A Fast Simulation Method for Ground Penetrating Radar in Dispersive Media Based on Ray Tracing

Abstract

The present invention relates to a fast simulation method for ground penetrating radar based on ray tracing for dispersive media, comprising the following steps: 1) constructing a subsurface dispersive medium structure model; 2) equally dividing the actual ground penetrating radar transmitted signal into N frequency sub-bands according to the bandwidth, and generating a single-frequency ground penetrating radar transmitted signal with a frequency being the center frequency of the frequency sub-band and an amplitude of 1; 3) performing ground penetrating radar simulation based on ray tracing to obtain the corresponding echo signal, and obtaining the value of the impulse response function of the ground penetrating radar system in the dispersive medium at the corresponding frequency points; 4) obtaining an approximate impulse response function H(jΩ) by means of interpolation; 5) applying the approximate impulse response function to filter the ground penetrating radar transmitted signal, obtaining an approximate received signal of the ground penetrating radar in the dispersive medium, and thus completing the simulation of the ground penetrating radar in the dispersive medium. Compared with the prior art, the present invention is applicable to dispersive media and can greatly improve the simulation speed of the ground penetrating radar under the condition that the simulation accuracy has an acceptable decrease.

Description

Technical Field

[0001] The present invention relates to the field of ground penetrating radar simulation, and particularly to a fast simulation method for ground penetrating radar based on ray tracing for dispersive media. Background Art

[0002] Ground penetrating radar is a device for non-destructively detecting underground media using electromagnetic waves. It is widely used in investigating and analyzing underground objects, such as mine detection, roadbed inspection, underground water source investigation, etc. Ground penetrating radar simulation is of great significance in the research of ground penetrating radar. It can provide cheap and indispensable simulated echo data for the research of ground penetrating radar. The simulation of ground penetrating radar for dispersive media is particularly important because in practice, ground penetrating radar is mainly used in dispersive media (such as soil, etc.).

[0003] Although the existing ground penetrating radar simulation method based on Finite-Difference Time-Domain (FDTD) can obtain highly accurate simulated echo data of ground penetrating radar, it has high requirements for computing resources, especially when simulating a large-scale ground penetrating radar scenario. In addition, although the existing ground penetrating radar simulation method based on ray tracing can quickly perform ground penetrating radar simulation, it cannot be used for dispersive media. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above-mentioned defects existing in the prior art and provide a fast simulation method for ground penetrating radar based on ray tracing for dispersive media.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A fast simulation method for ground penetrating radar based on ray tracing for dispersive media, the method comprising the following steps:

[0007] 1) Model the underground scene to construct an underground dispersive medium structure model;

[0008] 2) For each A-Scan during ground penetrating radar simulation, equally divide the actual ground penetrating radar transmitted signal s(n) into N frequency sub-bands according to the bandwidth. The center frequency of each frequency sub-band is ω k , k = 1, 2... N, and generate a single-frequency ground penetrating radar transmitted signal with a frequency equal to the center frequency of the frequency sub-band and an amplitude of 1 for each frequency sub-band. The propagation of these single-frequency ground penetrating radar transmitted signals in the dispersive medium will not be affected by the dispersion characteristics of the medium;

[0009] 3) Taking each single - frequency ground - penetrating radar (GPR) transmitted signal as a transmitted signal, perform GPR simulation based on ray - tracing proposed by Goodman respectively to obtain the corresponding echo signals, and obtain the values of the impulse response function of the GPR system in the dispersive medium at the corresponding frequency points according to the amplitude and phase of the echo signals.

[0010] 4) Fit the values of the impulse response function of the GPR system in all dispersive media at the corresponding frequency points by interpolation to obtain an approximate impulse response function H(jΩ).

[0011] 5) Apply the approximate impulse response function to filter the GPR transmitted signal to obtain an approximate received signal of the GPR in the dispersive medium, and thus complete the GPR simulation in the dispersive medium.

[0012] In the step 5) described above, the expression of the approximate received signal r(n) is:

[0013] r(n) = s(n)*h(n) = IDFT{S(k)H(k)}

[0014] Where, IDFT is the inverse discrete Fourier transform, s(n) is the actual GPR transmitted signal, S(k) is the k - th single - frequency GPR transmitted signal, that is, H(k) is the discrete Fourier transform of s(n), h(n) is the impulse response function of the GPR system in the dispersive medium, and H(k) is the discrete Fourier transform of h(n).

[0015] In the step 5) described above, by sampling the approximate impulse response function H(jΩ) to obtain the discrete Fourier transform H(k) of h(n), then there is:

[0016]

[0017] Where, Ω is the sampling frequency and T is the sampling interval.

[0018] In the step 1) described above, the underground dispersive medium structure model includes a cylindrical single - pole dispersive wet sand medium structure model.

[0019] Compared with the prior art, the present invention has the following advantages:

[0020] When electromagnetic waves propagate in a medium, the difference in propagation speed caused by frequency differences is called dispersion. The present invention establishes a propagation model of signals with different frequencies in the medium, analyzes the responses of each frequency of the transmitted signal in the medium, and thus establishes a method for simulating the echo signal of a ground penetrating radar propagating in a dispersive medium. This method can achieve fast simulation of a ground penetrating radar in a dispersive medium. By using the existing ground penetrating radar simulation method based on the ray tracing algorithm proposed by Goodman, which cannot be used for dispersive media, to obtain the values of the impulse response function of the ground penetrating radar system in a dispersive medium at a series of frequency points, and then approximately obtaining the impulse response function of the ground penetrating radar system in a dispersive medium through fitting, the simulated echo (received) signal of the ground penetrating radar in the dispersive medium is obtained, overcoming the disadvantage that the existing ground penetrating radar simulation method based on ray tracing cannot be used for dispersive media. At the same time, since the present invention is based on the existing fast ground penetrating radar simulation method based on ray tracing, the method of the present invention has a faster simulation speed than the existing FD-FDTD method that can be used for dispersive media. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 FIG. is a flowchart of simulating a ground penetrating radar in a dispersive medium provided in an embodiment of the present invention.

[0022] Figure 2 FIG. is a comparison diagram of the simulated echo (received) signal of the ground penetrating radar obtained by using the method of the present invention in an example of the present invention and the simulated echo (received) signal of the ground penetrating radar with higher accuracy obtained by using the existing FD-FDTD ground penetrating radar simulation method. Among them, FIG. (2a) is a comparison diagram of the 51st trace A-Scan results of the two, FIG. (2b) is the B-Scan result of the FD-FDTD method, and FIG. (2c) is the B-Scan result of the method proposed by the present invention.

[0023] Figure 3 FIG. is a comparison diagram of the running time of the method of the present invention and the running time of the existing FD-FDTD ground penetrating radar simulation method in an example of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0024] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0025] The present invention provides a fast ground penetrating radar simulation method based on ray tracing for dispersive media, including the following steps:

[0026] 1) Model the underground scene, construct an underground dispersive medium model, and lay a foundation for subsequent simulation of the propagation of electromagnetic waves of the transmitted signal of the ground penetrating radar using ray tracing;

[0027] 2) Divide the bandwidth of the actual ground penetrating radar (GPR) transmitted signal into multiple frequency sub-bands equally, and generate a single-frequency GPR transmitted signal with the center frequency of each frequency sub-band as the frequency and an amplitude of 1 (the GPR transmitted signal is modeled as the superposition of multiple single-frequency signals), and the propagation of these single-frequency signals in the dispersive medium will not be affected by the dispersion characteristics of the medium;

[0028] 3) Use each single-frequency signal as the transmitted signal, and perform GPR simulation using the existing ray-tracing-based GPR simulation method to obtain the corresponding echo signal. Obtain the value of the impulse response function of the GPR system in the dispersive medium at the corresponding frequency point according to the amplitude and phase of these echo signals;

[0029] 4) Connect and fit the values of the impulse response function of the GPR system in the dispersive medium at all corresponding frequency points through an interpolation method to obtain an approximate impulse response function;

[0030] 5) Apply the approximate impulse response function to filter the GPR transmitted signal to obtain an approximate received signal of the GPR in the dispersive medium, and then complete the GPR simulation in the dispersive medium.

[0031] Step 5) can be realized through discrete-time signal processing, so as to accelerate the signal processing process using the fast Fourier transform algorithm.

[0032] The specific principle of the present invention is as follows:

[0033] When the sampling interval T meets the requirements of the Nyquist sampling theorem, assume that the transmitted signal of the GPR after sampling is s(n), the impulse response function of the GPR system is h(n), and the received signal is r(n). Then, from the signal processing theory, it can be known that:

[0034] r(n) = s(n) * h(n) = IDFT{S(k)H(k)}

[0035] In the formula, IDFT is the inverse discrete Fourier transform, and H(k) and S(k) are the discrete Fourier transforms of s(n) and h(n) respectively.

[0036] Furthermore, H(k) can be expressed as:

[0037]

[0038] In the formula, H(e jω ) is the discrete-time Fourier transform of h(n).

[0039] From the continuous-time signal discrete-time processing theory, it is known that:

[0040]

[0041] In the formula, H(jΩ) is the frequency response function of the ground penetrating radar system.

[0042] From the above two formulas, we can get:

[0043]

[0044] Therefore, set the frequencies of the single-frequency signals corresponding to the frequency sub-bands of the transmitted signals of each ground penetrating radar in the previous steps to Then H(k) can be obtained.

[0045] So far, all the elements required to obtain the simulated echo (received) signal r(n) of the ground penetrating radar in the dispersive medium have been successfully obtained, so that the simulation of the ground penetrating radar in the case of the dispersive medium can be realized.

[0046] Embodiment

[0047] In this embodiment, the fast simulation method of the ground penetrating radar based on ray tracing for the dispersive medium includes the following steps:

[0048] 1) Establish a model based on the underground medium structure;

[0049] The underground medium structure established in this example is a single-pole dispersive wet sandy soil medium containing a cylinder. Among them, the radius of the cylinder is 1 cm and it is buried 0.3 m underground; the dispersive wet sandy soil is a Debye dispersive medium, and its relative permittivity can be expressed as:

[0050]

[0051] In the formula, ∈ rs and ∈ r∞ are the values of the relative permittivity at zero and infinite frequencies respectively, τ is the characteristic relaxation time of the Debye medium. In this example, the electromagnetic parameters of the wet sandy soil medium are ∈ rs = 2.6825, ∈ r∞ = 2.1413, τ = 5.5 ps, the conductivity σ = 1.3828×10 -3 S / m, and the relative permeability μ r = 1.

[0052] 2) The transmitted signal used in the ground penetrating radar simulation is a Blackman Harris pulse with a center frequency of 1 GHz, the sampling interval is the CFL limit value of 4.71731 ps during FD-FDTD simulation (which also satisfies the Nyquist sampling theorem), the receiving signal collection time is 10 ns, the transmitting and receiving antennas move 100 steps with a step size of 0.01 m, and they just move to directly above the cylinder at the 50th step.

[0053] 3) Use the single-frequency signal as the transmitted signal, and use the existing ground penetrating radar simulation method based on ray tracing to obtain the simulated echo (received) signal when the ground penetrating radar acts on the established underground medium model.

[0054] 3) Finally, in order to demonstrate the superiority of the method of the present invention over the existing FD-FDTD method in terms of simulation speed, in this example, the depth of the cylinder is gradually increased from 0.3 m to 0.9 m in 20 steps, and the corresponding received signal time is correspondingly increased from 10 ns to 30 ns, and the simulation times of the two methods at each step are recorded.

[0055] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the existing technology should fall within the protection scope determined by the claims.

Claims

1. A fast simulation method for ground penetrating radar based on ray tracing for dispersive media, characterized in that, The method comprises the following steps: 1) Modeling the underground scene to construct an underground dispersive medium structure model; 2) For each A-Scan during the ground penetrating radar simulation, the actual ground penetrating radar transmitted signal s(n) is equally divided into N frequency sub-bands according to the bandwidth, and the center frequency ω k , k = 1, 2... N of each frequency sub-band, and a single-frequency ground penetrating radar transmitted signal with a frequency equal to the center frequency of the frequency sub-band and an amplitude of 1 is generated for each frequency sub-band; 3) Take each single-frequency ground-penetrating radar transmitting signal as a transmitting signal, respectively perform ground-penetrating radar simulation based on ray tracing to obtain the corresponding echo signals, and obtain the values of the impulse response function of the ground-penetrating radar system in the dispersive medium at the corresponding frequency points according to the amplitude and phase of the echo signals 4) Fitting the values of the impulse response function of the ground penetrating radar system at corresponding frequency points in all dispersive media by interpolation to obtain an approximate impulse response function H(jΩ); 5) Applying the approximate impulse response function to filter the transmitted signal of the ground penetrating radar to obtain an approximate received signal of the ground penetrating radar in the dispersive medium, thereby completing the simulation of the ground penetrating radar in the dispersive medium.

2. The fast simulation method of a ground penetrating radar based on ray tracing for a dispersive medium according to claim 1, wherein In the said step 5), the expression of the approximate received signal r(n) is: r(n) = s(n) * h(n) = IDFT{S(k)H(k)} where IDFT is the inverse discrete Fourier transform, s(n) is the actual transmitted signal of the ground penetrating radar, S(k) is the transmitted signal of the k-th single-frequency ground penetrating radar, that is, S(k) is the discrete Fourier transform of s(n), h(n) is the impulse response function of the ground penetrating radar system in the dispersive medium, and H(k) is the discrete Fourier transform of h(n).

3. A fast simulation method for ground penetrating radar based on ray tracing for dispersive media according to claim 2, characterized in that In the said step 5), the discrete Fourier transform H(k) of h(n) is obtained by sampling the approximate impulse response function H(jΩ), then: where Ω is the sampling frequency and T is the sampling interval.

4. A rapid simulation method for ground penetrating radar based on ray tracing for dispersive media according to claim 1, characterized in that, In the said step 1), the underground dispersive medium structure model includes a cylindrical single-pole dispersive wet sand medium structure model.

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