitters. In this case, the EM field of the radio transmitter can be approximated by a plane vertical incident wave. This is one of the simplest models in geoelectrics (also used in the magnetotellurics). For plane wave model is many algorithms for data processing and inversion have been developed. The nearest distance from the source of the EM field, where the plane wave approximation is correct, usually called as far-field boundary. For a homogeneous half-space in the case of a vertical electric dipole, the far-field boundary corresponds to a distance near the 1.5d, where d is the skin-depth of the EM wave in the conductive half-space:

Here, as usual, r is the resistivity of the half-space in W*m, f is the frequency in Hz. The resulting value of the skin-depth expressed in meters. The lowest frequency of radio transmitters is 11-12 kHz. For example, for a resistivity of the order of 100,000 W*m, the far-field boundary will be located at a distance about 2300 meters from the source. With a conventionally normal resistivity of rocks of 1000 W*m, the far-field boundary is located at distance about 230 m from the radio transmitter. Therefore, we can assume that the measurement of the EM field of radio transmitters is always carried out in the far-field zone.

###### Data acquisition and processing

Modern receivers for the RMT method have five synchronous input channels: two for the horizontal electric field components Ex and Ey and three for the magnetic field components Hx, Hy, Hz (Figuer 4).

Figure 4. Five-channel receiverRMT-5 in the field.

Since beforehand we don't know the spectrum of available for measuring radio transmitters (as well as the mode of their operation, etc.), measurements are made in the time domain without any binding to the source of the field. It is only necessary to ensure synchronization of recording over all input channels of the receiver. High frequencies of the EM field (10-1000 kHz) allow to make fast measurement (few seconds or less). The obtained time series are transformed into the frequency domain by Fourier transform. An example of the obtained spectrum is shown in Figure 5.

Figure 5. Example of the power spectra of electrical and magnetic channels and corresponding two-channel coherence.

Figure 5 shows that the spectrum typically contains a number of different narrowband signals. Nevertheless, only some of them are signals from radio transmitters and only some of these signals are suitable for further processing: bearings on them lie in the sector of tolerance with respect to receiving antennas (see above).

Thus, we have to have some criteria for correct selection of suitable signals of radio transmitters.

The black chart at the top of Figure 5 is the spectrum of the squared coherence between the Ex and Hy channels. In this case, the squared coherence is a measure of the linearity of the relationship between two processes. Zero coherence indicates that there is no connection between the processes in the Ex and Hy channels at the current frequency. Coherence close to unity indicates that the processes in the channel Ex and Hy are coupled linearly and they are part of a single electromagnetic wave. Thus, the squared coherence is the first criterion for the selection of signals from radio transmitters.

The second criterion is the bearing to the radio transmitter relative to the direction of receiving antennas. As we mentioned above, the primary field of a radio transmitter is close to the field of a vertical electric dipole and has a linear polarization in the horizontal plane. The ellipse of polarization has three main parameters: the major semiaxis a, the minor semiaxis b, and the angle of rotation of the major semiaxis q relative to some reference axis (for example, the direction of the antenna Hx). The angle q` = q + p / 2 equals to the bearing to the radio transmitter (up to p). Comparing the orientation angles of the polarization ellipses of received signals with directions of the receiving antennas, it is possible to select radio transmitters with bearings close to directions of the Ex or Ey antennas.

Thus, in the best case, only a few dozen of the signals are sutable for recovering geoelectrilac properties of the Earth. Now we will discuss the parameters of the EM field, which provides information adout the resistivity of rocks and soils.

Since we don't know anything about the moment of the source, it is necessary to use parameters independent of the moment. An obvious choice is the ratio of the components of the EM field. Similar technique and theory has already been developed in the MT method. In the RMT method we use the same approach.

In the RMT method, similar to the MT, we analize components of the surface impedance tensor Zxy = Ex / Hy and Zyx = Ey / Hx. Components of the surface impedance are complex numbers with magnitude and phase. The magnitude of the impedance is usually normalized into an apparent resistivity:

Here ra is the apparent resistivity, w is the circular frequency, m0 is the magnetic permeability of the vacuum.

As a result of the impedance estimation, the sounding curves are obtained: the apparent resistivity and the phase of the impedance as a function of frequency. An example of the sounding curves is shown in Fig. 6.

Figure 6. An example of the RMT sounding curves.

###### Depth of investigation

In the RMT method, the depth of the investigation depends on the skin-depth of the EM wave in the rocks. Magnitude of EM field is decreased by e (2.718) times at the distance equals to the skin-depth. Let's repeat once again the expression for the skin-depth in a homogeneous half-space:

The depth of the investigation is depends both on the frequency of the field and the mean resistivity of the rocks. The lowest frequency of existing broadcasting radio transmitters is 11-12 kHz. If the area of exploration has mainly clayey rocks with a resistivity about 10 W*m, the depth of investigation will be limited by 15-20 meters. On the contrary, if the survey is carried out in an crystall rocks area with a mean resistivity about 1000-10000 W*m, the depth of investigation can reach hundreds of meters.

###### Inversion

In the PMT method, the far-field condition is always guarantees. Therefore, we can invert the RMT data using the already developed MT software, for example, the famous software ZondMT1D and ZondMT2D.