Method for determining optimal frequency of ground penetrating radar for detecting frozen soil

Abstract

The invention discloses a method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil, which relates to the technical field of frozen soil exploration and comprises the following steps: determining the type of frozen soil based on geological data, and acquiring a shallow soil dielectric constant by using a time-domain reflectometer; the low-frequency ground penetrating radar detects the contour and position of frozen soil; establishing a frozen soil simulation model by combining dielectric constants, and performing multi-frequency scanning to obtain a radar image; processing the image through Hilbert-Huang transform, drawing an instantaneous frequency-time curve, and calculating three groups of errors; according to the method provided by the invention, the signal-to-noise ratio of the ground penetrating radar during frozen soil detection is enhanced, the influence of clutters on frozen soil reflection waves is reduced, and the underground frozen soil range is clearly displayed in a radar image.

Description

Technical Field

[0001] The present invention belongs to the technical field of frozen soil exploration, and particularly relates to a method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil. Background Art

[0002] In recent years, with global warming and due to human activities such as deforestation, permafrost is prone to degradation. The degradation of permafrost will bring about many engineering problems when infrastructure is constructed in permafrost regions. Therefore, when constructing in areas containing permafrost, it is necessary to accurately determine the spatio-temporal distribution of the permafrost layer. The ground penetrating radar emits high-frequency electromagnetic waves underground and then receives the echo signals to generate a ground radar (General Purpose Radar, GPR) image. According to the image results, the specific situation of the detection target is judged, and the shape of the underground permafrost is displayed in the radar image, thereby realizing the efficient and non-destructive detection of underground permafrost. However, ground penetrating radars with different antenna frequencies have different sensitivities to underground permafrost. Since the antenna frequency of the ground penetrating radar suitable for permafrost detection is low, the low resolution results in unclear radar detection of permafrost. At the same time, due to the attenuation effect of deep electromagnetic waves and the influence of surrounding clutter, the horizon line of the permafrost interface is unclear or is easily affected by clutter and cannot be seen. The depth ranges of underground permafrost in different regions also vary, which results in that a ground penetrating radar with a single fixed antenna frequency does not have a high signal-to-noise ratio. Therefore, there is an urgent need for a method for determining the antenna frequency of a ground penetrating radar for permafrost detection, which can enhance the signal-to-noise ratio of the ground penetrating radar when detecting permafrost, reduce the influence of clutter on the reflected wave of permafrost, and clearly display the range of underground permafrost in the radar image. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil, which makes up for the technical problems in the prior art that a ground penetrating radar with a single fixed antenna frequency has a low signal-to-noise ratio and the horizon line of the permafrost interface is unclear.

[0004] The technical solution adopted by the present invention is a method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil, including: S1: Obtain the geological data of the area to be detected, use the geological data of the area to be detected to determine the type of permafrost in the area to be detected, and detect the area to be detected by a time domain reflectometer to obtain the dielectric constant of the shallow underground soil in the area to be detected; S2: Use a low-frequency ground penetrating radar to detect the area to be detected to obtain the contour and position of the underground permafrost in the area to be detected; S3: Establish a permafrost simulation model of the area to be detected by using the finite element method and the dielectric constant of the shallow underground soil in the area to be detected obtained in S1, and scan the permafrost simulation model with several antenna frequencies to obtain radar images at different antenna frequencies; S4: Perform Hilbert-Huang transform on the radar images at different antenna frequencies obtained in S3 respectively, draw the instantaneous frequency-time curve graphs at different antenna frequencies respectively, read the instantaneous frequency positions of the frozen soil corresponding to the y-axis on each instantaneous frequency-time curve graph in sequence, and calculate the first error, the second error, and the third error in sequence; S5: Analyze the errors obtained in S4 to obtain the optimal frequency of the ground penetrating radar antenna.

[0005] Furthermore, S1 specifically includes the following steps: S1.1: Collect and sort out the geological data of the area to be detected; S1.2: Obtain the properties of the underground frozen soil and the upper and lower depth limits of the frozen soil in the area to be detected by using the geological data obtained in S1.1; S1.3: Detect the dielectric constant of the shallow underground soil by using a TDR time domain reflectometer.

[0006] Furthermore, S2 specifically includes the following steps: S2.1: Calculate the ground penetrating radar frequency according to the prior knowledge about the upper depth limit of the frozen soil and the upper depth limit of the frozen soil in the area to be detected obtained in S1.2, and use the ground penetrating radar with the determined frequency to prospect the area to be detected to obtain radar data; S2.2: Perform linear piecewise gain on the radar data to obtain the contour and position parameters of the underground frozen soil in the area to be detected.

[0007] Furthermore, S3 specifically includes the following steps: S3.1: Establish a frozen soil simulation model of the area to be detected by using the finite element method and the dielectric constant of the shallow underground soil in the area to be detected obtained in S1; S3.2: Scan the frozen soil simulation model of the area to be detected with antenna frequencies of 100 MHz, 150 MHz, 200 MHz, and 270 MHz to obtain radar images at different frequencies.

[0008] Furthermore, S4 specifically includes the following steps: S4.1: Perform Hilbert-Huang transform on the radar images at different antenna frequencies respectively, take the instantaneous frequency as the eigenvalue, draw the instantaneous frequency-time curve graphs corresponding to different antenna frequencies in sequence, and read the instantaneous frequency peaks on the different frequency-time curve graphs; S4.2: Observe the instantaneous frequency-time curve graphs corresponding to different antenna frequencies to obtain the actual time points corresponding to the instantaneous frequency peaks at the interfaces between the ground surface and the upper medium of the frozen soil, between the upper medium of the frozen soil and the frozen soil, and between the frozen soil and the lower medium of the frozen soil corresponding to different antenna frequencies; S4.3: Use the frozen soil simulation model of the area to be detected obtained in S3 to calculate, in sequence, the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil, between the upper medium of the frozen soil and the frozen soil, and between the frozen soil and the lower medium of the frozen soil for different antenna frequencies; S4.4: Subtract the actual time points corresponding to the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil obtained in S4.2 from the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil obtained in S4.3 to obtain the first errors corresponding to different antenna frequencies in sequence. Subtract the actual time points corresponding to the instantaneous frequency peaks of the interfaces between the upper medium of the frozen soil and the frozen soil obtained in S4.2 from the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the upper medium of the frozen soil and the frozen soil obtained in S4.3 to obtain the second errors corresponding to different antenna frequencies in sequence. Subtract the actual time points corresponding to the instantaneous frequency peaks of the interfaces between the frozen soil and the lower medium of the frozen soil obtained in S4.2 from the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the frozen soil and the lower medium of the frozen soil obtained in S4.3 to obtain the third errors corresponding to different antenna frequencies in sequence.

[0009] Further, S5 specifically includes the following steps: S5.1: Compare the first errors, second errors, and third errors corresponding to different antenna frequencies one by one to obtain the antenna frequencies corresponding to the minimum first error, minimum second error, and minimum third error; S5.2: Compare the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil corresponding to different antenna frequencies obtained in S4.2 with the surrounding instantaneous frequencies to obtain the fourth error. Compare the instantaneous frequency peaks of the interfaces between the upper medium of the frozen soil and the frozen soil with the surrounding instantaneous frequencies to obtain the fifth error. Compare the instantaneous frequency peaks of the interfaces between the frozen soil and the lower medium of the frozen soil with the surrounding instantaneous frequencies to obtain the sixth error; S5.3: Compare the fourth errors, fifth errors, and sixth errors corresponding to different antenna frequencies one by one to obtain the antenna frequencies corresponding to the minimum fourth error, minimum fifth error, and minimum sixth error or the antenna frequencies corresponding to the maximum fourth error, maximum fifth error, and maximum sixth error; S5.4: Combine the antenna frequencies obtained in S5.1 and S5.3 to obtain the optimal antenna frequency of the ground penetrating radar suitable for the area to be detected.

[0010] The beneficial effects of the present invention are: 1. The method of the present invention innovatively proposes to use the peak value of the instantaneous frequency as the selection index for the ground penetrating radar antenna frequency. By comparing the interpolation of the time where the peak value of the instantaneous frequency is located in the simulation model under different antenna frequencies with the theoretical time, the most suitable antenna radar frequency for detecting frozen soil in the area to be measured is selected, filling the gap in the related research on detecting underground frozen soil based on the ground penetrating radar antenna frequency.

[0011] 2. The method of the present invention accurately obtains the dielectric constant of the soil around the frozen soil through preliminary exploration and initially obtains the position information of the underground frozen soil, and refines the simulation model to make it closer to the complex environment of the real underground, so that the optimized antenna frequency can display the frozen soil information more comprehensively and enhance the signal-to-noise ratio of the radar data. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0013] Figure 1 It is the instantaneous frequency-time curve diagram under different radar frequencies in the embodiment of the method of the present invention; Figure 2 It is the error diagram of the frozen soil thickness under different antenna frequencies in the simulation of the embodiment of the method of the present invention; Figure 3 It is the ground penetrating radar diagram of the measured frozen soil in the embodiment of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0014] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0015] The present invention first selects the most suitable antenna radar frequency for detecting frozen soil in the area to be measured by using the peak value of the instantaneous frequency as the selection index for the ground penetrating radar antenna frequency, and then accurately obtains the dielectric constant of the soil around the frozen soil through preliminary exploration and initially obtains the position information of the underground frozen soil, and refines the simulation model to make it closer to the complex environment of the real underground, so that the optimized antenna frequency can display the frozen soil information more comprehensively and enhance the signal-to-noise ratio of the radar data, including the following steps: S1: Obtain the geological data of the area to be detected. Using the geological data of the area to be detected, determine the type of frozen soil in the area to be detected, and detect the area to be detected by a time domain reflectometer to obtain the dielectric constant of the shallow subsurface soil in the area to be detected. The detailed steps of S1 are as follows: S1.1: Collect and collate the geological data of the area to be detected. The geological data includes: comprehensive analysis of the physical indicators of each layer of soil in the underground layers of the area to be detected through engineering geological horizontal and vertical plane maps, engineering geological longitudinal section maps, hydrogeological conditions, borehole columnar diagrams, and physical indicators of each layer of soil.

[0016] S1.2: Obtain the properties of the frozen soil in the area to be detected and the upper and lower depth limits of the frozen soil using the geological data obtained in S1.1. In this embodiment, the soil within 3m below the ground surface is frozen soil, and the depth of the frozen soil is approximately 3m. S1.3: Detect the dielectric constant of the shallow subsurface soil using a TDR (Time Domain Reflectometry) time domain reflectometer.

[0017] In this embodiment, the dielectric constant of the shallow subsurface soil is 8.5, and the shallow subsurface soil is the soil within 3m from the ground surface.

[0018] S2: Detect the area to be detected using a low-frequency (100MHz - 400MHz) ground penetrating radar to obtain the contour and position of the frozen soil in the area to be detected. The detailed steps of S2 are as follows: S2.1: Calculate the frequency of the ground penetrating radar based on the prior knowledge of the upper depth limit of the frozen soil and the upper depth limit of the frozen soil in the area to be detected obtained in S1.2. Use the ground penetrating radar with the determined frequency to explore the area to be detected to obtain radar data. In this example, the prior knowledge of the upper depth limit of the frozen soil is specifically: the upper depth limit of the frozen soil is generally below 2 meters from the ground surface.

[0019] The conditions for selecting the area to be detected are: select a section of the road surface that is relatively clean and flat and a survey line position. Clear the weeds on the ground surface to ensure that there are as few interference factors as possible around the survey line. The position where the survey line passes should avoid areas with water on the ground surface and areas with large undulations.

[0020] S2.2: Perform linear segmented gain on the radar data to obtain the contour and position parameters of the frozen soil in the area to be detected.

[0021] S3: Establish a frozen soil simulation model for the area to be detected using the finite element method and the dielectric constant of the shallow subsurface soil in the area to be detected obtained in S1. Scan the frozen soil simulation model using several antenna frequencies to obtain radar images at different antenna frequencies. The detailed steps of S3 are as follows: S3.1: Use the finite element method and the dielectric constant of the shallow subsurface soil in the detection area obtained in S1 to establish a frozen soil simulation model of the detection area in matlab; When using the finite element method, the set conditions are: boundary condition: scattering boundary condition; mesh division: select triangular mesh, and the side length of the smallest unit of the mesh is λ / 30, where λ is the wavelength corresponding to the center frequency of the ground penetrating radar; electromagnetic field excitation source: Ricker wave is used as the pulse excitation source for radar simulation.

[0022] S3.2: Use antenna frequencies of 100 MHz, 150 MHz, 200 MHz, and 270 MHz to scan the frozen soil simulation model of the detection area, and obtain radar images at different frequencies, that is, 4 images.

[0023] S4: Perform Hilbert-Huang transform on the radar images at different antenna frequencies obtained in S3 respectively, draw the instantaneous frequency-time spectra at different antenna frequencies respectively, read the instantaneous frequency positions of the frozen soil corresponding to the y-axis on each instantaneous frequency-time spectrum in turn, and calculate the first error, the second error, and the third error in turn; The detailed steps of S4 are as follows: S4.1: Perform Hilbert-Huang transform on the radar images at different antenna frequencies respectively, take the instantaneous frequency as the eigenvalue, and draw the instantaneous frequency-time curves corresponding to different antenna frequencies in turn, as Figure 1 shown. It can be seen from Figure 1 that the time point corresponding to the peak value of the instantaneous frequency at the interface between the upper medium of the frozen soil and the frozen soil is about 90 ns, and the time point corresponding to the peak value of the instantaneous frequency at the interface between the lower medium of the frozen soil and the frozen soil is about 180 ns. Read the peak values of the instantaneous frequencies on the different frequency-time curves. It can also be seen from Figure 1 that the difference between the peak values of the instantaneous frequencies of 100 MHz and 150 MHz and the surrounding instantaneous frequencies is not significant, so they are not suitable for being selected as better antenna frequencies.

[0024] S4.2: Observe the instantaneous frequency-time curve graphs corresponding to different antenna frequencies, and obtain the actual time points corresponding to the instantaneous frequency peaks at the interfaces between the surface and the upper permafrost medium, between the upper permafrost medium and the permafrost, and between the permafrost and the lower permafrost medium corresponding to different antenna frequencies; S4.3: Use the permafrost simulation model of the area to be detected obtained in S3 to calculate successively the theoretical time points corresponding to the instantaneous frequency peaks at the interfaces between the surface and the upper permafrost medium, between the upper permafrost medium and the permafrost, and between the permafrost and the lower permafrost medium corresponding to different antenna frequencies; S4.4: Subtract the theoretical time points corresponding to the instantaneous frequency peaks at the interfaces between the surface and the upper permafrost medium obtained in S4.3 from the actual time points corresponding to the instantaneous frequency peaks at the interfaces between the surface and the upper permafrost medium obtained in S4.2 to obtain the first errors corresponding to different antenna frequencies successively. Subtract the theoretical time points corresponding to the instantaneous frequency peaks at the interfaces between the upper permafrost medium and the permafrost obtained in S4.3 from the actual time points corresponding to the instantaneous frequency peaks at the interfaces between the upper permafrost medium and the permafrost obtained in S4.2 to obtain the second errors corresponding to different antenna frequencies successively. Subtract the theoretical time points corresponding to the instantaneous frequency peaks at the interfaces between the permafrost and the lower permafrost medium obtained in S4.3 from the actual time points corresponding to the instantaneous frequency peaks at the interfaces between the permafrost and the lower permafrost medium obtained in S4.2 to obtain the third errors corresponding to different antenna frequencies successively.

[0025] S5: Analyze the errors obtained in S4 to obtain the optimal frequency of the ground penetrating radar antenna; The detailed steps of S5 are as follows: Specifically, S5 is as follows: S5.1: Compare one by one the first errors, second errors, and third errors corresponding to different antenna frequencies to obtain the antenna frequencies corresponding to the minimum first error, minimum second error, and minimum third error; S5.2: Compare the instantaneous frequency peaks at the interfaces between the surface and the upper permafrost medium corresponding to different antenna frequencies obtained in S4.2 with the surrounding instantaneous frequencies to obtain the fourth error. Compare the instantaneous frequency peaks at the interfaces between the upper permafrost medium and the permafrost with the surrounding instantaneous frequencies to obtain the fifth error. Compare the instantaneous frequency peaks at the interfaces between the permafrost and the lower permafrost medium with the surrounding instantaneous frequencies to obtain the sixth error; Figure 2 The upper and lower permafrost interfaces are obtained by exploration with the antenna frequency corresponding to the minimum error. The peak at about 90 ns in the figure is the upper interface, and the peak at about 180 ns is the lower permafrost interface.

[0026] S5.3: Compare the fourth error, fifth error, and sixth error corresponding to different antenna frequencies one by one to obtain the antenna frequencies corresponding to the minimum fourth error, minimum fifth error, and minimum sixth error, or the antenna frequencies corresponding to the maximum fourth error, fifth error, and sixth error. S5.4: Based on the antenna frequencies obtained in S5.1 and S5.3, determine the optimal antenna frequency of the ground penetrating radar suitable for the area to be detected.

[0027] The specific embodiments are as follows: Based on the underground cross-section medium of the area to be measured obtained in S1 and S2, generally determine the location of the underground frozen soil. The frozen soil is located 3m below the ground surface, and the depth of the frozen soil is about 3m. The measured dielectric constant of the soil layer above the frozen soil is 20, and the dielectric constant of the frozen soil is taken as the value of 8.5 obtained from indoor tests. According to the propagation theory of the ground penetrating radar in the medium, the theoretical time for the radar to pass through the frozen soil is 58.3ns. After constructing the instantaneous frequency peak value diagrams under different antenna frequencies for simulation, error analysis is carried out. Figure 3 This represents the ground penetrating radar map of the measured frozen soil in the embodiment of the method of the present invention. According to Figure 3 It can be found that the radar with a frequency of 200MHz has the best detection effect on the underground anomalies in this area.

[0028] The inventive points of the method of the present invention are as follows: 1. The method of the present invention uses the instantaneous frequency peak value as the selection index for the antenna frequency of the ground penetrating radar.

[0029] 2. The method of the present invention accurately obtains the dielectric characteristics of the soil around the frozen soil through preliminary exploration and initially obtains the location information of the underground frozen soil, making the simulation model close to the actual underground frozen soil distribution and making the data analysis more reliable.

[0030] 3. Detecting with the antenna frequency preferably obtained by the method of the present invention can display the frozen soil information in more detail, enhancing the effectiveness and usability of the radar data.

[0031] Each embodiment in this specification is described in a related manner. For the same or similar parts among the embodiments, reference can be made to each other. Each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and reference can be made to the corresponding part of the method embodiment for the related content.

[0032] The above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil, characterized in that, It includes the following steps: S1: Obtain the geological data of the area to be detected. Use the geological data of the area to be detected to determine the type of frozen soil in the area to be detected, and detect the area to be detected by a time domain reflectometer to obtain the dielectric constant of the shallow soil layer underground in the area to be detected; S2: Detect the area to be detected by a low-frequency ground penetrating radar to obtain the contour and position of the frozen soil underground in the area to be detected; S3: Use the finite element method and the dielectric constant of the shallow soil layer underground in the area to be detected obtained in S1 to establish a frozen soil simulation model of the area to be detected, and scan the frozen soil simulation model with several antenna frequencies to obtain radar images at different antenna frequencies; S4: Perform Hilbert-Huang transform on the radar images at different antenna frequencies obtained in S3 respectively, draw the instantaneous frequency-time curve graphs at different antenna frequencies respectively, read the instantaneous frequency positions of the frozen soil corresponding to the y-axis on each instantaneous frequency-time curve graph in turn, and calculate the first error, the second error, and the third error in turn; S5: Analyze the errors obtained in S4 to obtain the optimal frequency of the ground penetrating radar antenna.

2. The method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil according to claim 1, characterized in that, S1 specifically includes the following steps: S1.1: Collect and sort out the geological data of the area to be detected; S1.2: Use the geological data obtained in S1.1 to obtain the properties of the frozen soil underground in the area to be detected, the upper limit depth and the lower limit depth of the frozen soil; S1.3: Detect the dielectric constant of the shallow soil layer underground by a TDR time domain reflectometer.

3. The method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil according to claim 1, characterized in that S2 specifically includes the following steps: S2.1: Calculate the ground penetrating radar frequency according to the prior knowledge of the upper limit depth of the frozen soil and the upper limit depth of the frozen soil in the area to be detected obtained in S1.2, and use the ground penetrating radar with the determined frequency to explore the area to be detected to obtain radar data; S2.2: Perform linear piecewise gain on the radar data to obtain the contour and position parameters of the frozen soil underground in the area to be detected.

4. The method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil according to claim 1, characterized in that S3 specifically includes the following steps: S3.1: Use the finite element method and the dielectric constant of the shallow soil layer underground in the area to be detected obtained in S1 to establish a frozen soil simulation model of the area to be detected; S3.2: Scan the frozen soil simulation model of the area to be detected with antenna frequencies of 100 MHz, 150 MHz, 200 MHz, and 270 MHz to obtain radar images at different frequencies.

5. The method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil according to claim 1, characterized in that, S4 specifically includes the following steps: S4.1: Perform Hilbert-Huang transform on the radar images at different antenna frequencies respectively, take the instantaneous frequency as the eigenvalue, draw the instantaneous frequency-time curve graphs corresponding to different antenna frequencies in turn, and read the instantaneous frequency peaks on the different frequency-time curve graphs; S4.2: Observe the instantaneous frequency-time curve graphs corresponding to different antenna frequencies to obtain the actual time points corresponding to the instantaneous frequency peaks of the interface between the ground surface and the upper medium of the frozen soil, the actual time points corresponding to the instantaneous frequency peaks of the interface between the upper medium of the frozen soil and the frozen soil, and the actual time points corresponding to the instantaneous frequency peaks of the interface between the frozen soil and the lower medium of the frozen soil corresponding to different antenna frequencies; S4.3: Use the frozen soil simulation model of the area to be detected obtained in S3 to calculate in sequence the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil, the interfaces between the upper medium of the frozen soil and the frozen soil, and the interfaces between the frozen soil and the lower medium of the frozen soil, corresponding to different antenna frequencies; S4.4: Subtract the actual time points corresponding to the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil obtained in S4.2 from the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil obtained in S4.3, to obtain the first errors corresponding to different antenna frequencies in sequence. Subtract the actual time points corresponding to the instantaneous frequency peaks of the interfaces between the upper medium of the frozen soil and the frozen soil obtained in S4.2 from the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the upper medium of the frozen soil and the frozen soil obtained in S4.3, to obtain the second errors corresponding to different antenna frequencies in sequence. Subtract the actual time points corresponding to the instantaneous frequency peaks of the interfaces between the frozen soil and the lower medium of the frozen soil obtained in S4.2 from the theoretical time points corresponding to the instantaneous frequency peaks of the interfaces between the frozen soil and the lower medium of the frozen soil obtained in S4.3, to obtain the third errors corresponding to different antenna frequencies in sequence.

6. The method for determining the optimal frequency of a ground penetrating radar for detecting frozen soil according to claim 1, wherein S5 specifically includes the following steps: S5.1: Compare one by one the first errors, second errors, and third errors corresponding to different antenna frequencies to obtain the antenna frequencies corresponding to the minimum first error, minimum second error, and minimum third error; S5.2: Compare the instantaneous frequency peaks of the interfaces between the ground surface and the upper medium of the frozen soil corresponding to different antenna frequencies obtained in S4.2 with the surrounding instantaneous frequencies to obtain the fourth error, compare the instantaneous frequency peaks of the interfaces between the upper medium of the frozen soil and the frozen soil with the surrounding instantaneous frequencies to obtain the fifth error, and compare the instantaneous frequency peaks of the interfaces between the frozen soil and the lower medium of the frozen soil with the surrounding instantaneous frequencies to obtain the sixth error; S5.3: Compare one by one the fourth errors, fifth errors, and sixth errors corresponding to different antenna frequencies to obtain the antenna frequencies corresponding to the minimum fourth error, minimum fifth error, and minimum sixth error, or the antenna frequencies corresponding to the maximum fourth error, maximum fifth error, and maximum sixth error; S5.4: Integrate the antenna frequencies obtained in S5.1 and S5.3 to obtain the optimal antenna frequency of the ground penetrating radar suitable for the area to be detected.

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