Use of Subharmonics of Base Frequencies in the CSRMT Method with Loop Sources

: In the controlled source radiomagnetotelluric (CSRMT) sounding method, a horizontal magnetic dipole, HMD (vertical loop) or a horizontal electric dipole, and HED (grounded line) are used as sources. When working with HMD, the source is usually tuned to resonance to increase the current in the loop. However, the disadvantage of this approach is the narrow frequency range realized in the CSRMT method (1–12 kHz) and the short operating distance from the source (600–800 m). The need to tune the source to resonance at each selected frequency reduces the efﬁciency of the survey. In the case of using HED for sounding, measurements are performed in a wider frequency range of 1 to 1000 kHz, and along with the signal of the base frequency, its subharmonics are measured. In this case, emitted signal measurements are possible at a distance of up to 3–4 km from the source. At the same time, the disadvantage of using HED is that it requires grounding, the arrangement of which requires additional time when working on frozen ground or dry stony soil. We consider the possibilities of generation and registration of signals of subharmonics of base frequencies when applying the CSRMT method with loop sources—HMD and VMD (horizontal loop). A matching unit (MU) based on a step-up transformer was developed, which increases the output voltage of the CSRMT transmitter. In a ﬁeld test with base frequencies of 20, 40, and 80 kHz, the signal amplitudes increased by a factor of two to four for subharmonics at frequencies of 60–200 kHz and by up to 10–13 times for subharmonics at frequencies of 200–500 kHz due to transformation of signal spectrum provided by MU. The possibility of using odd subharmonics of base frequencies for inversion has been demonstrated in the results of ﬁeld experiments with different sources (HED, HMD, and VMD). This expands the frequency range of the method when working with loop sources and increases the survey’s effectiveness. The use of loop sources in the CSRMT method is especially advantageous for winter work in Arctic regions.


Introduction
The radiomagnetotelluric (RMT) sounding method is based on the registration of signals from remote radio transmitters in the frequency range from 10 to 250-1000 kHz [1]. Electromagnetic fields of radio transmitters penetrate the conductive ground and induce electric currents, which, in turn, produce secondary electromagnetic fields that carry information about the distribution of electric properties with depth. On the ground surface, the sum of the initial and secondary fields is measured.
Values of the complex surface impedance (Z) are determined by measuring horizontal and mutually perpendicular components of the electric (Ex) and magnetic (Hy) fields: J 2023, 6 288 In recent years, the tensor variant of the CSRMT method, using two mutually perpendicular HEDs as electromagnetic field sources, has been developed jointly by the University of Cologne and St. Petersburg State University. New possibilities of the tensor technology have been demonstrated in studies of rock anisotropy [18][19][20] and of objects in permafrost areas [21,22]. To implement the tensor variant with two HED sources, approaches have been developed to create a rotating electromagnetic field [23]. Along with the soundings in the far-field zone, the techniques and software tools were elaborated to use the HED source in the transition zone. Examples of the bimodal inversion of field data using the tensor variant of the CSRMT method in the transition zone have been reported in articles [19,24].
Measurements of the three components of the magnetic field in the CSRMT survey implement the determination of a tipper. The secondary vertical magnetic field originates from lateral inhomogeneities of the conductivity; therefore, the tipper can be used in the study of two-dimensional and three-dimensional structures [2,25], extending the possibilities of the CSRMT method.
In addition to using HMD and HED, electromagnetic soundings with a vertical magnetic dipole (VMD) are also realized in near-surface studies [26][27][28][29]. This source can also be applied in the CSRMT method. An advantage of VMD (horizontal loop) is the possibility of carrying out winter work on snow and ice without groundings. Unlike HMD, there are no restrictions for VMD in increasing the size of the loop, which makes it possible to increase its operating distance. However, one should keep in mind that in the far field zone of VMD, the horizontal components of the electric and magnetic fields decrease in proportion to the fourth power of the distance and the vertical component of the magnetic field to the fifth power of the distance [30]. For HED and HMD, the components of the electric and magnetic fields decrease more slowly. The horizontal components are proportional to the third power of the distance, and the vertical component of the magnetic field to the fourth power of the distance [26]. Additionally, it is impossible to implement tensor measurements with VMD.
Each type of source (HED, HMD, VMD) has its own advantages and disadvantages. In the field of HED, both galvanic and inductive components are non-zero, and the data obtained contain information about both high-resistive and conductive objects. Induction sources (HMD, VMD) are less sensitive to high-resistive objects since they have only the eddy field component [31]. The use of sources of different types can be useful for increasing the reliability of the obtained resistivity models as well as for estimating the anisotropy of resistivity. The results of studies of rock anisotropy using the CSRMT method with HED were considered in our previous papers [18][19][20]32].
Because using loop sources that do not require grounding is promising in the winter work, especially in Arctic regions, we upgraded the GTS-1 transmitter and performed a number of field experiments to study the possibility of measuring signals of base frequency subharmonics when operating with HMD and VMD. The use of subharmonics makes it possible to extend the operating frequency range and increase the effectiveness of surveying with loop sources.
This article analyzes the results of experiments in comparison with the measurements using HED, which we traditionally employ as part of the CSRMT equipment. To check the possibilities of using subharmonic signals of loop sources, the results of the inversion of sounding curves obtained with various sources (HMD, VMD, and HED) are presented.

Field Tests of Different Sources
In the experiments, we used a GTS-1 transmitter, operating in a wide frequency range and providing output power of up to 1 kW [13]. Ensuring stable tuning of the output circuit to resonance for each selected frequency in a wide frequency range, from kHz to hundreds of kHz, presents a rather difficult task. Field surveys performed in this mode would take too long a time, so a different approach has been chosen. It is based on the use of a matching unit (MU) with a transformer that increases the maximal output voltage of the GTS-1 transmitter from 200-288 V to 560-700 V. The schematic diagram of the MU is shown in Figure 1.
In the experiments, we used a GTS-1 transmitter, operating in a wide frequency and providing output power of up to 1 kW [13]. Ensuring stable tuning of the circuit to resonance for each selected frequency in a wide frequency range, from hundreds of kHz, presents a rather difficult task. Field surveys performed in this would take too long a time, so a different approach has been chosen. It is based on of a matching unit (MU) with a transformer that increases the maximal output vol the GTS-1 transmitter from 200-288 V to 560−700 V. The schematic diagram of the shown in Figure 1. The voltage gain (G) is equal to 4 with a series connection of the output wind the transformer T1; with a parallel connection of the output windings, G is equ Experiments with a step-up transformer were carried out at four frequencies in t quency range of 10−80 kHz. The MU test showed that at frequencies of 10 and 20 is more optimal to use G = 2, whereas at frequencies of 40 and 80 kHz: G = 4.
Field tests with MU were carried out in two stages. In the first stage, the pos of increasing the output voltage in the frequency range of 10-80 kHz was tested loop source as a load. In this case, a vertical 5-turn pentagonal loop ( Figure 2) w equivalent area of 148.5 m 2 was used, approximating an HMD. The loop inductan 1.6 mH, and the DC resistance was 2.1 Ω. Since the GTS-1 transmitter is designed t ate with high load resistance values (tens of Ω), a ballast resistance of 23 Ω was in in the circuit to prevent the transmitter overload. Measurements of the input imp spectrum of the loop were carried out, and the values of the absolute impedanc proved to be quite high in the operating frequency range, about 20 Ω at a frequenc kHz and about 120 Ω at a frequency of 80 kHz ( Figure 3). This means that, in prin is possible to operate without ballast resistance.  The voltage gain (G) is equal to 4 with a series connection of the output windings of the transformer T1; with a parallel connection of the output windings, G is equal to 2. Experiments with a step-up transformer were carried out at four frequencies in the frequency range of 10-80 kHz. The MU test showed that at frequencies of 10 and 20 kHz, it is more optimal to use G = 2, whereas at frequencies of 40 and 80 kHz: G = 4.
Field tests with MU were carried out in two stages. In the first stage, the possibility of increasing the output voltage in the frequency range of 10-80 kHz was tested with a loop source as a load. In this case, a vertical 5-turn pentagonal loop ( Figure 2) with an equivalent area of 148.5 m 2 was used, approximating an HMD. The loop inductance was 1.6 mH, and the DC resistance was 2.1 Ω. Since the GTS-1 transmitter is designed to operate with high load resistance values (tens of Ω), a ballast resistance of 23 Ω was included in the circuit to prevent the transmitter overload. Measurements of the input impedance spectrum of the loop were carried out, and the values of the absolute impedance value proved to be quite high in the operating frequency range, about 20 Ω at a frequency of 10 kHz and about 120 Ω at a frequency of 80 kHz ( Figure 3). This means that, in principle, it is possible to operate without ballast resistance.

Field Tests of Different Sources
In the experiments, we used a GTS-1 transmitter, operating in a wide frequency range and providing output power of up to 1 kW [13]. Ensuring stable tuning of the output circuit to resonance for each selected frequency in a wide frequency range, from kHz to hundreds of kHz, presents a rather difficult task. Field surveys performed in this mode would take too long a time, so a different approach has been chosen. It is based on the use of a matching unit (MU) with a transformer that increases the maximal output voltage of the GTS-1 transmitter from 200-288 V to 560−700 V. The schematic diagram of the MU is shown in Figure 1. The voltage gain (G) is equal to 4 with a series connection of the output windings of the transformer T1; with a parallel connection of the output windings, G is equal to 2. Experiments with a step-up transformer were carried out at four frequencies in the frequency range of 10−80 kHz. The MU test showed that at frequencies of 10 and 20 kHz, it is more optimal to use G = 2, whereas at frequencies of 40 and 80 kHz: G = 4.
Field tests with MU were carried out in two stages. In the first stage, the possibility of increasing the output voltage in the frequency range of 10-80 kHz was tested with a loop source as a load. In this case, a vertical 5-turn pentagonal loop ( Figure 2) with an equivalent area of 148.5 m 2 was used, approximating an HMD. The loop inductance was 1.6 mH, and the DC resistance was 2.1 Ω. Since the GTS-1 transmitter is designed to operate with high load resistance values (tens of Ω), a ballast resistance of 23 Ω was included in the circuit to prevent the transmitter overload. Measurements of the input impedance spectrum of the loop were carried out, and the values of the absolute impedance value proved to be quite high in the operating frequency range, about 20 Ω at a frequency of 10 kHz and about 120 Ω at a frequency of 80 kHz ( Figure 3). This means that, in principle, it is possible to operate without ballast resistance.  The results of testing a loop source with MU are shown in Table 1. At a frequency of 10 kHz, the use of the MU did not significantly increase the output voltage. However, at this frequency, the transmitter provides a sufficiently large current of 5.9 A even without MU. The same results were obtained at lower frequencies, in the range of 1−10 kHz. Therefore, it is possible to work with the GTS-1 transmitter without MU at frequencies from 1 to 10−15 kHz, as the transmitter is in the optimal mode and does not require matching with a used loop source.  For higher frequencies, the use of MU is necessary. The effective voltage increases by a factor of about 2 at 20 kHz and by about 3 at 40 and 80 kHz. The output voltage of the transmitter is increased from 200−288 V to 560−700 V. MU ensures a sufficiently large current in a loop at high frequencies, 6.8 A at 20 kHz and 4.3 A at 80 kHz.
In the second stage, the electromagnetic fields of HMD (vertical loop) and HED (grounded line) were measured at a distance of 100 m from the sources to assess the possibility of recording signals of subharmonics of the base frequency. Taking into account the results obtained at the first stage, the frequencies of 20, 40, and 80 kHz were chosen for measurements. The measurement point was located broadside of the HMD and in line with the HED (Figure 4). With this orientation of the moments of the sources, their fields are equivalent. The results of testing a loop source with MU are shown in Table 1. At a frequency of 10 kHz, the use of the MU did not significantly increase the output voltage. However, at this frequency, the transmitter provides a sufficiently large current of 5.9 A even without MU. The same results were obtained at lower frequencies, in the range of 1-10 kHz. Therefore, it is possible to work with the GTS-1 transmitter without MU at frequencies from 1 to 10-15 kHz, as the transmitter is in the optimal mode and does not require matching with a used loop source.  For higher frequencies, the use of MU is necessary. The effective voltage increases by a factor of about 2 at 20 kHz and by about 3 at 40 and 80 kHz. The output voltage of the transmitter is increased from 200-288 V to 560-700 V. MU ensures a sufficiently large current in a loop at high frequencies, 6.8 A at 20 kHz and 4.3 A at 80 kHz.
In the second stage, the electromagnetic fields of HMD (vertical loop) and HED (grounded line) were measured at a distance of 100 m from the sources to assess the possibility of recording signals of subharmonics of the base frequency. Taking into account the results obtained at the first stage, the frequencies of 20, 40, and 80 kHz were chosen for measurements. The measurement point was located broadside of the HMD and in line with the HED (Figure 4). With this orientation of the moments of the sources, their fields are equivalent.  The signals of the base frequencies 20, 40, and 80 kHz and their odd subharmonics can be seen in the spectra. They also contain signals from remote radio transmitters. Note that the odd subharmonics of the base frequencies, indicated with red arrows, significantly exceed the noise level. Their coherence is quite high (above 0.8) up to 600-700 kHz. These signals can be used for the deriving of the sounding curves and the subsequent inversion.
The amplitudes of the HMD signals for the base frequencies of 20, 40, and 80 kHz and their odd subharmonics measured at a distance of 100 m with and without using MU, as well as normalized signals, are shown in Figure 6. When using MU, the signal amplitudes are increased by two to four times for subharmonics at low frequencies (60-200 kHz) and up to 10-13 times for subharmonics at higher frequencies (200-500 kHz). However, the subharmonics amplitudes are decreased at higher frequencies in the 600-1000 kHz range. The values of the amplification factor (AF) of the Ex and Hy components at different odd subharmonics of the base frequencies of 20, 40, and 80 kHz are given in Table 2. AF is defined as the ratio of the signal measured with the use of MU, normalized to the signal measured without using MU. The signals of the base frequencies 20, 40, and 80 kHz and their odd subharmonics can be seen in the spectra. They also contain signals from remote radio transmitters. Note that the odd subharmonics of the base frequencies, indicated with red arrows, significantly exceed the noise level. Their coherence is quite high (above 0.8) up to 600−700 kHz. as well as normalized signals, are shown in Figure 6. When using MU, the signal amplitudes are increased by two to four times for subharmonics at low frequencies (60−200 kHz) and up to 10−13 times for subharmonics at higher frequencies (200−500 kHz). However, the subharmonics amplitudes are decreased at higher frequencies in the 600−1000 kHz range. The values of the amplification factor (AF) of the Ex and Hy components at different odd subharmonics of the base frequencies of 20, 40, and 80 kHz are given in Table  2. AF is defined as the ratio of the signal measured with the use of MU, normalized to the signal measured without using MU.    The possibility of working with a loop source at low frequencies without using a MU is illustrated in Figure 7. It is seen that the amplitude of odd subharmonics of the signal with the base frequency of 0.5 kHz measured at the same distance of 100 m exceeds the noise level more than one order of magnitude, and the coherence of the Ex and Hy components of subharmonics is close to one in the frequency range 1-10 kHz. The possibility of working with a loop source at low frequencies without using is illustrated in Figure 7. It is seen that the amplitude of odd subharmonics of the s with the base frequency of 0.5 kHz measured at the same distance of 100 m exceed noise level more than one order of magnitude, and the coherence of the Ех and Ну ponents of subharmonics is close to one in the frequency range 1−10 kHz.   The amplitudes of the HED signals for the base frequencies of 20, 40, and 80 kHz and their odd subharmonics without MU and with MU switched on, as well as normalized signals at Us = 288 V and G = 2, are shown in Figure 9. The measurement results show that the use of MU with HED provides an increase in the amplitudes of the base frequency subharmonics in accordance with the used gain in the entire operating frequency range.

Comparison of Sounding Results with Different Sources
The next test of using subharmonics of the base frequencies for sounding with all considered sources was carried out at the Yablonovka geophysical test site on the Karelian Isthmus, Leningrad Region. The geological section in the depth range from 40-60 m down to 200 m is represented by Vendian mudstones and sandstones and Riphean carbonateterrigenous rocks. They are overlaid by Quaternary sediments with a thickness of several tens of meters [33]. The rather heterogeneous structure of the Quaternary sediments with the presence of gravel-pebble layers having an increased resistivity was revealed in this area based on the results of previous work by the CSRMT method.
The field experiment at the test site included measurements with the HED along with the use of HMD and VMD. Since only scalar measurements are possible with VMD, the surveys with HMD and HED were also performed in the scalar mode in order to compare the results obtained with different sources. In this case, the moments of HED (grounded line) and HMD (vertical loop) were directed mutually perpendicular to obtain the same polarization of their electromagnetic fields. Figure 10 shows

Comparison of Sounding Results with Different Sources
The next test of using subharmonics of the base frequencies for sounding with all considered sources was carried out at the Yablonovka geophysical test site on the Karelian Isthmus, Leningrad Region. The geological section in the depth range from 40-60 m down to 200 m is represented by Vendian mudstones and sandstones and Riphean carbonateterrigenous rocks. They are overlaid by Quaternary sediments with a thickness of several tens of meters [33]. The rather heterogeneous structure of the Quaternary sediments with the presence of gravel-pebble layers having an increased resistivity was revealed in this area based on the results of previous work by the CSRMT method.
The field experiment at the test site included measurements with the HED along with the use of HMD and VMD. Since only scalar measurements are possible with VMD, the surveys with HMD and HED were also performed in the scalar mode in order to compare the results obtained with different sources. In this case, the moments of HED (grounded line) and HMD (vertical loop) were directed mutually perpendicular to obtain the same polarization of their electromagnetic fields. Figure 10 shows Examples of sounding curves obtained with different sources at one of the profile stations (St-9) are shown in Figure 11. Signals of base frequencies of 0.5, 5, and 50 kHz and their odd subharmonics were used for drawing the curves. The apparent resistivity curves agree well with each other. The phase curves diverge at low frequencies, which is due to Examples of sounding curves obtained with different sources at one of the profile stations (St-9) are shown in Figure 11. Signals of base frequencies of 0.5, 5, and 50 kHz and their odd subharmonics were used for drawing the curves. The apparent resistivity curves agree well with each other. The phase curves diverge at low frequencies, which is due to different boundaries of the transition zone for the considered sources. Examples of sounding curves obtained with different sources at one of the profile stations (St-9) are shown in Figure 11. Signals of base frequencies of 0.5, 5, and 50 kHz and their odd subharmonics were used for drawing the curves. The apparent resistivity curves agree well with each other. The phase curves diverge at low frequencies, which is due to different boundaries of the transition zone for the considered sources.  Figures 12 and 13 show the results of 1D and 2D inversions of sounding data with different sources. One-dimensional inversion of sounding curves has been performed for each type of source using CS1D software, taking into account the influence of the transition zone [32]. In each case, the start model was a homogeneous half-space with a resistivity of 150 Ω·m. For the grounded transmitter line (HED) and the horizontal loop (VMD), their real size and shape were taken into account.  Figures 12 and 13 show the results of 1D and 2D inversions of sounding data with different sources. One-dimensional inversion of sounding curves has been performed for each type of source using CS1D software, taking into account the influence of the transition zone [32]. In each case, the start model was a homogeneous half-space with a resistivity of 150 Ω·m. For the grounded transmitter line (HED) and the horizontal loop (VMD), their real size and shape were taken into account.    Two-dimensional inversion taking into account the transition zone, has been performed using MARE2DEM software [34] with a modification for the impedance inversion of the field of the controlled source [11]. In this case, the real size of the grounded transmitter line (linear approximation) has been taken into account. For a horizontal loop, an approximation by a point dipole placed in the center of the loop was used. Sounding Two-dimensional inversion taking into account the transition zone, has been performed using MARE2DEM software [34] with a modification for the impedance inversion of the field of the controlled source [11]. In this case, the real size of the grounded transmitter line (linear approximation) has been taken into account. For a horizontal loop, an approximation by a point dipole placed in the center of the loop was used. Sounding curves in the stations near the loop may have some distortions due to this simplification; nevertheless, they did not significantly affect the data obtained.
The resistivity sections recovered from the 1D and 2D inversions of the data obtained from different sources look quite similar. The following features of the sections can be distinguished. In the near-surface sediments of Quarternary age, the gravel-pebble layers with increased resistivity are present. The thicknesses of these layers increase to the northeast. They are most prominent in the results of 1D and 2D inversions of sounding curves obtained with HED. This is due to the influence of the galvanic mode sensitive to high-resistive layers in the transition zone of this source.
The underlying strata are represented by the more conductive Quarternary sandyclay sediments that manifest themselves in the resistivity sections in approximately the same way. The sections obtained from 1D and 2D inversions of VMD and HMD data are characterized by relatively low resistivity values compared with the inversion results of HED data since the induction mode is less sensitive to high-resistive layers dominates in the fields of VMD and HMD.
The presented results show that the measurements of subharmonics of base frequencies when working with loop sources in the CSRMT method allow us to expand the used frequency range and obtain reliable and geologically meaningful resistivity sections of the studied area.

Conclusions
The possibility of recording signals of base frequencies subharmonics in the CSRMT method with loop sources is considered. Using MU based on a step-up transformer increases the output voltage of the GTS-1 transmitter of the CSRMT equipment. The output voltage of the transmitter increased by a factor of 2-3, from 200-288 V to 560-700 V, and the current in the loop source (HMD) was 7 A at a frequency of 20 kHz and 4.5 A at a frequency of 80 kHz.
As a result, the signals of the selected base frequencies of 20, 40 and 80 kHz and their odd subharmonics were reliably measured. The signal amplitudes increased by a factor of 2-4 for subharmonics at low frequencies (60-200 kHz) and up to 10-13 times for subharmonics at higher frequencies (200-500 kHz). At the same time, the amplitudes of the subharmonics of the signals in the range of 600-1000 kHz were decreased. When working with loop sources and the GTS-1 transmitter at frequencies from 1 to 10-15 kHz, there is no need to use MU to ensure reliable measurements of the subharmonic signals.
The combination of GTS-1 and MU has also been tested with HED (grounded line) as a source, which we traditionally use as a part of the CSRMT equipment. The amplitudes of the base frequency subharmonics increased in the entire operating range of the equipment up to 1000 kHz in accordance with the used gain of MU.
The results of the field experiment at the Yablonovka test site with different sources (HED, HMD, and VMD) demonstrated that the curves of apparent resistivity and impedance phase derived from signals of base frequencies and their subharmonics have a similar shape for three types of sources. Some discrepancies at low frequencies are associated with the different influences of the transition zone in the fields of these sources. In this case, more noticeable differences are seen in the phase curves.
To compare the results obtained with different sources, the surveys with HMD and HED were carried out in the scalar mode since only scalar measurements are possible with VMD. 1D and 2D inversions of sounding data were performed, taking into account the influence of the transition zone. On the whole, obtained resistivity sections look quite similar. In the upper part of the section (Quaternary sediments), the increased values of resistivity characteristic for the gravel-pebble layers are observed. These layers appear more pronounced in the resistivity sections obtained with HED, which is explained by the significant influence of the galvanic mode in the transition zone of this source. The underlying sandy-clay sediments are characterized by relatively low resistivity values. They are better seen in the sections obtained with VMD and HMD. This is explained by a more noticeable influence of the induction mode in the fields of these sources.
The presented results show that the use of the base frequency subharmonics for HMD and VMD sources in the CSRMT method is possible and allows us to increase the efficiency of measurements because only three base frequencies can be used to cover three decades of frequency from 1 to 1000 kHz. The use of loop sources in the CSRMT method would be particularly advantageous when conducting winter work in Arctic regions, where the use of HED is difficult.

Data Availability Statement:
The datasets generated and analyzed in the current study are available from the corresponding author upon reasonable request.