Method for optimizing imperfect lossy ground penetrating radar based on antenna

Abstract

The invention relates to the technical field of ground penetrating radars, and discloses an antenna-based imperfect lossy ground penetrating radar optimization method, which comprises the steps of performing time domain analysis on center transient current of an antenna based on a space-time Helen integral equation in combination with the influence of an air-earth interface, and constructing a transient current response model; a plurality of influence variables are randomly extracted by adopting an uncertainty quantification method, each influence variable is valued for multiple times and substituted into the transient current response model to be solved, and a simulation value of the total current of a plurality of antennas is obtained; calculating a statistical value of the analog value of the total current of the plurality of antennas; and generating a confidence interval corresponding to each influence variable by using the plurality of statistical values. According to the method, the influence degree of each influence variable on the ground penetrating radar in the imperfect lossy ground is judged through the confidence interval, the weight value of the influence of each influence variable on the ground penetrating radar is set, and the optimization of the ground penetrating radar on the imperfect lossy ground is realized.

Description

Technical Field

[0001] The invention relates to the technical field of ground penetrating radar, and in particular to an optimization method for an antenna-based imperfect lossy ground penetrating radar. Background Art

[0002] Ground Penetrating Radar (GPR) is a non-invasive geophysical detection technology that is used to obtain images and information of underground structures by emitting radar waves and measuring their reflection in underground structures. The basic principle of this technology is that when radar waves pass through underground materials, they will reflect with materials with different dielectric constants to form echo signals. By analyzing these signals, a profile of the underground structure can be created to show the distribution of various geological layers and materials. GPR systems usually include transmitting and receiving antennas. By recording the time delay and amplitude of the echo signal, the nature and depth of the underground structure can be inferred. GPR is widely used in civil engineering, archaeology, environmental monitoring and geological exploration, and is used to detect underground pipelines, cables, ancient sites, groundwater levels and rock structures.

[0003] During operation, GPR generates a profile with depth as the horizontal axis and electromagnetic wave propagation speed as the vertical axis to form a time-depth graph. These graphs provide an intuitive view of the underground structure. Different geological layers and materials have different effects on the reflection and propagation speed of electromagnetic waves, allowing GPR graphs to provide detailed information about underground structures.

[0004] However, the effectiveness of GPR is affected by the underground medium. The propagation speed of electromagnetic waves in different materials depends mainly on the dielectric constant. Therefore, highly conductive materials or highly hygroscopic soils may limit the penetration of signals. In addition, the detection depth of GPR is limited by the frequency of the device and the characteristics of the underground medium, so its effectiveness may vary under different specific geological conditions.

[0005] The present invention focuses on the performance analysis of ground penetrating radar (GPR) systems, especially the study of the effects of imperfect and destructive ground on the performance of GPR systems. GPR systems are of great significance in civil engineering applications and are used for non-destructive detection of underground structures and strata. In practical applications, GPR systems often face challenges of environmental changes, such as imperfect or layered ground, partial or complete unknowns of parameters such as antenna height, which may lead to rejection of measurement data and affect the accuracy of the system. Summary of the invention

[0006] The present invention aims to at least solve the technical problem that the prior art lacks research on the impact of imperfect and destructive ground on GPR performance.

[0007] To this end, an object of the present invention is to propose an antenna-based imperfect lossy ground penetrating radar optimization method, comprising:

[0008] Combined with the influence of the air-earth interface, the transient current of the center of the antenna is analyzed in the time domain based on the space-time Heron integral equation, and a transient current response model is constructed;

[0009] Adopting an uncertainty quantification method, randomly extracting multiple influencing variables, taking multiple values ​​of each influencing variable, substituting them into the transient current response model for solving, and obtaining simulated values ​​of the total current of multiple antennas;

[0010] Calculating statistical values ​​of the simulated values ​​of the total currents of the plurality of antennas;

[0011] Generating confidence intervals corresponding to the influencing variables using a plurality of the statistical values;

[0012] According to the confidence intervals corresponding to the influencing variables, the influence degree of each influencing variable on the ground penetrating radar in the imperfect lossy ground is judged, and the weight value of each influencing variable on the ground penetrating radar is set to achieve the optimization of the ground penetrating radar on the imperfect lossy ground.

[0013] Furthermore, an uncertainty quantification method is used to randomly extract multiple influencing variables, and each influencing variable is taken multiple times, and is substituted into the transient current response model for solution to obtain multiple simulated values ​​of the total current of the antenna, including:

[0014] A plurality of influencing variables are randomly selected, each of which takes values ​​multiple times according to a set probability distribution rule, and is substituted into the transient current response model to solve the simulated value of the total antenna current.

[0015] Furthermore, each influencing variable is multiplexed according to a set probability distribution law and substituted into the transient current response model, and the simulated values ​​of the total currents of multiple antennas are obtained by solving the model using the Bubnov-Galerkin method (Galerkin-Bubnov indirect boundary element method, GB-IBEM for short).

[0016] Furthermore, the probability distribution law is set to be a standard normal distribution or a uniform distribution.

[0017] Furthermore, combined with the influence of the air-earth interface, the transient current of the center of the antenna is analyzed in the time domain based on the space-time Heron integral equation, and a transient current response model is constructed, including:

[0018] The influence of the air-earth interface is considered by approximating the spatiotemporal Fresnel reflection coefficient, and the influence of the ground is considered by the reflection coefficient function r(θ, t):

[0019]

[0020] in:

[0021]

[0022] Where t is time; h is the height of the antenna; δ(t) is the Dirac pulse, I n (t) is the first kind nth order modified Bessel function; ε r is the relative dielectric constant; σ is the soil conductivity; x is the observation point; x' is the source point; soil conductivity; ε is the vacuum dielectric constant; K, α and β are all intermediate variables and have no real meaning; θ is the angle of incidence.

[0023] Furthermore, combined with the influence of the air-earth interface, the transient current of the center of the antenna is analyzed in the time domain based on the space-time Heron integral equation, and a transient current response model is constructed, including:

[0024] The calculation formula of the model is as follows:

[0025]

[0026] Where I is the simulated value of the total current of the antenna; c is the speed of light, Z 0 is the free space wave impedance, R represents the actual distance between the observation point x and the source point x'; R* represents the distance on the image line between the observation point x and the source point x'; F 0 and F L The function that characterizes the effect of multiple reflections at both ends of the antenna is determined by setting the current at the end of the antenna to zero; L is the length of the antenna; t is the time; is the tangential incident electric field; r(θ, t) is the reflection coefficient function; θ is the incident angle; τ is the integral operator symbol and has no real meaning.

[0027] Furthermore, the influencing variables include soil conductivity and antenna height.

[0028] Furthermore, the influencing variables also include soil type, humidity and salt content.

[0029] Furthermore, the statistical value includes mean, variance and standard deviation.

[0030] Furthermore, the confidence interval is equal to the mean ± 3 standard deviations.

[0031] The present invention provides an antenna-based imperfect lossy ground penetrating radar optimization method, which has the following beneficial effects:

[0032] The present invention models the transient current of the antenna to study the impact of imperfect and lossy ground on the performance of the GPR system. The present invention uses the space-time Hallen integral equation and solves it through the Bubnov-Galerkin method to provide an accurate time domain calculation tool for the performance of the system.

[0033] In order to more comprehensively understand the performance of the GPR system under environmental changes, the present invention adopts random technology, including the stochastic collocation (SC) method. By introducing influencing variables, such as soil conductivity and conductor height, the influence of these environmental parameters on the performance of the GPR system is studied. Each influencing variable is taken multiple times according to the set probability distribution law, and is introduced into the model to repeatedly solve the total antenna current, thereby generating multiple simulated values ​​of the total antenna current, and then the statistical data related to GPR detection (such as mean, variance, skewness, etc.) are obtained, so as to establish a reliable confidence interval, and the degree of influence of each influencing variable on the GPR performance in the destructive ground environment is judged through the confidence interval, and the weight value of each influencing variable on the ground penetrating radar is set according to the degree of influence, so as to achieve the optimization design of the non-perfect destructive ground ground penetrating radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0035] Figure 1 It is a flow chart of an antenna-based imperfect lossy ground penetrating radar optimization method in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] Various aspects and features of the present invention are described herein with reference to the accompanying drawings.

[0037] It should be understood that various modifications may be made to the embodiments of the present application. Therefore, the above description should not be considered as limiting, but only as an example of the embodiments. Other modifications within the scope and spirit of the present invention will occur to those skilled in the art.

[0038] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention and, together with the general description of the invention given above and the detailed description of the embodiments given below, serve to explain the principles of the invention.

[0039] These and other characteristics of the invention will become apparent from the following description of a preferred form of embodiment given as a non-limiting example, with reference to the accompanying drawings.

[0040] It should also be understood that, although the invention has been described with reference to some specific examples, those skilled in the art will be able to realize many other equivalent forms of the invention that have the characteristics recited in the claims and are therefore within the scope of protection defined thereby.

[0041] The above and other aspects, features and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings.

[0042] Specific embodiments of the present invention are described hereinafter with reference to the accompanying drawings; however, it should be understood that the embodiments claimed are merely examples of the present invention, which may be implemented in a variety of ways. Well-known and / or repeated functions and structures are not described in detail to avoid obscuring the present invention with unnecessary or redundant details. Therefore, the specific structural and functional details claimed herein are not intended to be limiting, but merely serve as a basis and representative basis for the claims to teach those skilled in the art to use the present invention in a variety of ways with substantially any suitable detailed structure.

[0043] In the description of the present invention, the description with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0044] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

[0045] Example

[0046] like Figure 1 As shown, this embodiment provides an antenna-based imperfect lossy ground penetrating radar optimization method, comprising the following steps:

[0047] Step S1: combining the influence of the air-earth interface, performing time domain analysis on the central transient current of the antenna based on the space-time Hallen integral equation, and constructing a transient current response model;

[0048] Step S2: using uncertainty quantification (UQ) method, randomly extracting multiple influencing variables, each influencing variable is substituted into the transient current response model in step S1 after taking a value according to a set probability distribution law, and solving the simulation values ​​of the total currents of multiple antennas by Bubnov-Galerkin method (Galerkin-Bubnov indirect boundary element method, referred to as GB-IBEM);

[0049] The simulated value of the total antenna current, that is, the total amount of current flowing through the antenna cross section at a certain time and position;

[0050] Step S3: Calculating statistical values ​​of the simulated values ​​of the total current of the antennas;

[0051] Step S4: using the statistical value to generate a confidence interval corresponding to each of the influencing variables;

[0052] Step S5: According to the confidence intervals corresponding to the influencing variables, the influence degree of each influencing variable on the ground penetrating radar in the imperfect lossy ground is obtained, and the weight value of each influencing variable on the ground penetrating radar is set to optimize the ground penetrating radar in the imperfect lossy ground.

[0053] Heron's equation is the core mathematical model for calculating the transient current response of an antenna above a lossy ground. This equation describes the temporal and spatial variations of the transient current on an antenna when it is excited by an external electric field (such as electromagnetic waves), involving multiple physical parameters such as the propagation speed of electromagnetic waves, the length of the wire, and the distance between the wire and the ground. The total antenna current in the model is the target to be solved, which can evaluate the performance of the GPR (such as electromagnetic wave propagation and reflection), and its value is affected by environmental factors around the wire (such as soil conductivity and antenna height). These factors usually have certain uncertainties in practical applications, so only the deterministic solution of Heron's equation may not accurately describe the behavior of the system in a complex environment.

[0054] The influencing variables represent the uncertain factors in the environment, such as soil conductivity and antenna height. These variables will affect the total antenna current, and ultimately affect the output of the GPR system. The present invention takes values ​​of each influencing variable multiple times according to the set probability distribution law, and introduces them into the model to repeatedly solve the total antenna current, thereby generating multiple simulated values ​​of the total antenna current, and then derives statistical data related to GPR detection (such as mean, variance, skewness, etc.), thereby establishing a reliable confidence interval, thereby realizing the analysis of the impact of these uncertain factors on the total antenna current, and then realizing the evaluation of the impact of the lossy ground environment on the GPR performance.

[0055] This method uses uncertainty quantification methods to provide more reliable statistical analysis, which can analyze the impact of different influencing variables on the GPR system and realize the performance evaluation of the GPR system under destructive ground conditions.

[0056] In step S1, the calculation formula of the model is as follows:

[0057]

[0058] Where I is the simulated value of the total current of the antenna; c is the speed of light, Z 0 is the free space wave impedance, R represents the actual distance between the observation point x and the source point x'; R* represents the distance on the image line between the observation point x and the source point x'; F 0 and F L The function that characterizes the influence of multiple reflections at both ends of the antenna is determined by substituting boundary conditions into the model, that is, it can be determined by assuming that the current at the end of the antenna is zero; L is the length of the antenna; t is the time; is the tangential incident electric field; r(θ, t) is the reflection coefficient function; θ is the incident angle, that is, the angle at which the electromagnetic wave is incident on the ground; τ is the integral operator symbol and has no real meaning;

[0059] According to another specific embodiment of the present invention, in step S1, the influence of the air-earth interface is considered by approximating the spatiotemporal Fresnel reflection coefficient, and the influence of the ground is considered by the reflection coefficient function r(θ, t):

[0060]

[0061] in:

[0062]

[0063] Where h is the height of the antenna; δ(t) is the Dirac pulse, I n (t) is the first kind nth order modified Bessel function; ε r is the relative dielectric constant; σ is the soil conductivity; ε is the vacuum dielectric constant; K, α and β are all intermediate variables and have no real meaning.

[0064] According to another specific embodiment of the present invention, in step S2, an uncertainty quantification (UQ) method is used to randomly extract multiple influencing variables, and the multiple influencing variables are respectively brought into the model in step S1 for calculation to obtain multiple simulation values ​​of the total antenna current corresponding to the influencing variables one by one, including: using the Galerkin-Bubnov indirect boundary element method to solve the model in step S1.

[0065] The uncertainty quantification method is preferably a random collocation (SC) method: by selecting a number of sigma points, the influencing variables are sampled to perform numerical simulations on the current response.

[0066] According to another specific embodiment of the present invention, in step S2, the influencing variables include soil conductivity, antenna height, soil type, humidity and salt content.

[0067] In order to better deal with the uncertainty of influencing variables in a destructive ground environment, the random collocation (SC) method is used to select influencing variables as random variables, and it is assumed that the random variables take values ​​according to a certain set probability distribution law, such as normal distribution, so that the generated confidence interval is more credible.

[0068] According to another specific embodiment of the present invention, a detailed description is given, where the antenna length L=1m, the antenna height from the ground h=0.5m, the antenna radius a=0.002m, and only the soil conductivity is randomly distributed. Considering the antenna height and the soil conductivity:

[0069] Single variable case. First, assuming that the soil conductivity is uniformly distributed between 100 and 10000 mS / m, multiple soil conductivity values ​​are achieved by increasing the number of required sigma points according to the uncertainty quantification principle relationship in order to calculate the mean and standard deviation of the simulated values ​​of the total antenna current.

[0070] Multiple random variable case. Soil conductivity and wire height are randomly distributed according to the random situation, that is, the calculation of the single variable case is repeated twice.

[0071] The present invention enhances competitive experimental design by reducing the number of input data points. Relative to the assumed physical problem, the current I ([I]u, where u represents a given statistical moment) induced at the center of the ground penetrating radar antenna above the destructive ground is calculated under a carefully selected basis function Φ u (X) is expanded depending on the statistical order u) as follows:

[0072]

[0073] in, represents the expansion weight of a random vector X with dimension N (X=(X 1 ,X 2 ,…,X N )T, thus modeling the N random components or parameters of the problem. w +1 sigma point in the random matching method (according to the random matching method n w The random component X is calculated in a direct way w The necessity of; the number of sigma points, that is, the number of sampling points.

[0074] The following table gives the calculation results of the 1st to 4th order statistical moments (e.g., from mean to kurtosis) involving only one influencing variable. Without loss of generality, similar expressions can be obtained for the case of multiple influencing variables (according to the above [I] u Relationship, N>1).

[0075]

[0076] When using the statistical moment given by the random collocation method with 1 influencing variable:

[0077]

[0078] The weight of an influencing variable distributed according to the standard normal law Sigma Point I i :

[0079]

[0080] The table above presents an overview of the points / weights required for the case of a single influencing variable (e.g. following a standard normal distribution). The case involving multiple influencing variables can be constructed directly with the tensor product (including each influencing variable). The previous set of points can be extended to the values ​​provided in the numerical application (one or two influencing variables) including the chosen statistical distribution. Since the introduction of the sigma points is achieved non-intrusively, the numerical results are obtained directly via the Bubnov-Galerkin method.

[0081] According to another specific embodiment of the present invention, in step S4, the statistical values ​​include mean, variance, skewness and kurtosis.

[0082] In step S5, the confidence interval is calculated by using statistical data such as variance. The mean defines the central trend of the total antenna current, and the standard deviation represents the fluctuation range of the system output around the mean. On this basis, a practical confidence interval can be generated to represent the possible output range of the system under random input. The specific confidence interval is the mean ± 3 standard deviations, which means that within the range of variation of the influencing variables, more than 95% of the simulated values ​​of the total antenna current will fall within this interval.

[0083] The confidence interval can reflect the statistical distribution of the GPR system output and provide statistical significance for the results. For example, in GPR detection, the confidence interval can show how the current response of the GPR system changes under different random input conditions. The confidence interval helps to understand the overall behavior of the system and can also help identify extreme situations, thereby providing a reference for the design and application of the GPR system. If the confidence interval is too large, it means that the system output fluctuates greatly under the influence of the influencing variables, and it may be necessary to optimize the system or increase the accuracy of the data. If the confidence interval is small, it means that the system output is relatively stable, and more accurate decisions can be made based on this range.

[0084] In summary, confidence intervals of the GPR system under different random conditions are generated, which is of great significance for evaluating the reliability and accuracy of the system.

[0085] According to another specific embodiment of the present invention, in archaeology, ground penetrating radar is a commonly used non-destructive detection technology for detecting underground structures, such as tombs, ancient architectural remains, cultural relics, etc. Since the ground conditions at the archaeological site are complex and changeable, including soil type, humidity, salt content, etc., these factors will affect the detection effect of GPR. Therefore, the transient current response model proposed in this article, combined with the random method, can effectively deal with these uncertain factors and improve the accuracy and reliability of GPR detection.

[0086] The constructed transient current response model is as follows:

[0087]

[0088] Where I is the simulated value of the total current of the antenna; c is the speed of light, Z 0 is the free space wave impedance, R is the actual distance between the observation point x and the source point x'; R* is the distance on the image line between the observation point x and the source point x'; t is the time; is the tangential incident electric field; r(θ, t) is the reflection coefficient function; τ is the integral operator symbol and has no real meaning.

[0089] In the application scenario of archaeological detection, we can assume that:

[0090] The length, height and radius of the antenna are known.

[0091] The electrical conductivity of the soil is an influencing variable because it is affected by factors such as soil type and moisture.

[0092] In order to deal with the uncertainty of soil conductivity, the Stochastic Collocation (SC) method mentioned in the paper is used. For example, if the soil conductivity S is unknown at the archaeological site and may vary within a certain range, it is assumed that the soil conductivity follows a uniform distribution, and its range is [s min ,s max ], where S max is the maximum value of soil conductivity, S min The minimum value of soil conductivity. Then, the soil conductivity is taken multiple times, the simulated value of the total antenna current is calculated, and the confidence interval is obtained to optimize the GPR performance.

[0093] The present invention realizes accurate modeling of the center current of the ground penetrating radar antenna line above the lossy ground by combining analytical and deterministic time modeling based on the space-time Hallen integral equation and the influence of the air-earth interface. This innovation provides a reliable theoretical basis for more accurate analysis of underground structures in GPR technology. Compared with traditional numerical modeling methods, analytical and deterministic time modeling is more intuitive and computationally efficient, laying the foundation for further optimization of GPR technology.

[0094] The present invention introduces the uncertainty quantification principle, quantifies uncertainty through random matching, expands the antenna center current on a carefully selected basis function, and considers the randomness of soil conductivity and antenna height, so that GPR technology can more comprehensively consider the uncertainty of underground structures, providing an effective analysis tool for random factors in practical application scenarios. The introduction of uncertainty quantification helps to more accurately evaluate the confidence interval of GPR measurements and improves the reliability and practicality of the technology.

[0095] This invention expands the consideration of single parameters in traditional GPR technology by studying the situation of multiple influencing variables, including the random distribution of soil conductivity and antenna height, and analyzing the statistical characteristics of antenna current through random matching method, and more comprehensively considers the influence of multiple random variables on current response. In practical applications, underground structures are often affected by multiple factors. This innovation improves the applicability and accuracy of GPR technology in complex environments.

[0096] Through comprehensive analysis, including analytical modeling, uncertainty quantification, and research on multiple random variable scenarios, the present invention provides a more comprehensive consideration for the actual application scenarios of GPR technology, applies the technology to civil engineering, archaeology, environmental monitoring and other fields, considers the needs of different fields, optimizes the settings and parameters of the GPR system, makes GPR technology closer to practical applications, and improves its practicality and applicability in complex environments.

Claims

1. An antenna-based imperfect lossy ground penetrating radar optimization method, characterized in that: include: Combined with the influence of the air-earth interface, the transient current of the center of the antenna is analyzed in the time domain based on the space-time Heron integral equation, and a transient current response model is constructed; Adopting an uncertainty quantification method, randomly extracting multiple influencing variables, taking multiple values ​​of each influencing variable, substituting them into the transient current response model for solving, and obtaining simulated values ​​of the total current of multiple antennas; Calculating statistical values ​​of the simulated values ​​of the total currents of the plurality of antennas; Generating confidence intervals corresponding to the influencing variables using a plurality of the statistical values; According to the confidence intervals corresponding to the influencing variables, the influence degree of each influencing variable on the ground penetrating radar in the imperfect lossy ground is judged, and the weight value of each influencing variable on the ground penetrating radar is set to achieve the optimization of the ground penetrating radar on the imperfect lossy ground.

2. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 1, characterized in that: By adopting the uncertainty quantification method, multiple influencing variables are randomly selected, and each influencing variable is taken multiple times, and is substituted into the transient current response model for solution to obtain the simulated values ​​of the total current of multiple antennas, including: A plurality of influencing variables are randomly selected, each of which takes values ​​multiple times according to a set probability distribution rule, and is substituted into the transient current response model to solve the simulated value of the total antenna current.

3. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 2, characterized in that: Each influencing variable is multiplexed according to a set probability distribution rule and substituted into the transient current response model, and the simulated values ​​of the total currents of multiple antennas are obtained by solving the Bubnov-Galerkin method.

4. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 2, characterized in that: The probability distribution law is set to standard normal distribution or uniform distribution.

5. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 1, characterized in that: Combined with the influence of the air-earth interface, the transient current of the center of the antenna is analyzed in the time domain based on the space-time Heron integral equation, and a transient current response model is constructed, including: The influence of the air-earth interface is considered by approximating the spatiotemporal Fresnel reflection coefficient, and the influence of the ground is considered by the reflection coefficient function r(θ, t): in: Where t is time; h is the height of the antenna; δ(t) is the Dirac pulse, I n (t) is the first kind nth order modified Bessel function; ε r is the relative dielectric constant; σ is the soil conductivity; x is the observation point; x' is the source point; soil conductivity; ε is the vacuum dielectric constant; K, α and β are all intermediate variables and have no real meaning; θ is the angle of incidence.

6. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 5, characterized in that: Combined with the influence of the air-earth interface, the transient current of the center of the antenna is analyzed in the time domain based on the space-time Heron integral equation, and a transient current response model is constructed, including: The calculation formula of the model is as follows: Where I is the simulated value of the total antenna current; c is the speed of light, Z0 is the free space wave impedance, R is the actual distance between the observation point x and the source point x'; R* is the distance on the image line between the observation point x and the source point x'; F0 and F L This is a function that characterizes the effects of multiple reflections at both ends of the antenna, and is determined by setting the current at the end of the antenna to zero; L is the length of the antenna; t is the time; is the tangential incident electric field; r(θ, t) is the reflection coefficient function; θ is the incident angle; τ is the integral operator symbol and has no real meaning.

7. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 1, characterized in that: The influencing variables include soil conductivity and antenna height.

8. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 7, characterized in that: The influencing variables also include soil type, moisture and salt content.

9. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 1, characterized in that: The statistical values ​​include mean, variance and standard deviation.

10. The antenna-based imperfect lossy ground penetrating radar optimization method according to claim 9, characterized in that: The confidence interval is equal to the mean ± 3 standard deviations.

Images