A method for determining the optimal frequency of ground penetrating radar for detecting frozen ground

Abstract

The application discloses a kind of ground penetrating radar optimal frequency determination methods for detecting frozen soil, it is related to frozen soil survey technical field, including determining frozen soil type based on geological data, shallow soil dielectric constant is obtained using time domain reflectometer;Low-frequency ground penetrating radar detects frozen soil profile and position;Combined with dielectric constant, establish frozen soil simulation model, obtain radar image by multi-frequency scanning;Hilbert Huang transform processes image, draws instantaneous frequency-time curve, calculates three groups of errors;Analysis error determines the best antenna frequency, the method proposed in the application enhances the signal-to-noise ratio when ground penetrating radar detects frozen soil, reduces the influence of clutter on frozen soil reflection wave, clearly shows the range of underground frozen soil in radar image.

Description

Technical Field

[0001] This invention belongs to the field of permafrost exploration technology, and specifically relates to a method for determining the optimal frequency of ground-penetrating radar for detecting permafrost. Background Technology

[0002] In recent years, with global warming and human activities such as deforestation, permafrost has become increasingly prone to degradation. This degradation presents numerous engineering challenges when constructing infrastructure in permafrost regions. Therefore, accurately determining the spatiotemporal distribution of the permafrost layer is crucial for construction in permafrost areas. Ground-penetrating radar (GPR) emits high-frequency electromagnetic waves into the ground and receives the echo signals to generate a general-purpose radar (GPR) image. Based on the image results, the specific characteristics of the target are determined, and the shape of the underground permafrost is displayed in the radar image, thus achieving efficient and non-destructive detection of underground permafrost. However, different antenna frequencies of GPR have varying sensitivities to underground permafrost. Because GPR antenna frequencies suitable for permafrost detection are relatively low, their resolution is low, resulting in blurred images when detecting permafrost. Simultaneously, the attenuation effect of deep electromagnetic waves and the influence of surrounding clutter can blur or obscure the stratigraphic boundaries of the permafrost interface, making them difficult to see. Furthermore, the depth range of underground permafrost varies in different regions, meaning that a single fixed antenna frequency GPR cannot achieve a high signal-to-noise ratio. Therefore, there is an urgent need for a method to determine the frequency of ground-penetrating radar antennas for permafrost detection, to enhance the signal-to-noise ratio of ground-penetrating radar when detecting permafrost, reduce the influence of clutter on the reflected waves of permafrost, and clearly display the extent of underground permafrost in radar images. Summary of the Invention

[0003] The purpose of this invention is to provide a method for determining the optimal frequency of ground-penetrating radar for detecting permafrost, which overcomes the technical problems of low signal-to-noise ratio and unclear stratigraphic lines at the permafrost interface in existing technologies with a single fixed antenna frequency.

[0004] The technical solution adopted in this invention is a method for determining the optimal frequency of ground-penetrating radar for detecting permafrost, comprising:

[0005] S1: Obtain geological data of the area to be explored, use the geological data of the area to be explored to determine the permafrost type of the area to be explored, and use a time domain reflectometer to explore the area to be explored to obtain the dielectric constant of the shallow soil in the area to be explored.

[0006] S2: Use low-frequency ground-penetrating radar to detect the area to be detected, and obtain the outline and location of the underground permafrost in the area to be detected.

[0007] S3: Using the finite element method and the dielectric constant of the shallow soil in the area to be detected obtained in S1, a frozen soil simulation model of the area to be detected is established. The frozen soil simulation model is scanned using several antenna frequencies to obtain radar images at different antenna frequencies.

[0008] S4: Perform Hilbert-Huang transform on the radar images obtained in S3 at different antenna frequencies, and plot the instantaneous frequency-time curves at different antenna frequencies. Read the instantaneous frequency position of the frozen soil corresponding to the y-axis on each instantaneous frequency-time curve, and calculate the first error, the second error, and the third error in sequence.

[0009] S5: Analyze the error obtained in S4 to obtain the optimal frequency for the ground-penetrating radar antenna.

[0010] Furthermore, S1 specifically includes the following steps: S1.1: Collect and organize geological data of the area to be explored;

[0011] S1.2: Using the geological data obtained in S1.1, obtain the properties of the underground permafrost in the area to be explored and the upper and lower limits of the permafrost depth;

[0012] S1.3: Detect the dielectric constant of shallow underground soil using a TDR (Time Domain Reflectometer).

[0013] Furthermore, S2 specifically includes the following steps: S2.1: Based on prior knowledge about the upper limit depth of permafrost and the upper limit depth of permafrost in the area to be explored obtained in S1.2, calculate the ground penetrating radar frequency, and use the ground penetrating radar with the determined frequency to explore the area to be explored to obtain radar data;

[0014] S2.2: Linear segmented gain is applied to the radar data to obtain the outline and location parameters of the underground permafrost in the area to be detected.

[0015] Furthermore, S3 specifically includes the following steps: S3.1: Establish a simulation model of frozen soil in the area to be investigated using the finite element method and the dielectric constant of the shallow subsurface soil obtained in S1;

[0016] S3.2: Scan the permafrost simulation model of the area to be detected using antenna frequencies of 100MHz, 150MHz, 200MHz, and 270MHz to obtain radar images at different frequencies.

[0017] Furthermore, S4 specifically includes the following steps: S4.1: Perform Hilbert-Huang transform on radar images at different antenna frequencies, take the instantaneous frequency as the feature value, and plot the instantaneous frequency-time curves corresponding to different antenna frequencies in sequence, and read the instantaneous frequency peaks on the different frequency-time curves.

[0018] S4.2: Observe the instantaneous frequency-time curves corresponding to different antenna frequencies to obtain the actual time points corresponding to the peak instantaneous frequency at the interface between the surface and the upper permafrost medium, the peak instantaneous frequency at the interface between the upper permafrost medium and the permafrost, and the peak instantaneous frequency at the interface between the permafrost and the lower permafrost medium.

[0019] S4.3: Using the permafrost simulation model of the area to be investigated obtained in S3, calculate the theoretical time points corresponding to the instantaneous peak frequency of the interface between the surface and the upper permafrost medium at different antenna frequencies, the theoretical time points corresponding to the instantaneous peak frequency of the interface between the upper permafrost medium and the permafrost at different antenna frequencies, and the theoretical time points corresponding to the instantaneous peak frequency of the interface between the permafrost and the lower permafrost medium at different antenna frequencies.

[0020] S4.4: Subtract the actual time point corresponding to the instantaneous peak frequency of the interface between the surface and the upper frozen soil medium corresponding to different antenna frequencies obtained in S4.2 from the theoretical time point corresponding to the instantaneous peak frequency of the interface between the surface and the upper frozen soil medium corresponding to different antenna frequencies obtained in S4.3 to obtain the first error corresponding to different antenna frequencies. Subtract the actual time point corresponding to the instantaneous peak frequency of the interface between the upper frozen soil medium and the frozen soil corresponding to different antenna frequencies obtained in S4.2 from the theoretical time point corresponding to the instantaneous peak frequency of the interface between the upper frozen soil medium and the frozen soil corresponding to different antenna frequencies obtained in S4.3 to obtain the second error corresponding to different antenna frequencies. Subtract the actual time point corresponding to the instantaneous peak frequency of the interface between the frozen soil and the lower frozen soil medium corresponding to different antenna frequencies obtained in S4.2 from the theoretical time point corresponding to the instantaneous peak frequency of the interface between the frozen soil and the lower frozen soil medium corresponding to different antenna frequencies obtained in S4.3 to obtain the third error corresponding to different antenna frequencies.

[0021] Furthermore, S5 specifically includes the following steps:

[0022] S5.1: Compare the first error, second error, and third error 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.

[0023] S5.2: Compare the peak instantaneous frequency of the interface between the surface and the upper frozen soil medium corresponding to different antenna frequencies obtained in S4.2 with the instantaneous frequencies around them to obtain the fourth error; compare the peak instantaneous frequency of the interface between the upper frozen soil medium and the frozen soil with the instantaneous frequencies around them to obtain the fifth error; compare the peak instantaneous frequency of the interface between the frozen soil and the lower frozen soil medium with the instantaneous frequencies around them to obtain the sixth error.

[0024] S5.3: Compare the fourth, fifth, and sixth errors corresponding to different antenna frequencies one by one to obtain the antenna frequencies corresponding to the minimum fourth, minimum fifth, and minimum sixth errors, or the antenna frequencies corresponding to the maximum fourth, maximum fifth, and maximum sixth errors.

[0025] S5.4: Combining the antenna frequencies obtained from S5.1 and S5.3, the optimal antenna frequency for the ground-penetrating radar suitable for the area to be detected is obtained.

[0026] The beneficial effects of this invention are:

[0027] 1. This invention innovatively proposes using the instantaneous frequency peak as a selection criterion for the ground-penetrating radar antenna frequency. By comparing the interpolation of the time of the instantaneous frequency peak in the simulation model with the theoretical time under different antenna frequencies, the most suitable antenna radar frequency for permafrost detection in the area to be tested is selected, filling the gap in research on ground-penetrating radar antenna frequency detection of underground permafrost.

[0028] 2. The method of the present invention accurately obtains the dielectric constant of the soil surrounding the permafrost through preliminary survey and obtains the location information of the underground permafrost. It 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 permafrost information more comprehensively and enhance the signal-to-noise ratio of radar data. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 These are instantaneous frequency-time curves at different radar frequencies in embodiments of the method of the present invention.

[0031] Figure 2 This is a simulation diagram of the frozen soil thickness error under different antenna frequencies in an embodiment of the method of the present invention;

[0032] Figure 3 This is a ground-penetrating radar image of frozen soil as an embodiment of the method of the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] This invention first selects the most suitable antenna radar frequency for permafrost detection in the area under test by using the instantaneous peak frequency as the selection index. Then, through preliminary surveying, the dielectric constant of the soil surrounding the permafrost is accurately obtained, and the location information of the underground permafrost is preliminarily obtained. The simulation model is refined to make it more closely resemble the complex environment of the real underground environment. As a result, the selected antenna frequency can display the permafrost information more comprehensively and enhance the signal-to-noise ratio of the radar data. The invention includes the following steps:

[0035] S1: Obtain geological data of the area to be explored, use the geological data of the area to be explored to determine the permafrost type of the area to be explored, and use a time domain reflectometer to explore the area to be explored to obtain the dielectric constant of the shallow soil in the area to be explored.

[0036] The detailed steps of S1 are as follows:

[0037] S1.1: Collect and organize geological data of the area to be explored;

[0038] The geological data includes: engineering geological plan and longitudinal profile, engineering geological longitudinal section, hydrogeological conditions, borehole columnar section, physical indicators of each soil layer, etc., to comprehensively analyze the types of underground soil layers in the area to be tested.

[0039] S1.2: Using the geological data obtained in S1.2, we can obtain the properties of the underground permafrost in the area to be explored and the upper and lower limits of the permafrost depth;

[0040] In this embodiment, the ground surface is 3m below the frozen soil, and the depth of the frozen soil is approximately 3m.

[0041] S1.3: Use TDR (Time Domain Reflectometry) to detect the dielectric constant of shallow subsurface soil.

[0042] In this embodiment, the dielectric constant of the shallow soil is 8.5, and the shallow soil is the soil within 3m of the ground surface.

[0043] S2: Use low-frequency (100MHz-400MHz) ground-penetrating radar to detect the area to be detected, and obtain the outline and location of the underground permafrost in the area to be detected;

[0044] The detailed steps of S2 are as follows:

[0045] S2.1: Based on prior knowledge about the upper limit depth of permafrost and the upper limit depth of permafrost in the area to be explored obtained in S1.2, calculate the frequency of ground penetrating radar, and use the ground penetrating radar with the determined frequency to explore the area to be explored and obtain radar data.

[0046] In this example, the prior knowledge regarding the upper limit depth of frozen soil is that the upper limit depth of frozen soil is generally 2 meters below the ground surface.

[0047] The conditions for selecting the area to be detected are as follows: select a relatively clean and flat road section and a survey line location, clear surface weeds, ensure that there are as few interfering factors as possible around the survey line, and avoid areas with water on the ground and areas with excessive unevenness and undulation.

[0048] S2.2: Linear segmented gain is applied to the radar data to obtain the outline and location parameters of the underground permafrost in the area to be detected.

[0049] S3: Using the finite element method and the dielectric constant of the shallow soil in the area to be detected obtained in S1, a frozen soil simulation model of the area to be detected is established. The frozen soil simulation model is scanned using several antenna frequencies to obtain radar images at different antenna frequencies.

[0050] The detailed steps for S3 are as follows:

[0051] S3.1: Using the finite element method and the dielectric constant of the shallow subsurface soil in the area to be investigated obtained in S1, a simulation model of the frozen soil in the area to be investigated is established in MATLAB.

[0052] When using the finite element method, the following conditions are set: Boundary conditions: scattering boundary conditions; Mesh generation: triangular mesh is selected, the side length of the smallest mesh element is λ / 30, where λ is the wavelength corresponding to the center frequency of the ground penetrating radar; Electromagnetic field excitation source: Ricker wavelet is used as the pulse excitation source for radar simulation.

[0053] S3.2: Scan the permafrost simulation model of the area to be detected using antenna frequencies of 100MHz, 150MHz, 200MHz, and 270MHz to obtain radar images at different frequencies, i.e., 4 images.

[0054] S4: Perform Hilbert-Huang transform on the radar images obtained in S3 at different antenna frequencies, and plot the instantaneous frequency-time spectrum at different antenna frequencies. Read the instantaneous frequency position of the frozen soil corresponding to the y-axis on each instantaneous frequency-time spectrum, and calculate the first error, the second error, and the third error in sequence.

[0055] The detailed steps for S4 are as follows:

[0056] S4.1: Perform Hilbert-Huang transform on radar images at different antenna frequencies, take the instantaneous frequency as the characteristic value, and plot the instantaneous frequency-time curves corresponding to different antenna frequencies, as shown below. Figure 1 As shown, from Figure 1 It can be seen that the peak instantaneous frequency at the interface between the upper medium and the frozen soil corresponds to a time point of approximately 90 ns, while the peak instantaneous frequency at the interface between the lower medium and the frozen soil corresponds to a time point of approximately 180 ns. The peak instantaneous frequency values ​​on different frequency-time curves were then analyzed. Figure 1 It can also be seen that the instantaneous frequency peaks of 100MHz and 150MHz are not much different from the surrounding instantaneous frequencies, and are not suitable as good antenna frequencies to choose.

[0057] S4.2: Observe the instantaneous frequency-time curves corresponding to different antenna frequencies to obtain the actual time points corresponding to the peak instantaneous frequency at the interface between the surface and the upper permafrost medium, the actual time points corresponding to the peak instantaneous frequency at the interface between the upper permafrost medium and the permafrost, and the actual time points corresponding to the peak instantaneous frequency at the interface between the permafrost and the lower permafrost medium, all corresponding to different antenna frequencies. S4.3: Using the permafrost simulation model of the area to be investigated obtained in S3, calculate the theoretical time points corresponding to the peak instantaneous frequency at the interface between the surface and the upper permafrost medium, the theoretical time points corresponding to the peak instantaneous frequency at the interface between the upper permafrost medium and the permafrost, and the theoretical time points corresponding to the peak instantaneous frequency at the interface between the permafrost and the lower permafrost medium, all corresponding to different antenna frequencies. S4.4: Calculate the instantaneous frequency at the interface between the surface and the upper permafrost medium obtained in S4.2. The first error corresponding to different antenna frequencies is obtained by subtracting the actual time point corresponding to the peak value of the interface between the surface and the upper frozen soil medium obtained from S4.3 from the actual time point corresponding to the peak value of the interface between the upper frozen soil medium and the frozen soil obtained from S4.2 from the theoretical time point corresponding to the peak value of the interface between the upper frozen soil medium and the frozen soil obtained from S4.3 from the actual time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.2 from the theoretical time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.3 from the actual time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.2 from the actual time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.3 from the actual time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.2 from the actual time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.3 from the actual time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.3 from the actual time point corresponding to the peak value of the interface between the frozen soil and the lower frozen soil medium obtained from S4.3.

[0058] S5: Analyze the error obtained in S4 to obtain the optimal frequency for the ground-penetrating radar antenna;

[0059] The detailed steps for S5 are as follows:

[0060] S5 specifically consists of: S5.1: Comparing the first, second, and third errors corresponding to different antenna frequencies one by one to obtain the antenna frequencies corresponding to the minimum first, second, and third errors; S5.2: Comparing the instantaneous frequency peak of the interface between the surface and the upper permafrost medium corresponding to different antenna frequencies obtained in S4.2 with the instantaneous frequencies around it to obtain the fourth error; comparing the instantaneous frequency peak of the interface between the upper permafrost medium and the permafrost with the instantaneous frequencies around it to obtain the fifth error; and comparing the instantaneous frequency peak of the interface between the permafrost and the lower permafrost medium with the instantaneous frequencies around it to obtain the sixth error. Figure 2 The upper and lower interfaces of the permafrost are obtained from the antenna frequency exploration corresponding to the minimum error. In the figure, the peak value of about 90 ns is the upper interface, and the peak value of about 180 ns is the lower interface of the permafrost.

[0061] S5.3: Compare the fourth, fifth, and sixth errors corresponding to different antenna frequencies one by one to obtain the antenna frequencies corresponding to the minimum fourth, minimum fifth, and minimum sixth errors or the antenna frequencies corresponding to the maximum fourth, fifth, and sixth errors.

[0062] S5.4: Combining the antenna frequencies obtained from S5.1 and S5.3, the optimal antenna frequency for the ground-penetrating radar suitable for the area to be detected is obtained.

[0063] The specific implementation method is as follows:

[0064] Based on the underground cross-sectional media of the test area obtained from S1 and S2, the approximate location of the underground permafrost was determined. The permafrost is approximately 3m below the surface. The measured dielectric constant of the upper layer of permafrost is 20, and the dielectric constant of the permafrost itself is taken as 8.5 obtained from laboratory tests. According to the propagation theory of ground-penetrating radar in the medium, the theoretical transit time of the radar in the permafrost is 58.3ns. After constructing simulation diagrams of instantaneous frequency peaks at different antenna frequencies, error analysis was performed. Figure 3 This image shows a ground-penetrating radar (GPR) image of frozen soil obtained from an embodiment of the method of the present invention. Figure 3 It can be observed that the 200MHz radar is most effective at detecting underground anomalies in the region.

[0065] The inventive point of this invention is: 1. This invention uses the instantaneous frequency peak value as the selection index for the frequency of the ground-penetrating radar antenna.

[0066] 2. The method of the present invention accurately obtains the dielectric properties of the soil surrounding the permafrost through pre-survey and initially obtains the location information of the underground permafrost, making the simulation model closer to the actual distribution of underground permafrost and making the data analysis more reliable.

[0067] 3. The preferred antenna frequency obtained by the method of the present invention can display permafrost information in more detail, thereby enhancing the effectiveness and usability of radar data.

[0068] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0069] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for determining the optimal frequency of ground-penetrating radar for detecting permafrost, characterized in that, Includes the following steps: S1: Obtain geological data of the area to be explored, use the geological data of the area to be explored to determine the permafrost type of the area to be explored, and use a time domain reflectometer to explore the area to be explored to obtain the dielectric constant of the shallow soil in the area to be explored. S2: Use low-frequency ground-penetrating radar to detect the area to be detected, and obtain the outline and location of the underground permafrost in the area to be detected. S3: Using the finite element method and the dielectric constant of the shallow soil in the area to be detected obtained in S1, a frozen soil simulation model of the area to be detected is established. The frozen soil simulation model is scanned using several antenna frequencies to obtain radar images at different antenna frequencies. S4: Perform Hilbert-Huang transform on the radar images obtained in S3 at different antenna frequencies, and plot the instantaneous frequency-time curves at different antenna frequencies. Read the instantaneous frequency position of the frozen soil corresponding to the y-axis on each instantaneous frequency-time curve, and calculate the first error, the second error, and the third error in sequence. The first error corresponding to different antenna frequencies is obtained by subtracting the actual time point corresponding to the instantaneous frequency peak of the interface between the surface and the upper permafrost medium corresponding to different antenna frequencies from the theoretical time point corresponding to the instantaneous frequency peak of the interface between the surface and the upper permafrost medium corresponding to different antenna frequencies. The second error corresponding to different antenna frequencies is obtained by subtracting the actual time point corresponding to the instantaneous frequency peak of the interface between the upper permafrost medium and the permafrost medium corresponding to different antenna frequencies from the theoretical time point corresponding to the instantaneous frequency peak of the interface between the upper permafrost medium and the permafrost medium corresponding to different antenna frequencies. The third error corresponding to different antenna frequencies is obtained by subtracting the actual time point corresponding to the instantaneous frequency peak of the interface between the permafrost and the lower permafrost medium corresponding to different antenna frequencies from the theoretical time point corresponding to the instantaneous frequency peak of the interface between the permafrost and the lower permafrost medium corresponding to different antenna frequencies. S5: Analyze the error obtained in S4 to obtain the optimal frequency for the ground-penetrating radar antenna.

2. The method for determining the optimal frequency of ground-penetrating radar for detecting permafrost according to claim 1, characterized in that, S1 specifically includes the following steps: S1.1: Collect and organize geological data of the area to be explored; S1.2: Using the geological data obtained in S1.1, obtain the properties of the underground permafrost in the area to be explored and the upper and lower limits of the permafrost depth; S1.3: Detect the dielectric constant of shallow underground soil using a TDR (Time Domain Reflectometer).

3. The method for determining the optimal frequency of ground-penetrating radar for detecting permafrost according to claim 1, characterized in that, S2 specifically includes the following steps: S2.1: Based on prior knowledge about the upper limit depth of permafrost and the upper limit depth of permafrost in the area to be explored obtained in S1.2, calculate the frequency of ground penetrating radar, and use the ground penetrating radar with the determined frequency to explore the area to be explored and obtain radar data. S2.2: Linear segmented gain is applied to the radar data to obtain the outline and location parameters of the underground permafrost in the area to be detected.

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

5. The method for determining the optimal frequency of ground-penetrating radar for detecting permafrost according to claim 1, characterized in that, S4 specifically includes the following steps: S4.1: Perform Hilbert-Huang transform on radar images at different antenna frequencies, take the instantaneous frequency as the feature value, and plot the instantaneous frequency-time curves corresponding to different antenna frequencies in turn, and read the instantaneous frequency peaks on the different frequency-time curves. S4.2: Observe the instantaneous frequency-time curves corresponding to different antenna frequencies to obtain the actual time points corresponding to the peak instantaneous frequency at the interface between the surface and the upper permafrost medium, the peak instantaneous frequency at the interface between the upper permafrost medium and the permafrost, and the peak instantaneous frequency at the interface between the permafrost and the lower permafrost medium. S4.3: Using the permafrost simulation model of the area to be investigated obtained in S3, calculate the theoretical time points corresponding to the instantaneous peak frequency of the interface between the surface and the upper permafrost medium at different antenna frequencies, the theoretical time points corresponding to the instantaneous peak frequency of the interface between the upper permafrost medium and the permafrost at different antenna frequencies, and the theoretical time points corresponding to the instantaneous peak frequency of the interface between the permafrost and the lower permafrost medium at different antenna frequencies. S4.4: Subtract the actual time point corresponding to the instantaneous peak frequency of the interface between the surface and the upper frozen soil medium corresponding to different antenna frequencies obtained in S4.2 from the theoretical time point corresponding to the instantaneous peak frequency of the interface between the surface and the upper frozen soil medium corresponding to different antenna frequencies obtained in S4.3 to obtain the first error corresponding to different antenna frequencies. Subtract the actual time point corresponding to the instantaneous peak frequency of the interface between the upper frozen soil medium and the frozen soil corresponding to different antenna frequencies obtained in S4.2 from the theoretical time point corresponding to the instantaneous peak frequency of the interface between the upper frozen soil medium and the frozen soil corresponding to different antenna frequencies obtained in S4.3 to obtain the second error corresponding to different antenna frequencies. Subtract the actual time point corresponding to the instantaneous peak frequency of the interface between the frozen soil and the lower frozen soil medium corresponding to different antenna frequencies obtained in S4.2 from the theoretical time point corresponding to the instantaneous peak frequency of the interface between the frozen soil and the lower frozen soil medium corresponding to different antenna frequencies obtained in S4.3 to obtain the third error corresponding to different antenna frequencies.

6. The method for determining the optimal frequency of ground-penetrating radar for detecting permafrost according to claim 1, characterized in that, S5 specifically includes the following steps: S5.1: Compare the first error, second error, and third error 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 peak instantaneous frequency of the interface between the surface and the upper frozen soil medium corresponding to different antenna frequencies obtained in S4.2 with the instantaneous frequencies around them to obtain the fourth error; compare the peak instantaneous frequency of the interface between the upper frozen soil medium and the frozen soil with the instantaneous frequencies around them to obtain the fifth error; compare the peak instantaneous frequency of the interface between the frozen soil and the lower frozen soil medium with the instantaneous frequencies around them to obtain the sixth error. S5.3: Compare the fourth, fifth, and sixth errors corresponding to different antenna frequencies one by one to obtain the antenna frequencies corresponding to the minimum fourth, minimum fifth, and minimum sixth errors, or the antenna frequencies corresponding to the maximum fourth, maximum fifth, and maximum sixth errors. S5.4: Combining the antenna frequencies obtained from S5.1 and S5.3, the optimal antenna frequency for the ground-penetrating radar suitable for the area to be detected is obtained.

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