Estimation of the optimal frequency range of EM waves for the implementation of a wireless channel of charge activation during drilling and blasting operations

The article analyzes the methods of wireless detonation of underground charges during drilling and blasting operations. The technologies considered are intended mainly for disrupting the integrity of rocks during tunneling and extraction of mineral resources in mines and quarries, as well as for the controlled demolition of buildings. The methods presented in the scientific press do not provide sufficient accuracy of time synchronization between the moment of the explosion and the command to launch the operator of the explosive machine, which is a necessary requirement for seismic exploration, and are also based on the use of magnetic antennas for wireless activation of detonators located at a depth of 30 m. The article, by the authors, on the basis of the analytical solution of equations and computational modeling, considers the physical processes of propagation of electromagnetic fields and currents induced by a grounded electric dipole, which is an alternative method of transmitting radio signals to a linear group of detonators. The most favorable operating frequency range of the channel is also analyzed based on the absorbing properties of the medium.

• Duplex channel using RFID technology and tracking the signal of underground detonators according to the individual frequencies of the recorded signal, the loss of which from the spectrum indicates the successful activation of the charge [8]. • Channel with retransmission of the signal of the explosive machine between detonators under the surface of the earth [19]. • Channel for blasting operations in underground mines, working with a magnetic loop as a radiating antenna, stretched through a closed tunnel located above the place of charge activation [6,9,11].
Also known are works in the field of wireless data transmission through rocks for the purpose of general notification of mine personnel, based on long-length radiating antennas located on the surface of the earth or in an underground tunnel, and grounded to the metal structure of the mine. This method of low-frequency communication allows you to provide a large coverage area of the radio channel [20][21][22][23].
All presented methods and technologies are not intended for seismic exploration and do not meet the requirements for quality indicators, such as time deviation accuracy. In addition, when operating at low frequencies of 1-8 kHz, the channel has redundancy in the depth of penetration of the EM field into the conductive medium, which is an advantage when working in mines, but is not suitable for shallow ground boreholes with low electrical conductivity compared to ore minerals. negatively affecting the EM field.
Magnetic loop transmitting antennas are not optimal for activating long line profiles for seismic surveys involving multiple wells. The method of radiation using a long-length electric dipole grounded in the ground, which is actively used for electrical exploration of polymetallic ore deposits near the earth's surface, seems to be more suitable for this purpose. The article investigates the energy potential of transmitting a useful signal through layered media using a grounded dipole, and substantiates the optimal frequency range. The study was carried out taking into account the electrodynamic properties of soils. A comparative analysis of the direct solution of the electrodynamic problem and computational modeling by the finite element method is also implemented.

Material and methods
It is customary to determine the properties of soil as a current conductor by its specific electrical resistance ρ, or the reciprocal value -electrical conductivity σ. The value of the resistivity ρ depends on the type of soil, moisture content, the content of alkalis, salts and acids, and temperature. Also, this parameter is influenced by the properties of natural solutions that fill pores and cracks. For example, natural waters, depending on the salts dissolved in them, have a resistance of 0.07-600 Ω•m.
An increase in the content of dissolved substances in the soil, total moisture content, compaction of its particles, and an increase in temperature (at constant moisture content) lead to a decrease in ρ. Soil impregnation with oils and oil, as well as freezing, significantly increase the resistivity index. Because analytical calculation of the factors influencing ρ is an extremely difficult task; obtaining soil parameters remains the result of direct measurements. For the task of assessing the absorbing properties of the medium, it is necessary to estimate the value of the resistivity ρ (Ω•m), according to reference data.
From these data it can be deduced that the bulk of the soils that make up the surface layer have a specific resistance ρ of 1500-10 Ω•m and a dielectric constant ε 10-30. It should be noted that the most extensive part of the surface salt has a resistance of 500-100 Ω•m, lower values of this parameter are rare, in the presence of water layers with high salinity, which can occur in the area of wet salt layers, but for most environments, typical such a low total resistivity of rocks is unusual for seismic surveys [23,24].
Based on considerations of the practical application of the BDZ technology, the most expedient is dipole profiling with a radiating antenna size of the order of several hundred meters, which provides a sufficient penetration depth when operating at higher frequencies and is the optimal length for activating a linear group of borehole detonators. Structurally, it consists of two long cable lines connected to the transmitter, stretched along the surface of the earth and connected to galvanically grounded electrodes. The electromagnetic field of a long line is formed under the influence of three factors [25]: • galvanic spreading currents between grounding; • capacitive currents of the wire line; • induction currents excited in the ground by the magnetic field of the antenna.
Thus, the resulting electromagnetic field is formed with the participation of currents flowing both in the cable forming the dipole antenna (first component) and in the ground layers above (second component) and below the observation point (third component), which creates a complex structure of the formation of the electromagnetic field ... To calculate currents and fields, in this case, it is necessary to divide the calculated conducting area into equivalent conductors Δz, through which elementary spreading currents flow. The spreading current density in the Cartesian coordinate system has three components jx, jy, jz. Let us analyze a two-dimensional problem in the XZ plane [26]: where Iis current in the cable.
The current element is determined based on the cross-section of the equivalent conductor Δz, into which the computational domain is divided and the current density in this area [26].
where d is the cross-sectional diameter of the equivalent conductor. The magnetic field of the current element is determined according to the Bio-Savart law [26]: unit vector of radius vector ri; ridistance from current element to point М; listream line; k՛the absorption coefficient of the EM field in the rock at the frequency f.
The field of the ground-based current dipole H0 is determined according to a different principle (figure 1). A dipole of length dl and connected to an alternating current source is directed along an arbitrary unit vector d . The dipole supplies alternating harmonic current I=I0e -iωt , with known electrodynamic parameters of the medium σ, μ, ε. It is necessary to find the value of the field components E and H at any point in space [24]. In the case when the dipole source is directed along the x axis, with a dipole moment p, the field components are calculated using the expressions [24]: where sin(θ)=y/r; ) ( 2 2 1 r k o contribution of members with a degree higher (k1r) 2 . Using analytical expressions (6,7), the calculation of the strength of the component of the magnetic field Hz and the corresponding voltage on the receiver with a ferrite antenna with an effective area of 1 m 2 was realized. The analysis was carried out for the range of electrical conductivity of the medium σ=1E-4-1E-1 сm/m when emitted by a magnetic and electric dipole without grounding into the ground, and also without taking into account the parameters of radiation efficiency and antenna matching, except for the dipole moment as the main parameter linking the antenna current and its electromagnetic fields.
For reception in a ground borehole, it is advisable to use a compact ferrite antenna designed to register a magnetic field [27]: Where With an electrical conductivity of 1E-2 cm/m, the field strength decreases with increasing frequency to 100 kHz, but the decrease in this parameter is 2.4 times. In this case, the voltage at the receiver rises to a frequency of 40 kHz and stably remains at the same level in the investigated frequency range. With an electrical conductivity of 1E-1 cm/m, the level of the magnetic field decreases by 3 orders of magnitude with increasing frequency. Such parameters of the environment give a maximum voltage at a frequency of 7 kHz, above which this characteristic decreases 22 times at a frequency of 100 kHz. Analysis of the attenuation of the EM field in a homogeneous environment indicates the possibility of using higher frequencies up to 60 kHz for the most difficult cases and up to 100 kHz for driest soils. The need to evaluate the joint propagation and mutual influence of the electric dipole fields and elementary spreading currents in the soil makes the calculation using classical methods a multistage and technically difficult task, due to the need to divide the section of the conducting half-space into many elementary conductors for currents. In addition, this method does not allow assessing the distribution of magnetic fields in space with a sufficiently high accuracy. Solving the problem of the propagation of currents and electromagnetic fields in layered media, typical of surface soils, introduces additional restrictions into the calculation, which complicates the analysis of the interaction of currents and electromagnetic fields in media with many boundaries and different parameters.
For numerical estimates of the propagation of a magnetic field in a layered medium, computational modeling was carried out using the finite element method, which consists in splitting the computational three-dimensional model. In this case, the solution of the differential equations is given, occurs at the nodes of the elements, n which the model is broken down. In each element, an approximating function is additionally applied, the coefficients of which are selected from taking into account the numerical solutions of equations in neighboring elements. The accuracy of the numerical solution of a physical The dipole is located in the air above a conductive half-space, imitating a geological section with a known layered structure, numbering 4 layers at the required depth of study of 30 m (figure 3 c). The calculation was carried out for three cases: dry soil (model 1); the top layer of sand moistened by rainwater (model 2); bottom layer of crushed stone moistened with groundwater (model 3). Layer parameters for computational models are shown in table 1.

Results
When simulating the propagation of the field of a grounded dipole in a layered medium, a calculation was carried out in models of soil media similar in geometric parameters and the parameters of the magnetic field strength at a depth of 30 m were obtained. The most favorable for the propagation of an EM field is model 1, which contains only dry soils. In this case, an 8-fold increase in the magnetic field level is noted with an increase in frequency to 100 kHz, similarly, the voltage at the receiver increases. For model 2, which is characterized by the presence of two moist layers on the surface, the absorbing properties of the medium increase ( figure 4). So, this model is the most difficult case of propagation of EM fields due to the shielding properties of the upper layer, however, with increasing frequency, the magnetic field strength also increases by 2 orders of magnitude when comparing 1 and 100 kHz. The most controversial case is presented by model 3 with the presence of groundwater in the lower layers in the presence of dry sand on the surface. The magnetic field strength for this case reaches its maximum at a frequency of 50-70 kHz, when this range is exceeded, a tendency to a drop in the field strength is noticeable ( figure 4).

Conclusion
The emitting antenna in the form of a horizontal electric dipole is the most optimized for activating a linear array of detonators widely used in seismic exploration. Analysis of the distribution of magnetic fields in the models shows the inhomogeneity of the distribution of fields and currents in layered media, as well as the different nature of the frequency characteristics. Modeling, in combination with calculated estimates, allows us to conclude that the most favorable frequency range for most surface soils under conditions of high humidity is the 40-80 kHz band. Modeling shows the predominance of the horizontal component of the magnetic field Hy, orthogonal to the antenna position. Based on these data, it is recommended to use compact ferrite antennas for signal reception from the surface, located horizontally and orthogonally to each other to receive the dominant field component.