Computer-implemented contact-free method for measuring the attenuation coefficient of electromagnetic waves and a device for measuring the attenuation coefficient of electromagnetic waves in the substrate

Abstract

A computer-implemented contact-free spectral method for measuring the attenuation coefficient of electromagnetic waves in substrates, adapted for use with an FMCW ground-penetrating radar (GPR) producing a continuous frequency-modulated sinusoidal signal, directed to a transmitting antenna (2) producing beams of coherent electromagnetic waves which, after being reflected from substrate structures, are received by a receiving antenna (3), including the following consecutive steps: a signal (111) transmitted from an FMCW generator (5) and a signal (131) received from the output of the receiving antenna (3) are digitised (200); power spectra of the transmitted signal's digital form (112) and the received signal's digital form (132) are determined (201); the quotient (152) of the received signal's power spectrum (142) by the transmitted signal's power spectrum (122) is determined (202); with the use of a geophysical calculation block (17), an auxiliary signal (172) is determined (203) according to the formula (2), where Gt (f) - energy gain of the transmitting antenna TX, Gr (f) - energy gain of the receiving antenna RX, ϵr(r,f) - relative dielectric permeability of the tested substrate, Σ(r,f) - active cross-section describing the reflection of waves to the receiving antenna, µr(r,f) - relative magnetic permeability of the tested substrate; subsequently, based on the quotient of the power spectra (141,122) and the auxiliary signal (172), the depth of penetration (162) of the wave field into the substrate is determined (204) according to the formula (3), the inverse of which represents the attenuation coefficient of the wave in the substrate as a function of frequency A device (1) for measuring the attenuation coefficient of electromagnetic waves in the substrate, adapted for cooperation with an FMCW GPR, comprising: a transmitted signal A / D converter (11), a received signal A / D converter (13), and further comprising: a transmitted signal power spectrum determination module (12), a received signal power spectrum determination module (14), a power spectra quotient calculation block (15), a depth of penetration of the wave field into the substrate determination module (16), a geophysical calculation block (17), where the functions of the modules (12,14,16) and blocks (15) and (17) are implemented using a computer system comprising at least a microprocessor, a volatile memory, a non-volatile memory, which are connected on a common data bus, and the device is adapted to implement the method.

Description

[0001] Computer-implemented contact-free method for measuring the attenuation coefficient of electromagnetic waves and a device for measuring the attenuation coefficient of electromagnetic waves in the substrate

[0002] Field of the Invention

[0003]

[0001] An object of the invention is a non-contact spectral method for measuring the attenuation coefficient of electromagnetic waves in the substrate (ground). The method is adapted to be implemented using electromagnetic waves transmitted and received by a ground-penetrating radar (GPR) operating based on FMCW modulation.

[0004] Description of the State of the Art

[0005]

[0002] The dominant factor in wave attenuation in homogeneous substrates is the presence of electrical conductivity, characterised by the specific conductivity coefficient of the substrate material.

[0006]

[0003] A number of methods are used in geophysics to measure the specific conductivity of the substrate. The most popular of these include vertical electrical sounding (VES) and electrical resistivity tomography (ERT). The basis of the said electrical resistivity measurement methods is the application of an electric current of known intensity between current electrodes driven into the ground and the measurement of potential differences occurring at the ground surface by means of potential electrodes. Low-frequency direct current (DC) or alternating current (AC) sources are used for this purpose.

[0007]

[0004] The transient geo-electromagnetics method is also used for this purpose. The measurement system consists of two coils: a transmitting one and a receiving one. The transmitting coil generates an alternating magnetic field that produces induction currents in the medium. The receiver coil records the magnitude of the induced secondary magnetic field and the amplitude and phase relationships between the primary and secondary fields. The secondary magnetic field is determined by the electrical conductivity of the medium.

[0008]

[0005] Both the electrode method and the magnetic method record data within a limited area, with a fixed measurement step along a fixed profile grid. The distance between measurement points is determined by the expected size of the measured areas and the assumed resolution capacity of the measurement. The readings are then processed using specialised 2D and 3D software.

[0009]

[0006] The disadvantage of electrical resistivity methods is the need to physically drive the electrodes, which is inconvenient and labour-intensive. Electromagnetic methods are non-contact and therefore faster. Hence, there is a need to develop new methods for measuring the attenuation coefficient of electromagnetic waves in the substrate (ground) that are contact-free in nature.

[0010] Summary

[0011]

[0007] The essence of the invention is a computer-implemented contact-free spectral method for measuring the attenuation coefficient of electromagnetic waves in substrates, adapted for use with an FMCW GPR producing a continuous frequency-modulated sinusoidal signal, directed to a transmitting antenna producing beams of coherent electromagnetic waves which, after being reflected from substrate structures, are received by a receiving antenna, and which allows 2D or 2D / 3D mapping of the attenuation coefficient of EM waves in the substrate by recording data from the GPR along passes according to a predetermined measurement grid.

[0012]

[0008] The method includes the following consecutive steps: a signal transmitted from an FMCW generator and a signal received from the output of the receiving antenna are digitised and then power spectra of the transmitted signal's digital form and the received signal's digital form are determined. Further, the quotient of the received signal's power spectrum by the transmitted signal's power spectrum is determined. Then, with the use of a geophysical calculation block, an auxiliary signal is determined according to the formula X172(f, r) = 4n)~3c2£rfir)~1GtGrf~2r~4S f, r , where Gt (f) - energy gain of the transmitting antenna TX , Gr (f) - energy gain of the receiving antenna RX, er(r,f) - relative dielectric permeability of the tested substrate, Z(r,f) - active crosssection describing the reflection of waves to the receiving antenna, pr(r,f) - relative magnetic permeability of the tested substrate. Subsequently, based on the quotient of the power spectra and the auxiliary signal, the depth of penetration of the wave field into the substrate is determined according to the formula Xi62 the inverse of which represents the attenuation coefficient of the wave in the substrate.

[0013]

[0009] Such a measurement allows for fast monitoring of attenuation as a function of substrate frequency while simultaneously carrying out GPR surveys. These measurements can be carried out using low-altitude flying platforms such as drones, which is impossible with other known methods.

[0014]

[0010] Another object of the invention is a computer-based contact-free method for 2D or 2D / 3D mapping of the substrate's resistivity. The method includes the following consecutive steps: based on the depth of penetration of the wave field into the substrate determined by the contact-free method for measuring the attenuation coefficient of electromagnetic waves according to the invention, the specific conductivity of the substrate material given by the formula X181(f, r) = l / nn0nrfXl62(J, r) and the resistivity which is the inverse thereof are determined. The signals from the previous step correlated with the geographic coordinates of the GPR pass (x,y,z) are then visualised, creating a map of the specific conductivity of the terrain in the given GPR sounding depth range (rmin, r max) .

[0015]

[0011] The measurement allows for fast monitoring of the substrate's resistivity as a function of frequency while simultaneously carrying out GPR surveys, with the possibility of using low-altitude flying platforms such as drones for this purpose, which is impossible with other known methods.

[0016]

[0012] Preferably, in the contact-free method for 2D / 3D mapping of the substrate's resistivity, the depth of penetration of the wave field into the substrate is additionally verified using the formula162( ,r)-2= a(r) / , where a( r ) is a constant for a given penetration depth r.

[0017]

[0013] Another object of the invention is a device for measuring the attenuation coefficient of electromagnetic waves in the substrate as a function of frequency, adapted for cooperation with the FMCW radar, comprising: a transmitted signal A / D converter, a received signal A / D converter, and further comprising a transmitted signal power spectrum determination module, a received signal power spectrum determination module, a power spectra quotient calculation module, a depth of penetration of the electromagnetic wave field into the substrate determination module, a geophysical calculation block. The functions of the modules and blocks are realised with the use of a computer system comprising at least a microprocessor, a volatile memory, a non-volatile memory, which are connected on a common data bus, and the device is adapted to implement the method for measuring the attenuation coefficient of electromagnetic waves in substrates according to the invention.

[0018]

[0014] The device's design can cooperate with the FMCW radar and is a natural extension of it, not interfering with its basic functions. It allows for simultaneous measurement of attenuation coefficients as a function of frequency and mapping of the substrate's geological parameters. The device for the spectral measurement of the attenuation coefficient of electromagnetic waves in the substrate uses relationships characterising the propagation of EM waves in the substrate based on which the attenuation coefficient based on coherent detection is inferred.

[0019]

[0015] The invention further relates to a device for 2D / 3D mapping of the substrate's resistivity, comprising a device for measuring the attenuation of electromagnetic waves in the substrate according to the invention. The device for 2D / 3D mapping of the substrate's resistivity, additionally comprises a specific conductivity calculation module and a visualisation module, and is adapted to realise the method for 2D / 3D mapping of the substrate's resistivity.

[0020]

[0016] Preferably, the device according to the invention further comprises a verifier system and is adapted to implement a preferable version of the method for 2D / 3D mapping of the substrate's resistivity according to the invention.

[0021]

[0017] The invention also comprises a system comprising any of the devices according to the invention and an FMCW GPR.

[0022]

[0018] Preferably, the system according to the invention comprises a GPR, a first mixer, a second mixer and a heterodyne generator, all configured in such a way that they reduce the frequency of the input signals supplied to the device according to the invention.

[0023]

[0019] Another object of the invention is a map of the specific conductivity of the substrate layers, generated by means of the method for 2D / 3D mapping of the substrate's resistivity according to the invention.

[0024]

[0020] The invention also relates to a computer program comprising program code means for performing all steps of the computer-implemented methods according to the invention, when said program is run on the computer.

[0021] Another object of the invention is a computer-readable medium storing computer-implemented instructions performing all steps of the computer- implemented methods according to the invention performed on the computer.

[0025] Description of the Drawing Figures

[0026]

[0022] The objects of the invention are presented in embodiments in the drawing, in which:

[0027]

[0023] Fig. 1 shows a block diagram of a device for measuring the attenuation coefficient of electromagnetic waves in the substrate;

[0028]

[0024] Fig. 2 shows a device for 2D / 3D mapping of the substrate's resistivity;

[0029]

[0025] Fig. 3 shows a device for 2D / 3D mapping of the substrate's resistivity, equipped with a verifier system;

[0030]

[0026] Fig. 4 shows a system using the device for 2D / 3D mapping of the substrate's resistivity and an FMCW GPR;

[0031]

[0027] Fig. 5 shows a system using the device for 2D / 3D mapping of the substrate's resistivity and the FMCW GPR, with the use of frequency reduction of the input signals supplied to the mapping device;

[0032]

[0028] Fig. 6 shows a system using the device for 2D / 3D mapping of the substrate's resistivity and the FMCW GPR in a homodyne configuration;

[0033]

[0029] Fig. 7 shows a diagram of a method for measuring the attenuation coefficient of electromagnetic waves in the substrate;

[0034]

[0030] Fig. 8 shows a diagram of a method for 2D / 3D mapping of the substrate's resistivity;

[0035]

[0031] Fig. 9 shows an example of a 2D cross-section of the substrate attenuation coefficient obtained based on the method according to the invention using the FMCW GPR. The visible anomaly in the attenuation coefficient is related to a geological fault. Vertical scale 40 m, horizontal scale 220 m.

[0036] Notation and nomenclature

[0037]

[0032] Some parts of the detailed description that follows are presented within procedures, data processing steps or other symbolic representations of operations on bit data that can be performed in computer memory. Therefore, the logical steps are performed by the computer, which requires physical manipulation of physical quantities. Typically, these quantities take the form of electrical or magnetic signals, suitable for storing, transmitting, combining, comparing or other ways of data manipulation in the computer system. Due to its widespread use, these data are referred to as signals, time waveforms, bits, packets, messages, values, elements, symbols, characters, terms, numbers and the like. In addition, all of these terms, or similar ones, should be identified with the corresponding physical quantities, and are merely convenient terms for these physical quantities. Terms such as "processing" or "creating", or "transmitting", or "performing", or "determining", or "detecting", or "receiving", or "selecting", or "calculating", or "generating", or the like, refer to the activities and processes of the computer system that manipulates and transforms data represented as physical (electronic) quantities in computer registers and memories into other data similarly represented as physical quantities in memories or registers or other information stores. A computer-readable medium (memory), as defined herein, may typically be non-volatile and / or contain a nonvolatile device. In this context, a non-volatile storage medium may contain a device that can be tangible, meaning that the device has a specific physical form, although the device may change its physical state. Thus, by way of example, the term non-volatile refers to a device that remains tangible, although it changes its state.

[0038] Example 1 - method for measuring the attenuation coefficient of electromagnetic waves in the substrate

[0039]

[0033] The method for measuring the attenuation coefficient of electromagnetic waves in the substrate according to the invention is illustrated schematically in Fig. 7. It is performed with the use of a device 1 for measuring the attenuation coefficient of electromagnetic waves in the substrate. To the input of the device 1 for measuring the attenuation coefficient of electromagnetic waves, shown in Fig.

[0040] 1 , a signal 1 11 from a GPR FMCW generator and a signal 131 from the output of a GPR receiving antenna 3 are fed. It is assumed that the power gain characteristics as a function of the frequency of the GPR receiving path are known. The signal 1 1 1 is converted by a transmitted signal A / D converter 1 1 into an FMCW generator signal digital form 1 12. Identically, the signal 131 is converted into a digital form by a received signal A / D converter 13. The signal 112 from the output of the converter 11 is routed to a transmitted signal power spectrum module 12, which calculates its power spectrum 122.

[0041]

[0034] All the modules and blocks performing the calculations mentioned in this and further embodiments are implemented by means of a computer system comprising at least a microprocessor, a volatile memory, a non-volatile memory, which are connected on a common data bus.

[0042]

[0035] A signal 132 from the output of the converter 13 is routed to a received signal power spectrum module 14, which calculates the power spectrum 142 received by the receiving antenna 3. The signals 122 and 142 are then routed to a power spectra quotient calculation block 15, which produces the power spectra quotient 152 according to the formula

[0043]

[0036]

[0044]

[0037] The power spectra quotient 152 from the output of the block 15 is routed to the depth of penetration of the wave field into the substrate module 16, to which an auxiliary signal 172 generated in a geophysical calculation block 17 is also routed, and given by the formula:

[0045]

[0038]

[0046]

[0039] The following parameters are set for the calculations in the geophysical calculation block 17:

[0047]

[0040] a = Gt ( / ) - energy gain of the transmitting antenna TX

[0048]

[0041] b = Gr ( / ) - energy gain of the receiving antenna RX

[0049]

[0042] c = er(r, - relative dielectric permeability of the tested substrate

[0050]

[0043] d = Z(r, / ) - active cross-section describing the reflection of waves to the receiving antenna

[0051]

[0044] e = \ir(r,f) - relative magnetic permeability of the tested substrate

[0052]

[0045] The auxiliary signal 172 is calculated over the entire range of frequency variations f, covering the range of FM modulation used in the GPR and the variable sounding depth r. The sounding depth r is calculated based on the measurement of the time course of the reflected electromagnetic wave propagating back and forth in the substrate and the velocity of electromagnetic waves in the substrate. It requires the use of substrate parameters: relative dielectric permeability srand relative magnetic permeability / / ,..

[0053]

[0046] In addition, an active cross-section distribution function is introduced which describes the active cross-section of wave reflection in the substrate E(f,r) as a function of frequency and depth r. The active cross-section distribution function E(f,r) is determined based on the analysis of the GPR echoes.

[0054]

[0047] Subsequently, in the depth of penetration of the wave field into the substrate module 16, the following transformation is made:

[0055]

[0049] The inverse of the X162 signal is the attenuation coefficient of the wave in the substrate.

[0056] Example 2 - method for 2D / 3D mapping of the substrate's resistivity

[0057]

[0050] The method for 2D / 3D mapping of the substrate's resistivity is illustrated schematically in Fig. 8. The method is implemented using the device 1A illustrated in Fig. 2.

[0058]

[0051] In the initial phase, the steps of the method for measuring the attenuation coefficient of electromagnetic waves in the substrate that are identical to those in Example 1 are performed.

[0059]

[0052] A penetration depth signal 162 is then converted in a specific conductivity calculation module 18 into signals 181 representing the specific conductivity and 182 representing the resistivity according to the formulas

[0060]

[0053] X181( / , r) = l / Ttp0prfXl62f, r) (4)

[0061]

[0054] X182( / , r) = l / X181( / ,r) . (5)

[0062]

[0055] The signals 181 and 120

[0182] are then routed to a visualisation block. The topographical coordinates of the GPR pass (x,y,z) also go to the visualisation block. The visualisation block, based on the signals 181 and 182, plots the EM wave attenuation profile and the electrical resistivity profile on the terrain map within the set GPR sounding depth range (rmin, rmax).

[0063]

[0056] The profile of resistivity as a function of frequency will be correctly reproduced when there are no other factors leading to attenuation of the electromagnetic wave, such as scatter attenuation.

[0064]

[0057] Based on the attenuation coefficient of the electromagnetic wave, the depth of penetration of the electromagnetic field in the substrate is determined, and on this basis the resistivity (or specific conductivity) of the substrate material is determined.

[0065]

[0058] Based on the same signals, the calculation of resistivity in layers of specified thickness Ar, within a given GPR sounding depth range (rm / n, rmax), can also be carried out.

[0066] Example 3 - numerical representation of a typical measurement of the substrate's resistivity

[0067]

[0059] An SGPR-H4 GPR was used with an FM modulation range of 300 to 1200 MHz. The calculation for a single frequency equal to half the maximum frequency will be carried out. The GPR with power delivered to the transmitting antenna X106 = 1 W measured a received power of X11= 1 .07 10-15 W.

[0068]

[0060] The resistivity of the ground at a depth of r = 10 m is calculated.

[0069]

[0061] Data: f= 600 MHz.

[0070] G = 10 (10 dBi)

[0071] £r= 4

[0072] Pr = 1 po = 1.257 * 10’6r= 10 m

[0073] Z(f,r) = 1 m2

[0074] X142= 1.07 * 10’15W

[0075] X122= 1 .00 W

[0076]

[0062] Calculations:

[0077]

[0063] The above example applies to a single measurement frequency and, when using our method, the resistivity is calculated for the entire tuning range of the FMCW GPR used.

[0078] Example 4 - complementing the method for 2D / 3D mapping of the substrate's resistivity with verification

[0079]

[0064] In the initial phase, the steps of the method for 2D / 3D mapping of the substrate's resistivity as in Example 2 are performed.

[0080]

[0065] Fig. 3 illustrates a device for 2D / 3D mapping of the substrate's resistivity. This device comprises a verifier system 117. The verifier checks the frequency dependence of the signal 162. The dependence is given by the formula:

[0081]

[0066]

[0082]

[0067] where a(r) is a constant for each penetration depth r. Deviations from this dependence can be used to assess the correctness of the determination of the specific conductivity / resistivity distribution as a function of sounding depth and the method's reach limit. The verification information is output as a verification signal 192.

[0083] Embodiments of systems with devices according to the invention

[0084] Embodiment 5

[0085]

[0068] Fig. 4 illustrates a system comprising a device 1 A for 2D / 3D mapping of the substrate's resistivity, referred to simply as a resistivity meter, and an FMCW GPR.

[0069] The resistivity meter is incorporated into the output and input paths of the FMCW GPR. The FMCW GPR is equipped with a frequency-modulated FM generator 4, a transmitting antenna 2 and a receiving antenna 3. The dependence between the signals 111 and 131 occurring at the terminals of the antennas 2 and 3 is described by the transmittance function of the 4th GPR channel h (r,f). It is assumed that the transmitting and receiving antennas have known energy gains in the GPR operating frequency range. The transmitting TX track and the receiving RX track are typical GPR tracks and the frequency and amplitude characteristics of these tracks are fully known, allowing the transmitted and received power to be measured in absolute units.

[0086] Embodiment 6

[0087]

[0070] System as in Embodiment 5, except that instead of the device 1 A for 2D / 3D mapping of the substrate's resistivity, the system includes a device 1 for measuring the attenuation coefficient of electromagnetic waves in the substrate.

[0088] Embodiment 7

[0089]

[0071] Fig. 5 illustrates a system comprising a device 1A for 2D / 3D mapping of the substrate's resistivity, referred to simply as a resistivity meter, and an FMCW GPR using frequency mixing systems for the transmitted signal by means of a first mixer 6 and for the received signal (echo) by means of a second mixer 7. The mixers 6 and 7 are supplied with a signal from a heterodyne signal generator 8. Signals 111 A and 131 A, which are the result of mixing, are produced to reduce the frequency of the signals directed to the resistivity meter. This allows for easier processing of the signal reaching the resistivity meter.

[0090] Embodiment 8

[0091]

[0072] System as in Embodiment 7, except that instead of the device 1 A for 2D / 3D mapping of the substrate's resistivity, the system includes a device 1 for measuring the attenuation coefficient of electromagnetic waves in the substrate. Embodiment 9

[0092]

[0073] Fig. 6 illustrates a system comprising a device 1 A for 2D / 3D mapping of the substrate's resistivity, referred to simply as a resistivity meter, and an FMCW GPR with a homodyne system. A transmitting FMCW generator 5 is connected via a transmitting antenna delay line 21 to a transmitting antenna 2 and the input of a second mixer 7 acting as a homodyne mixer. A receiving antenna 3 is connected via a receiving antenna delay line 24 to the second input of the second mixer 7. A differential signal from the output of the second mixer is fed to a low-pass filter 25. An output signal 131 L of the filter 24 representing the echo signal is fed into one of the inputs of the resistivity meter 1 A. A second transmitting reference signal 111 L transmitted to the resistivity meter 1 A is produced by a first mixer 6. The first input of the first mixer 6 is connected directly to the output of the FMCW generator 5 of the transmitted signal. The signal from the first input is routed to the second input of the mixer after passing through a generator signal delay line 22. The output of the first mixer 6 is, via a transmitting-part low-pass filter 23, incorporated into the input of the resistivity meter 1 A.

[0093] Embodiment 10

[0094]

[0074] System as in Embodiment 9, except that instead of the device 1 A for 2D / 3D mapping of the substrate's resistivity, the system includes a device 1 for measuring the attenuation coefficient of electromagnetic waves in the substrate.

[0095] Other Embodiments of systems with devices according to the invention

[0075] In each of Embodiments 5 to 10, the transmitting antenna 2 and the receiving antenna 3 may be replaced by a single antenna to which the transmitting signal 111 and the receiving signal 131 are applied via a circulator / directional coupler.

[0096]

[0076] List of references

[0097] 1 - device for measuring the attenuation coefficient of electromagnetic waves in the substrate;

[0098] 1 A - device for 2D / 3D mapping of the substrate's resistivity

[0099] 2 - transmitting antenna;

[0100] 3 - receiving antenna; - transmittance of the GPR system; - FMCW generator; - first mixer; - second mixer; - heterodyne signal generator; - transmitted signal A / D converter; - transmitted signal power spectrum module; - received signal A / D converter; - received signal power spectrum module; - power spectra quotient calculation block; - depth of penetration of the wave field into the substrate module; - geophysical calculation block; - specific conductivity calculation module; - verifier system; 20 - visualisation module; - transmitting antenna delay line; - generator signal delay line; - transmitting-part low-pass filter; - receiving antenna delay line; - receiving-part low-pass filter; 1 - signal from the FMCW generator; 1 A - signal from the FMCW generator shifted to a lower frequency band; 1 L - FMCW signal after homodyne system transformations; 2 - digital form of the signal from the FMCW generator; 2 - transmitted signal's power spectrum; 1 - received signal; 1 A - received signal shifted to a lower frequency band; 1 L - received signal after homodyne system transformations; 2 - received signal's digital form; 2 - received signal's power spectrum; 2 - power spectra quotient; 172 - auxiliary signal; 2 - penetration depth; a - Gt (f) - energy gain of the transmitting antenna TX; b - Gr (f) - energy gain of the receiving antenna RX; c - er(r,f) - relative dielectric permeability of the tested substrate; 17d - Z(r,f) - active cross-section describing the reflection of waves to the receiving antenna;

[0101] 17e - pr(r,f) - relative magnetic permeability of the tested substrate;

[0102] 181 - specific conductivity; 182 - inverse of the specific conductivity;

[0103] 192 - verification result signal;

Claims

CLAIMS1 . A computer-implemented contact-free spectral method for measuring the attenuation coefficient of electromagnetic waves in substrates, adapted for use with an FMCW ground-penetrating radar (GPR) producing a continuous frequency- modulated sinusoidal signal, directed to a transmitting antenna (2) producing beams of coherent electromagnetic waves which, after being reflected from substrate structures, are received by a receiving antenna (3), characterised in that it comprises the following consecutive steps:— a signal (1 1 1 ) transmitted from an FMCW generator (5) and a signal (131 ) received from the output of the receiving antenna (3) are digitised (200);— power spectra of the transmitted signal's digital form (1 12) and the received signal's digital form (132) are determined (201 );— the quotient (152) of the received signal's power spectrum (142) by the transmitted signal's power spectrum (122) is determined (202);— with the use of a geophysical calculation block (17), an auxiliary signal (172) is determined (203) according to the formula X172( / ,r) =energy gain of the transmitting antenna TX , Gr (f) - energy gain of the receiving antenna RX, er(r,f) - relative dielectric permeability of the tested substrate, Z(r,f) - active crosssection describing the reflection of waves to the receiving antenna, pr(r,f) - relative magnetic permeability of the tested substrate;— Subsequently, based on the quotient of the power spectra (141 ,122) and the auxiliary signal (172), the depth of penetration (162) of the wave field into the substrate is determined (204) according to the formula X162(f, r) = the inverse of which represents the attenuation coefficient ofthe wave in the substrate as a function of frequency. A computer-implemented contact-free method for 2D / 3D mapping of the substrate's resistivity as a function of frequency, characterised in that it includes the following consecutive steps:— based on the depth of penetration (162) of the wave field into the substrate, determined by the method according to claim 1 , the specific conductivity (181 )of the substrate material given by the formula X181(f,r) = l / -n:fi0firfX62(f,r) and the resistivity (182) which is the inverse thereof are determined (205).— the signals from the previous step correlated with the geographic coordinates of the GPR pass (x,y,z) are visualised (206), creating a map of the specific conductivity of the terrain in the given GPR sounding depth range (rmin, rmax) and frequency range. The method according to claim 2, characterised in that the depth of penetration (162) of the wave field into the substrate is additionally verified using the formula Xi62 ( / , r)-2= a(r) / , where a( r ) is a constant for a given penetration depth r. A device (1 ) for measuring the attenuation coefficient of electromagnetic waves in the substrate as a function of frequency, adapted for cooperation with an FMCW GPR, comprising:— a transmitted signal A / D converter (11 ),— a received signal A / D converter (13), and further comprising:— a transmitted signal power spectrum determination module (12),— a received signal power spectrum determination module (14),— a power spectra quotient calculation block (15),— a depth of penetration of the wave field into the substrate determination module (16),— a geophysical calculation block (17), where the functions of the modules (12,14,16) and blocks (15) and (17) are implemented using a computer system comprising at least a microprocessor, a volatile memory, a non-volatile memory, which are connected on a common data bus, and the device is adapted to implement the method according to claim 1 .

5. A device (1 A) for 2D / 3D mapping of the substrate's resistivity as a function of frequency, comprising the device (1 ) according to claim 4, characterised in that it further comprises:— a specific conductivity calculation module (18),— a visualisation module (20) and is adapted to implement the method according to claim 2.

6. The device according to claim 5, further comprising a verifier system (19), adapted to implement the method according to claim 3.

7. The system comprising:— the device (1 ,1 A) according to any of claims 4 to 6,— an FMCW GPR.

8. The system according to claim 11 , wherein the FMCW GPR further comprises:— a first mixer (7),— a second mixer (8),— and a heterodyne generator (9), which are configured to reduce the frequency of the input signals delivered to the device (1 , 1 A).

9. A map of the specific conductivity of the substrate layers, generated using the method according to claim 2 or 3.

10. A computer program comprising program code means for performing all steps of the computer-implemented method according to claims 1 do 3, when said program is run on the computer.11 . A computer-readable medium storing computer-implemented instructions executing all steps of the computer-implemented method according to any one of claims 1 or 3 performed on the computer.

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