A method for inversion of layered medium parameters using ground penetrating radar
By combining the CMP method with Snell's law and utilizing the enumeration method and pattern search method, the problems of large computational complexity and large errors in traditional ground penetrating radar detection of multi-layer media are solved, and the accurate inversion of layered medium parameters is achieved, providing accurate information for subsequent imaging and identification.
Patent Information
- Application Number
- CN202210201235.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-03
- Publication Date
- 2025-09-05
- Estimated Expiration
- 2042-03-03
AI Technical Summary
Traditional ground penetrating radar methods cannot achieve accurate inversion of medium parameters in multi-layer medium detection, and have problems such as large computational complexity and severe signal interference.
The CMP method is used to invert the first layer parameters. Combining the layered medium model and Snell's law, the cost function of medium parameter inversion is established by combining the propagation equation with Snell's law, and the enumeration method and pattern search method are used for accurate inversion.
It achieves accurate inversion of multi-layer media with low computational complexity, reduces errors, and provides precise prior structural information for underground target imaging and identification detection.
Smart Images
Figure CN114994658B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of ground penetrating radar, and in particular to a layered medium parameter inversion method of ground penetrating radar. Background Art
[0002] Ground Penetrating Radar (GPR) is a nondestructive testing tool used for road detection and underground exploration, with broad application prospects in municipal transportation, infrastructure construction, and other fields. GPR technology primarily utilizes the reflection, refraction, and scattering properties of high-frequency, ultra-wideband electromagnetic waves in underground dielectric layers to estimate structural information such as thickness and dielectric constant. In practical applications, GPR often involves detecting multi-layered media. The multiple reflections and refractions caused by these multi-layered structures prevent traditional inversion methods from accurately inverting dielectric parameters, compromising subsequent target imaging and identification.
[0003] Traditional parameter inversion methods include the Common Middle Point (CMP) method and the velocity spectrum method. The CMP method is one of the most widely used methods. It estimates layer parameters by constructing a multilayer medium model and solving the propagation equations at different offsets. However, solving the propagation equations requires a large amount of computation. The velocity spectrum method constructs reflection wave trajectories at different propagation velocities, performs amplitude superposition, plots the coherent power, obtains the reflection response at the layer interface, and finally uses the Dix formula to achieve parameter inversion. However, due to the oscillatory nature of the signal and the multiple reflections of the layered structure, there is a lot of interference in the spectrum, making it difficult to accurately obtain the layered response. Summary of the Invention
[0004] In view of this, the present invention proposes a method for inverting layered medium parameters using ground penetrating radar, which can achieve accurate inversion of layered media with low computational complexity and is suitable for multi-layer medium models.
[0005] To achieve the above object, the technical solution of the present invention is:
[0006] The present invention provides a method for inverting parameters of layered media using a ground penetrating radar. The method implements first-layer parameter inversion through a CMP method, then utilizes the information to construct propagation equations at different offset distances based on a layered medium model, and simultaneously utilizes Snell's law to represent the position of the refraction point at the layered interface. A cost function for medium parameter inversion is established by combining the propagation equation with Snell's law. The position of the approximate refraction point is obtained, and then the approximate refraction point position is substituted into the cost function of the propagation equation to construct a cost function for the approximate refraction point. Based on the cost function for the approximate refraction point, an enumeration method is used to implement estimation, and then, based on the cost function of Snell's law, a pattern search method is used to implement medium parameter inversion.
[0007] The first layer parameter inversion is achieved by the CMP method as follows: a single-layer CMP model is established. According to the propagation equation under different transmission and reception spacings, the relative dielectric constant and layer thickness of the first layer are expressed as follows:
[0008]
[0009]
[0010] Where m represents the number of A-scan channels measured by the ground penetrating radar, d1, ε r1 Represent the thickness and relative dielectric constant of the first layer of medium, ε r1,j d 1,j They represent the relative dielectric constant and thickness of the first layer of medium solved for the jth group of transmitting and receiving spacing, j = 1, 2, 3…m-1.
[0011] Among them, according to the propagation equation under different transmit-receive spacing, the corresponding least squares cost function is:
[0012]
[0013] Where m represents the number of A-scan channels measured by the ground penetrating radar, n represents the number of layers of the layered medium, c represents the speed of light, and L j represents the spacing between the transmitting and receiving antennas in the jth A-scan, j = 1, 2, 3…m-1, ε ri,j ,d i,j They represent the relative dielectric constant and thickness of the i-th layer of the layered medium under the j-th A-scan, i = 1, 2, 3…n, x i,j represents the position of the refraction point at the i-th layer interface under the j-th A-scan, Δt i,j It represents the propagation time difference between the reflected wave from the interface of layer i and the direct wave from the air under the j-th A-scan.
[0014] Among them, the least squares cost function based on Snell's law is:
[0015]
[0016] Where x1 represents the refraction point position of the first layer interface, and d1 represents the thickness of the first layer of medium.
[0017] The cost function for medium parameter inversion is established by combining the propagation equation and Snell's law. Specifically, the total cost function of the hierarchical model is obtained by combining two types of cost functions based on the propagation equation and Snell's law:
[0018] δ(ε rn ,d n ,x 1,1,...,x n,m )=a1δ1(ε rn ,d n ,x 1,1 ,...,x n,m )+a2δ2(ε rn ,d n ,x 1,1 ,...,x n,m )
[0019] Among them, a1, a2 are adjustable parameters that control the ratio of the two types of cost functions, x 1,1 ,...,x n,m represents the set of refraction point positions at each layer interface under different A-scans, ε rn ,d n Represents the relative dielectric constant and thickness of the nth layer of layered medium.
[0020] Beneficial effects:
[0021] The present invention implements GPR parameter inversion for layered media based on the CMP model and pattern search. To address the computationally intensive problem of solving the propagation equations of the CMP method, the first layer of parameters is inverted using the traditional CMP method. This information is then used to construct propagation equations at different offsets based on the layered medium model. Snell's law is then used to represent the position of the refraction points at the layered interface, minimizing the error caused by the refraction effect at the layered location. A cost function for medium parameter inversion is established by combining the propagation equation and Snell's law. Furthermore, to address the difficulty of deriving the cost function for multiple independent variables, an enumeration method is used to roughly optimize the initial values. A pattern search method is then used to precisely optimize the parameters, outputting ideal solutions for the multi-layer parameters. This achieves precise inversion of the layered medium and provides accurate prior structural information for subsequent imaging and identification of underground targets.
[0022] The present invention is applied to the parameter inversion of layered media using ground penetrating radar. Due to the complex refraction effect of radar signals in layered media models, traditional methods have large parameter inversion errors and are not applicable to multi-layer media models. However, the present invention can achieve better parameter inversion performance and is a robust and efficient layered media parameter inversion method. BRIEF DESCRIPTION OF THE DRAWINGS
[0023] Figure 1 1 is a signal processing flow chart of the method of the present invention.
[0024] Figure 2 This is a single-layer CMP model established by the method of the present invention.
[0025] Figure 3 It is a multi-layer CMP model established by the method of the present invention.
[0026] Figure 4 It is a schematic diagram of the approximate geometric relationship of the refraction points based on the method of the present invention.
[0027] Figure 5 It is a schematic diagram of a three-layer CMP model adopted in the simulation of the method of the present invention.
[0028] Figure 6 It is a schematic diagram of the CMP medium model adopted in the actual measurement of the method of the present invention. DETAILED DESCRIPTION
[0029] The present invention is described in detail below with reference to the accompanying drawings and embodiments.
[0030] Figure 1 This is a flow chart of the signal processing of the present invention. Based on the fact that the reflected echo can be separated in the time domain, the present invention is implemented by the following steps after obtaining the delay of the reflected wave at each interface:
[0031] Step 1: Establish a single-layer CMP model and invert the first-layer parameters as follows:
[0032] like Figure 2 In the single-layer CMP model shown, the incident electromagnetic wave is reflected at the bottom of the single-layer medium. The propagation distance equation of the electromagnetic wave can be expressed as:
[0033]
[0034]
[0035] Among them, d1,ε r1 They represent the thickness and relative dielectric constant of the first layer of medium, c represents the speed of light, 2L1 represents the distance between the transmitting and receiving antennas under the first A-scan, 2L2 represents the distance between the transmitting and receiving antennas under the second A-scan, t1 represents the distance between the transmitting and receiving antennas under the first A-scan, x End to R x The reflected wave propagation time at the end, t2 represents the second A-scan by T x End to R x The propagation time of the reflected wave at the end.
[0036] According to the propagation equation under different transmission and reception spacing, the relative dielectric constant and layer thickness of the first layer can be expressed as:
[0037]
[0038]
[0039] Where m represents the number of A-scan channels measured by the ground penetrating radar, ε r1,j d 1,jThey represent the relative dielectric constant and layer thickness of the first layer of medium solved under the jth group of transmitting and receiving spacing.
[0040] Step 2: Establish a multi-layer CMP model and construct the cost function of the propagation equation;
[0041] like Figure 3 As shown, the multi-layer CMP model has complex refraction phenomena, and the propagation distance equation is expressed as:
[0042]
[0043] Where n represents the number of layers of the layered medium, d i ,ε ri represent the thickness and relative dielectric constant of the i-th layer of medium, x i represents the refraction point position of the i-th layer interface, Δt i It represents the propagation time difference between the reflected wave from the interface of layer i and the direct wave from the air, i = 1, 2, 3…n.
[0044] According to the propagation equation under different transmission and reception distances, the corresponding least squares cost function can be expressed as:
[0045]
[0046] where ε ri,j ,d i,j represents the relative dielectric constant and thickness of the i-th layer of the layered medium under the j-th A-scan, x i,j represents the position of the refraction point at the i-th layer interface under the j-th A-scan, Δt i,j It represents the propagation time difference between the reflected wave from the interface of layer i and the direct wave from the air under the j-th A-scan, j = 1, 2, 3…m-1.
[0047] Step 3: Construct the cost function of Snell's law;
[0048] Assume that the refraction process satisfies the geometric optics assumptions, such as Figure 4 The refraction point shown satisfies Snell's law, which can be expressed as:
[0049]
[0050] Among them, θ1 and θ2 represent the incident angle and refraction angle of the layered interface, n1 and n2 represent the refractive index of medium 1 and medium 2, respectively, and v1 and v2 represent the speed of electromagnetic wave propagation in medium 1 and medium 2, respectively.
[0051] Therefore, when the medium parameters of the first layer to the n-1th layer are known, the refraction point position of the nth layer can be expressed as:
[0052]
[0053] Therefore, the least squares cost function based on Snell's law can be expressed as:
[0054]
[0055] By combining the two cost functions based on the propagation equation and Snell's law, the total cost function of the hierarchical model is expressed as:
[0056] δ(ε rn ,d n ,x 1,1 ,...,x n,m )=a1δ1(ε rn ,d n ,x 1,1 ,...,x n,m )+a2δ2(ε rn ,d n ,x 1,1 ,...,x n,m )
[0057] Among them, a1 and a2 are adjustable parameters that control the ratio of the two types of cost functions.
[0058] Step 4: Construct the cost function of the refraction point approximation;
[0059] like Figure 4 As shown, the refraction point approximation method is used to simplify the solution of the multivariable equation system, and the position of the refraction point is estimated using a single algebraic operation, which is expressed as:
[0060]
[0061] Among them, y b represents the position of the refraction point on the layered interface, y1 represents the intersection of the electromagnetic wave and the layered interface under the assumption of straight-line propagation, y2 represents the position where the electromagnetic wave is perpendicularly mapped to the layered interface after refraction, and v1 and v2 represent the propagation speeds of the electromagnetic wave in medium 1 and medium 2, respectively.
[0062] By bringing the approximate refraction point position into the cost function of the propagation equation, the cost function of the refraction point approximation can be reconstructed:
[0063]
[0064] Step 5: Use enumeration method to make a rough estimate and pattern search to make a precise inversion;
[0065] The present invention adopts an optimization strategy combining enumeration method with pattern search. First, based on the cost function of refraction point approximation, a rough estimate is achieved by using the enumeration method with a larger search step. Then, based on the cost function of Snell's law, a pattern search method is used to achieve accurate inversion of medium parameters.
[0066] The present invention utilizes the CMP method to invert the first layer parameters, utilizes the proposed optimization strategy to perform layer-by-layer distribution inversion, and iteratively realizes the parameter inversion of multi-layer media.
[0067] Since then, a method for inversion of layered medium parameters by ground penetrating radar based on CMP model and pattern search has been completed.
[0068] In order to verify the proposed method of GPR layered medium parameter inversion based on CMP model and pattern search, a simulation experiment was designed for analysis. Figure 5 As shown, the simulation uses gprMax software to construct a three-layer medium model, and the simulation parameters are shown in Table 1.
[0069] Table 1 Simulation parameter settings
[0070]
[0071] The simulation results are shown in Table 2. The proposed method achieves excellent inversion accuracy. Based on the inversion of the first layer using the traditional CMP method, the relative errors of the layer thickness and relative dielectric constant of the second and third layers are controlled within 1% and 2%, respectively.
[0072] Table 2 Simulation inversion results
[0073]
[0074]
[0075] Table 3 Measured parameter settings
[0076]
[0077] Further measures Figure 6 The measured dielectric scene and experimental parameters are shown in Table 3. The radar system consists of a vector network analyzer and an array antenna, with the antenna placed on a sliding rail. The bottom of the scene is covered with absorbing material. The experiment uses a four-layer dielectric model: air-PVC material-autoclaved aerated concrete-autoclaved sand-lime brick. As shown in Table 4, the layer thickness inversion error of the measured model is within 6%, and the relative dielectric constant of each layer is also controlled within a reasonable range.
[0078] Table 4 Measured inversion results
[0079]
[0080] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.
Claims
1. A method for inverting parameters of layered media using ground penetrating radar, characterized in that: The first layer parameter inversion is achieved through the CMP method. This first layer parameter inversion information is then used to construct propagation equations at different offsets based on a layered medium model. Snell's law is used to represent the position of the refraction point at the layered interface. The cost function for medium parameter inversion is established by combining the propagation equation and Snell's law. The approximate refraction point position is obtained and then substituted into the cost function of the propagation equation to construct a cost function for the refraction point approximation. Based on the cost function of the refraction point approximation, the enumeration method is used to achieve estimation, and then based on the cost function of Snell's law, the pattern search method is used to achieve medium parameter inversion; The method of inverting the first layer parameters by the CMP method is to establish a single-layer CMP model. According to the propagation equation under different transmission and reception spacing, the relative dielectric constant and layer thickness of the first layer are expressed as: Where m represents the number of A-scan channels measured by the ground penetrating radar, d1, ε r1 Represent the thickness and relative dielectric constant of the first layer of medium, ε r1,j d 1,j They represent the relative dielectric constant and thickness of the first layer of medium obtained under the jth group of transmitting and receiving spacing, j = 1, 2, 3…m-1; According to the propagation equation under different transmit-receive spacing, the corresponding least squares cost function is: Where m represents the number of A-scan channels measured by the ground penetrating radar, n represents the number of layers of the layered medium, c represents the speed of light, and L j represents the spacing between the transmitting and receiving antennas in the jth A-scan, j = 1, 2, 3…m-1, ε ri,j ,d i,j They represent the relative dielectric constant and thickness of the i-th layer of the layered medium under the j-th A-scan, i = 1, 2, 3…n, x i,j represents the position of the refraction point at the i-th layer interface under the j-th A-scan, Δt i,j It represents the propagation time difference between the reflected wave from the interface of layer i and the direct wave from the air under the j-th A-scan; The least squares cost function based on Snell's law is: Where x1 represents the refraction point position of the first layer interface, and d1 represents the thickness of the first layer of medium.
2. The method according to claim 1, wherein The cost function for medium parameter inversion is established by combining the propagation equation and Snell's law. Specifically, the total cost function of the hierarchical model is obtained by combining two types of cost functions based on the propagation equation and Snell's law: d(e rn ,d n ,x 1,1 ,...,x n,m )=a1δ1(ε rn ,d n ,x 1,1 ,...,x n,m )+a2δ2(ε rn ,d n ,x 1,1 ,...,x n,m ) Among them, a1, a2 are adjustable parameters that control the ratio of the two types of cost functions, x 1,1 ,...,x n,m represents the set of refraction point positions at each layer interface under different A-scans, ε rn ,d n Represents the relative dielectric constant and thickness of the nth layer of layered medium.