Ground penetrating radar imaging method and system

Abstract

The invention discloses a ground penetrating radar imaging method and system, relates to the technical field of ground penetrating radars, and solves the problem that complex electromagnetic characteristics of an underground detection domain are difficult to accurately represent in the traditional technology. According to the method, the equivalent dielectric constant is calculated, so that the problem of phase distortion caused by the traditional homogeneous medium hypothesis in the underground detection of the non-homogeneous medium is solved, the electromagnetic waves can still keep the accurate expression of the propagation path in the non-homogeneous medium, and the accurate characterization of the complex electromagnetic characteristics of the underground detection domain is realized; meanwhile, by detecting the vertical incidence hypothesis of the electromagnetic wave signal, the electromagnetic wave propagation path can be simplified, a non-uniform medium incidence field which is difficult to analyze and calculate is simplified into an equivalent uniform medium incidence field which can be analyzed and expressed, and the calculation complexity of an inversion reflectivity function is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ground penetrating radar, and in particular to a ground penetrating radar imaging method and system. BACKGROUND

[0002] In application scenarios such as underground structure health monitoring, underground pipeline detection, and hydrogeological exploration, electromagnetic wave detection technology has been widely used due to its high efficiency, non-destructive, and other characteristics.

[0003] However, the non-uniformity of underground media such as soil causes electromagnetic waves to reflect, refract, and scatter multiple times during propagation, resulting in disordered propagation paths. At the same time, the wave impedance of non-uniform underground media has a sudden change phenomenon, which not only causes the attenuation of electromagnetic wave signal strength, but also may cause signal distortion, affecting the accuracy of target echoes.

[0004] Traditional underground detection methods often simplify the dielectric constant as a uniform or layered model when dealing with medium characteristics. In the uniform model, it is assumed that the dielectric constant of the medium in the entire detection area is a constant single value, ignoring the subtle differences and local changes within the medium. This simplified processing method, when faced with real underground environments, due to the randomness of factors such as soil particle size, shape, arrangement, and water content, porosity, etc. at different positions, the dielectric constant of the soil presents continuous changes at the microscopic scale, and the traditional model cannot capture these details, making it difficult to accurately represent the complex electromagnetic characteristics of the actual soil.

[0005] In view of this, there is a need for a ground penetrating radar imaging method and system. SUMMARY

[0006] To solve the problem that the prior art cannot accurately represent the complex electromagnetic characteristics of the underground detection domain, the present application provides a ground penetrating radar imaging method and system, which can improve the representation accuracy of the complex electromagnetic characteristics of the underground detection domain. The specific technical solutions are as follows: In a first aspect, the present application provides a ground penetrating radar imaging method, comprising: The scattering signal of the underground target and the depth-soil dielectric constant data of a detection domain where the underground target is located are acquired, the scattering signal being a return signal of the underground target based on a detection electromagnetic wave signal transmitted by a transmitting antenna; based on the depth-soil dielectric constant data, an equivalent dielectric constant is calculated; based on the assumption that the underground target is vertically below the transmitting antenna and the equivalent dielectric constant, a reflectivity function to the scattering signal is constructed; wherein the reflectivity function is used to quantify the influence of the difference in electromagnetic properties between the underground target and the soil medium in the detection domain on electromagnetic wave reflection, and the linear operator is used to describe the mapping of the reflectivity function to the scattering signal; based on the linear operator and the scattering signal, the reflectivity function is inverted by a regularization inversion algorithm; and based on the reflectivity function, a ground penetrating radar profile is generated.

[0007] Preferably, the linear operator of the reflectivity function to the scattering signal is constructed based on the assumption that the underground target is vertically below the transmitting antenna and the equivalent dielectric constant, which includes: dividing the detection domain into M non-overlapping grid cells; representing the scattering signal in a discrete matrix in units of the grid cells to obtain a first matrix corresponding to the scattering signal; each element in the first matrix corresponds to a grid cell; and based on the first matrix, a third matrix corresponding to the linear operator is calculated.

[0008] Preferably, the reflectivity function is inverted by the regularization inversion algorithm based on the linear operator and the scattering signal, which includes: singular value decomposition of the third matrix to obtain a singular spectrum of the linear operator; and based on the singular spectrum of the linear operator and a second corresponding to the scattering signal, the reflectivity function is inverted by a truncated singular value decomposition inversion method.

[0009] Preferably, the calculation formula of the reflectivity function inverted by the truncated singular value decomposition inversion method includes: ; wherein, is the reflectivity function inverted, x and z are horizontal displacement and depth displacement respectively, is a truncation index, n is an index of singular values, is a scattering signal, are singular values in the singular spectrum, an orthogonal norm basis of a data space, and an orthogonal norm basis of an unknown space respectively.

[0010] Preferably, the ground penetrating radar profile is generated based on the reflectivity function, which includes: based on the reflectivity function, the equivalent dielectric constant and the electromagnetic wave propagation time, a correspondence between coordinates and reflectivity in the detection domain is established; and based on the correspondence between coordinates and reflectivity in the detection domain, the ground penetrating radar profile is generated.

[0011] Preferably, an equivalent permittivity between the transmitting antenna and the underground target is a first constant, an equivalent permittivity of an area where the underground target is located is a second constant, and the first constant and the second constant are different.

[0012] Preferably, the calculating the equivalent permittivity based on the depth-soil permittivity data comprises: calculating the equivalent permittivity based on the depth-soil permittivity data by a fitting method or a numerical integral method.

[0013] In a second aspect, an embodiment of the present application provides a ground penetrating radar imaging system, applied to the method in the first aspect, and the system comprises: An acquisition module is configured to acquire a scattering signal of an underground target and depth-soil permittivity data of a detection domain where the underground target is located, the scattering signal being a return signal of the underground target based on a detection electromagnetic wave signal sent by a transmitting antenna; A calculation module is configured to calculate an equivalent permittivity based on the depth-soil permittivity data by an average equivalent method; A construction module is configured to construct a reflectivity function to a linear operator of the scattering signal based on an assumption that the underground target is vertically below the transmitting antenna and the equivalent permittivity, wherein the reflectivity function is used to quantify an electromagnetic characteristic difference between the underground target and soil medium in the detection domain, and the linear operator is used to describe a mapping of the reflectivity function to the scattering signal; An inversion module is configured to invert the reflectivity function based on the linear operator and the scattering signal by a regularization inversion algorithm; A generation module is configured to generate a ground penetrating radar profile based on the reflectivity function.

[0014] In a third aspect, an embodiment of the present application provides a computing device, comprising: a memory configured to store a program; and a processor configured to load the program to execute the method in the first aspect.

[0015] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, comprising a stored program, wherein the program controls a device where the computer readable storage medium is located to execute the method in the first aspect when the program is running.

[0016] Compared with the prior art, the beneficial effects of the present application are: by calculating the equivalent dielectric constant, the phase distortion problem caused by the traditional uniform medium assumption in non-uniform medium underground detection is solved, so that the electromagnetic wave can still maintain the accurate expression of the propagation path in the non-uniform medium, and the accurate characterization of the complex electromagnetic characteristics of the underground detection domain is realized; at the same time, by detecting the vertical incidence assumption of the electromagnetic wave signal, the electromagnetic wave propagation path can be simplified, the non-uniform medium incident field which is difficult to analytically calculate is simplified into an analytically expressed equivalent uniform medium incident field, and the calculation complexity of the inversion reflectivity function is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the specific embodiments or prior art description will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, each element or part is not necessarily drawn according to the actual proportion.

[0018] Figure 1 A flowchart of a ground penetrating radar imaging method provided by an embodiment of the present application is shown in the figure; Figure 2 A schematic diagram of a ground penetrating radar detecting an underground target provided by an embodiment of the present application is shown in the figure; Figure 3 A structural schematic diagram of a ground penetrating radar imaging system provided by an embodiment of the present application is shown in the figure; Figure 4 A structural schematic diagram of a computing device provided by an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0019] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0020] It should be understood that when used in the present specification and the appended claims, the terms "comprise" and "include" indicate the presence of the described features, integers, steps, operations, elements, and / or components, but do not exclude one or more other features, integers, steps, operations, elements, components, and / or sets thereof.

[0021] It should also be understood that the terms used in the specification of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the specification and the appended claims of the present application, the singular forms "a," "an," and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0022] It should be further understood that the term "and / or" used in the specification and the appended claims of the present application means any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0023] To solve the problem that the conventional technology is difficult to accurately characterize the complex electromagnetic characteristics of the underground exploration domain, the present application provides a ground penetrating radar imaging method and system, which can improve the accuracy of characterization of the complex electromagnetic characteristics of the underground exploration domain.

[0024] Please refer to Figure 1 , Figure 1 A flowchart of a ground penetrating radar imaging method is provided for the embodiments of the present application, which is applied to a computing device; as shown in Figure 1 The method comprises the following steps: Step 101, the computing device acquires the scattering signal of the underground target and the depth-soil dielectric constant data of the exploration domain where the underground target is located.

[0025] The computing device can be a terminal or a server, and the server can be a blade server, a high-density server, a rack-mounted server, a cabinet-mounted server, a general-purpose server, a graphics processing unit (GPU) server, a data processing unit (DPU) server, or an artificial intelligence (AI) server, etc. The terminal can be a personal computer, a notebook computer, a smart phone, a tablet computer, an Internet of Things device, a portable wearable device, and other devices with data processing capabilities.

[0026] The scattering signal includes the echo signal generated by the underground target based on the detection electromagnetic wave signal sent by the transmitting antenna.

[0027] For details, please refer to Figure 2 , Figure 2 A schematic diagram of a ground penetrating radar detecting an underground target is provided for the embodiments of the present application, Figure 2 The two-dimensional geometric shape in For simplicity, the soil medium is assumed to be lossless, non-dispersive, non-magnetic and non-homogeneous, whose relative permittivity varies along the depth z-axis, i.e. .

[0028] The detection domain D is probed by ground penetrating radar in a multi-antenna and multi-frequency configuration. Wherein, the transmitting antenna and the receiving antenna with negligible horizontal offset move along the x-axis on the air-soil interface; the transmitting antenna radiates an ultra-wideband pulse to the detection domain, and the receiving antenna records the scattering signal scattered by the underground target. Both the transmitting antenna and the receiving antenna are modeled as being polarized along the y-axis, and the angular frequency of the ultra-wideband pulse is in the interval Ω=[min,max]. min, max].

[0029] Specifically, when the ultra-wideband pulse encounters the underground target, part of the energy will be reflected, refracted or diffused by the target to form a return, i.e. a scattering signal; the shape, material, position, etc. of the underground target will be encoded into the scattering signal.

[0030] For example, the underground target includes underground pipelines, underground structures and underground water flow.

[0031] Specifically, the computing device can obtain the scattering signal received by the receiving antenna in real time through wired or wireless communication connection with the receiving antenna; or obtain the scattering signal from other devices, storage media or network databases.

[0032] Wherein, the detection domain where the underground target is located is a region to be determined in advance; since in ground penetrating radar imaging, the ground penetrating radar profile presents the electromagnetic property distribution of the underground medium in two-dimensional form, the horizontal axis usually represents the horizontal distance of the detection, and the vertical axis corresponds to the underground depth, therefore when performing correlation calculation of ground penetrating radar data, the computing device models both the transmitting antenna and the receiving antenna as being polarized along the y-axis, which can simplify the model while ensuring that the scattering signal received by the receiving antenna corresponds to the matching of the detection electromagnetic wave signal transmitted by the transmitting antenna. Therefore, the detection domain can be represented as a two-dimensional plan view as shown in Figure 2 .

[0033] Wherein, the underground target in the detection domain D exists a reflectivity function r(x,z) which considers the local variation of the electromagnetic properties of the underground target relative to the soil medium.

[0034] Wherein, the depth-soil permittivity data is the known distribution of the soil permittivity with depth in the detection domain. The depth-soil permittivity data is obtained by pre-collecting and testing, and is pre-stored in a storage medium or database accessible by the computing device, and the computing device can directly obtain the depth-soil permittivity data from the storage medium or database.

[0035] The computing device performs a pre-processing operation of filtering and denoising, gain compensation and time calibration on the scattering signal after obtaining the scattering signal, so as to perform subsequent calculation.

[0036] It can be understood that in an actual detection scene, the propagation process of the electromagnetic wave not only has a return wave of a direct reflection of the underground target to the receiving antenna, but also has a reflection and scattering between various objects, forming a complex electromagnetic wave superposition effect. This coupling causes the received signal to contain a large amount of redundant information, increasing the difficulty of imaging interpretation. Therefore, the computing device uses a simplified electromagnetic scattering model in subsequent imaging calculation, which uses a linear approximation assumption, that is, assuming that the scattering of electromagnetic waves by various objects in the underground scene is independent, and ignoring the mutual coupling between the objects. By simplifying the complex multi-target scattering problem to linear superposition of independent targets, the calculation difficulty of the imaging algorithm is reduced.

[0037] In step 102, the computing device calculates an equivalent dielectric constant based on the depth-soil dielectric constant data.

[0038] As shown in Figure 2 The equivalent dielectric constant refers to a dielectric constant parameter of an equivalent homogeneous medium, which is given to the equivalent homogeneous medium in the modeling process of replacing the actual curved propagation path of the electromagnetic wave in the inhomogeneous medium with a straight path, so that the phase change corresponding to the straight path is consistent with the phase change of the real curved path, and is used to represent the electromagnetic properties of the equivalent homogeneous medium.

[0039] Preferably, the equivalent dielectric constant between the transmitting antenna and the underground target is a first constant, and the equivalent dielectric constant of the region where the underground target is located is a second constant, and the first constant and the second constant are different.

[0040] The inhomogeneity of the real underground medium often presents a layered feature, and the use of a layered homogeneous equivalent dielectric constant for description can preserve the structure of the real medium while maintaining the simplification advantage of the equivalent model.

[0041] Preferably, the computing device can calculate the equivalent dielectric constant based on the depth-soil dielectric constant data by a fitting method and a numerical integration method.

[0042] The numerical integration includes trapezoidal integration and Simpson integration, which are used to discretize the depth-soil dielectric constant data, and the fitting method includes polynomial fitting and Gaussian process regression, which are used to smooth the depth-soil dielectric constant data containing noise.

[0043] Specifically, the calculation formula of the equivalent dielectric constant includes: ; (1) wherein, Let z be the equivalent dielectric constant, z be the depth, and z' be the integral variable in the depth direction.

[0044] Equivalent dielectric constant Used to consider the location of the antenna. To the detection point Phase change along the propagation path. For example... Figure 2 As shown, the rays emitted by the transmitting antenna are affected by the true dielectric constant of the soil. The change propagates along a curved trajectory underground. In the equivalent dielectric constant model, the curved ray propagation from the transmitting antenna to P is equivalent to a straight ray path.

[0045] As long as the phase change along the curved ray path in the actual scene matches the phase change along the straight path in the equivalent scene, that is: ; (2) in, Represents the propagation constant in free space ( =3×10 8 m / s (corresponding to the speed of light) Measurement point To any point in the detection domain D The distance is denoted by s, where s represents the arc length coordinate along the ray path of the curve. When s=0, the corresponding point is... And arc length coordinates The corresponding point at that time The left side of the equation This represents the equivalent optical path from the Earth's surface to P(x,z) in an equivalent homogeneous medium. The right side... For a real non-uniform medium, the optical path from the surface to depth P(x,z) is equal to the phase change when the two are matched.

[0046] Specifically, the physical meaning of optical path is to equate the actual path in a non-uniform medium to a straight path in a vacuum. The phase change of electromagnetic waves is positively correlated with the optical path; if the optical paths of the two paths are equal, then their phase changes are equal.

[0047] To simplify the calculation of the equivalent dielectric constant, the computing device can assume that the distance between x and xm is very small, i.e., x ≈ xm, such that the propagation of the incident field is essentially perpendicular to the soil interface. Under this assumption, the equivalent dielectric constant is approximated by considering only rays propagating perpendicularly to the incident direction (i.e., propagating along the z-axis), resulting in... = And thus obtain Then divide both sides simultaneously. Square, Divide by z 2 After the calculation, the formula for calculating the equivalent dielectric constant is obtained.

[0048] Step 103, the computing device constructs a reflectivity function to the scattering signal linear operator based on the assumption that the subsurface target is vertically below the transmitting antenna and the equivalent permittivity.

[0049] wherein the reflectivity function is used to quantify the electromagnetic property difference between the subsurface target and the soil medium in the detection domain affecting the electromagnetic wave reflection, and the linear operator is used to describe the mapping of the reflectivity function to the scattering signal.

[0050] wherein, in the case of using a simplified electromagnetic scattering model and ignoring the mutual coupling between different objects, the relationship between the scattering signal and the reflectivity function can be expressed as a linear integral equation: ; (3) wherein, is the scattering signal, is the x-axis coordinate of the transmitting antenna and the receiving antenna with negligible horizontal offset, is the angular frequency of the ultra-wideband pulse, is the Green function, is the incident field signal, and r(x,z) is the reflectivity function.

[0051] wherein the Green function and the incident field signal in the detection domain D have the following relationship: ; (4) wherein j is the imaginary unit, is the vacuum permeability, is the current spectrum associated with the transmitting antenna.

[0052] Combining the above formulas (3), (4), and the layered homogeneous equivalent permittivity model, we can get: ; (5) wherein A is a linear operator describing the mapping of the reflectivity function to the scattering signal, and C is a constant term used to collect all unnecessary constant factors.

[0053] wherein it is assumed that the subsurface target is at least several wavelengths away from the antenna, so that the bulk approximation of the Hankel function is valid.

[0054] Under the premise of formula (1), the incident field in the detection domain D can be simplified by the homogeneous medium Green function to obtain: ; (6) Therefore, under the normal incidence approximation, the phase of the incident field is determined by the equivalent permittivity, and the amplitude decays with the propagation distance R, and the non-essential constant factor has been ignored. Formula (6) is similar to the Wentzel-Kramers-Brillouin approximation (WKB) of a plane wave propagating in a non-uniform medium with a refractive index slowly changing along the propagation direction (z axis).

[0055] In combination with the above formulas (1), (5), and (6), another relationship between the scattering signal and the reflectivity function can be obtained as follows: ; (7) wherein the equivalent permittivity is an analytical expression derived by equivalent path length of the vertical path, and the integral kernel is no longer dependent on the complex non-uniform medium full-wave simulation, but can be analytically calculated or quickly numerically calculated; at this time, the computing device can construct a linear operator A.

[0056] Preferably, the computing device can divide the detection domain into M non-overlapping grid cells; in units of the grid cells, the reflectivity function and the scattering signal are represented in discrete matrices to obtain a first matrix corresponding to the reflectivity function and a second matrix corresponding to the scattering signal; each element in the first matrix and the second matrix corresponds to a grid cell; based on the first matrix, a third matrix corresponding to the linear operator is calculated.

[0057] wherein each grid cell can be denoted as , and the total number of grid cells is M; the grid cell shape is rectangular, and the horizontal step size and the depth step size are less than , is the wavelength of the electromagnetic wave in the equivalent medium to ensure that the details of the reflectivity can be reflected after discretization.

[0058] wherein the reflectivity inside each grid cell is assumed to be the same constant, and the reflectivity of each grid cell can be the same or different, denoted as ; at this time, the continuous function r(x, z) can be discretized into a first matrix r=[ , ,..., ].

[0059] wherein N observation points , i.e., the positions of the receiving antennas, are uniformly spaced on the ground detection line (x axis); the horizontal interval step size is equal to or an integer multiple of the step size of the grid cell. The scattering signal corresponding to each observation point is denoted as ; at this time, the continuous scattering signal can be discretized into a second matrix =[ , ,..., ].

[0060] The process by which the computing device calculates the third matrix based on the first matrix includes: The computing device can first calculate the distance from the grid center point to the observation point. distance Then, substitute the equivalent dielectric constant to calculate the equivalent wavenumber. Then calculate the discrete integral kernel value of the grid cell. Where C is a global constant, This represents the area of ​​a grid cell.

[0061] Then, the elements of the third matrix are assigned: the third matrix A corresponding to the discretized linear operator is an N×M matrix, where the nth row, the... The elements of a column are defined as: A[n, ]= Each row of the third matrix corresponds to the mapping relationship between the scattered field of an observation point and the reflectivity of all grid cells; each column corresponds to the contribution of the reflectivity of a grid cell to the scattered field of all observation points.

[0062] It is understandable that, for the grid cell in the i-th row and j-th column, under the row-major numbering rule, its position index in the one-dimensional vector is... .

[0063] Through the above process, the continuous integral relation can be obtained. =Ar is transformed into discrete linear algebraic equations =Ar.

[0064] This discretization process transforms the integral mapping in the continuous function space into matrix multiplication in the finite-dimensional vector space, enabling the efficient solution of continuous integrals that were previously impossible to calculate directly. This provides a feasible numerical basis for the subsequent inversion of the reflectivity function. Furthermore, a reasonable selection of grid precision and observation point density achieves a balance between computational efficiency and inversion accuracy.

[0065] Step 104: The computing device uses a regularized inversion algorithm to invert the reflectivity function based on the linear operator and the scattering signal.

[0066] The linear inversion problem defined by formula (7) employs the same solution strategy as the classical ground-penetrating radar imaging problem, which assumes that the soil medium is uniformly distributed. Given the ill-posed nature of this problem, a regularization method is needed to find a physical solution in the presence of measurement errors and data noise. Therefore, the computing device can use a truncated singular value decomposition inversion scheme to achieve a regularized solution to the inverse problem.

[0067] Preferably, the computing device can perform singular value decomposition on the third matrix to obtain a singular spectrum of the linear operator; and perform inversion based on the singular spectrum of the linear operator and the scattering signal to obtain the reflectivity function by a truncated singular value decomposition inversion method.

[0068] Preferably, the calculation formula for inverting the reflectivity function by the truncated singular value decomposition inversion method comprises: ; wherein, is the reflectivity function obtained by inversion, x and z are horizontal displacement and depth displacement respectively, is a truncation index, n is an index of singular values, is the scattering signal, are singular values in the singular spectrum, an orthonormal basis of a data space, and an orthonormal basis of an unknown space respectively.

[0069] Specifically, the truncated singular value decomposition can make the inversion result more stable by retaining large singular values and truncating small singular values, and only retaining inversion channels that are energy dominant and insensitive to noise; the truncation index is a regularization parameter, whose value is fixed to find a proper trade-off between accuracy and stability of the solution.

[0070] Step 105, the computing device generates a ground penetrating radar profile based on the reflectivity function.

[0071] Preferably, the computing device can generate the ground penetrating radar profile based on the reflectivity corresponding to each grid cell.

[0072] Preferably, the computing device can establish a correspondence between coordinates and reflectivity in the detection domain based on the reflectivity function, the equivalent permittivity, and the electromagnetic wave propagation time; and generate the ground penetrating radar profile based on the correspondence between coordinates and reflectivity in the detection domain, with horizontal displacement as the horizontal axis, depth displacement as the vertical axis, and reflectivity size encoded by color or grayscale.

[0073] Preferably, the reflectivity function obtained by inversion is essentially a set of discrete numerical values, and the correspondence between coordinates and reflectivity in the detection domain needs to be further calculated; and the ground penetrating radar profile is generated based on the reflectivity corresponding to each spatial coordinate (x, z).

[0074] Specifically, the computing device can arrange the discrete reflectivity numerical values according to their actual spatial coordinates to form a two-dimensional array, with rows corresponding to horizontal positions and columns corresponding to depths, to prepare for subsequent visualization.

[0075] Then, the propagation speed of the electromagnetic wave in the detection domain D is calculated based on the equivalent dielectric constant; since the scattering signal is the double-path time of the electromagnetic wave to the target and back, the corresponding depth z can be converted based on the double-path time of the scattering signal and the propagation speed; then, the reflectivity of the grid unit is mapped to each spatial coordinate (x, z) based on the relationship between the starting coordinates of the coordinate system corresponding to the grid unit and the x-axis coordinates of the ground and the antenna, as well as the horizontal step and the depth step, so as to obtain the ground penetrating radar profile.

[0076] In the embodiments of the present application, by calculating the equivalent dielectric constant, the phase distortion problem caused by the traditional uniform medium assumption in the underground detection of non-uniform medium is solved, so that the electromagnetic wave can still maintain the accurate expression of the propagation path in the non-uniform medium, and the accurate characterization of the complex electromagnetic characteristics of the underground detection domain is realized; at the same time, by the vertical incidence assumption of the detection electromagnetic wave signal, the electromagnetic wave propagation path can be simplified, the non-uniform medium incident field which is difficult to analytically calculate is simplified to the analytically expressible equivalent uniform medium incident field, and the calculation complexity of the inversion reflectivity function is reduced.

[0077] The traditional method needs to rely on numerical simulation or ray tracing technology to model the electromagnetic wave propagation in the non-uniform medium, and the calculation complexity is high and it is difficult to process large-scale data. In the embodiments of the present application, by introducing the equivalent dielectric constant, the wave propagation in the complex medium is simplified to a straight path phase matching problem based on the WKB approximation, and combined with the analytical expression of the integral equation kernel, the calculation time consumption can be reduced while ensuring that the positioning error is small enough.

[0078] By establishing a continuous variation model of the equivalent dielectric constant, the phase distortion problem caused by the traditional uniform medium assumption is successfully solved, so that the electromagnetic wave can still maintain the accurate expression of the propagation path in the non-uniform medium. The WKB approximation combined with the integral equation adopted by the present application converts the complex wave propagation problem in the non-uniform medium into an analytically solvable phase accumulation problem, which is suitable for key scenes such as underground cavity detection and ground creep monitoring where the dielectric parameter changes significantly in space.

[0079] The above describes the method provided by the embodiments of the present application, and the system part provided by the embodiments of the present application will be described below.

[0080] Please refer to Figure 3 , Figure 3 The structure diagram of a ground penetrating radar imaging system provided by the embodiments of the present application is shown in Figure 3 , and the system 30 comprises: The acquisition module 301 is configured to acquire the scattering signal of the underground target and the depth-soil dielectric constant data of the detection domain where the underground target is located, and the scattering signal is the echo signal generated by the detection electromagnetic wave signal sent by the transmitting antenna based on the underground target. The computing module 302 is configured to calculate an equivalent dielectric constant based on the depth-soil dielectric constant data by using an average equivalent method. The constructing module 303 is configured to construct a reflectivity function to a linear operator of the scattering signal based on an assumption that the underground target is vertically below the transmitting antenna and the equivalent dielectric constant, wherein the reflectivity function is used to quantify the influence of the difference in electromagnetic properties between the underground target and the soil medium in the detection domain on electromagnetic wave reflection, and the linear operator is used to describe the mapping of the reflectivity function to the scattering signal. The inversion module 304 is configured to invert the reflectivity function based on the linear operator and the scattering signal by using a regularization inversion algorithm. The generating module 305 is configured to generate a ground penetrating radar profile based on the reflectivity function.

[0081] Preferably, the constructing module 303 is specifically configured to divide the detection domain into M non-overlapping grid cells; the scattering signal is represented in a discrete matrix in units of the grid cells to obtain a first matrix corresponding to the scattering signal; each element in the first matrix corresponds to one of the grid cells; and a third matrix corresponding to the linear operator is calculated based on the first matrix.

[0082] Preferably, the inversion module 304 is specifically configured to perform singular value decomposition on the third matrix to obtain a singular spectrum of the linear operator; and the reflectivity function is inverted based on the singular spectrum of the linear operator and a second matrix corresponding to the scattering signal by using a truncated singular value decomposition inversion method.

[0083] Preferably, the calculation formula of the reflectivity function inverted by the truncated singular value decomposition inversion method comprises: ; wherein, is the inverted reflectivity function, x and z are horizontal displacement and depth displacement respectively, is a truncation index, n is an index of singular values, is the scattering signal, are singular values in the singular spectrum, an orthogonal norm basis of a data space, and an orthogonal norm basis of an unknown space respectively.

[0084] Preferably, the generating module 305 is specifically configured to establish a correspondence between coordinates and reflectivity in the detection domain based on the reflectivity function, the equivalent dielectric constant, and electromagnetic wave propagation time; and generate the ground penetrating radar profile by using color or gray scale coding of reflectivity size with horizontal displacement as the horizontal axis and depth displacement as the vertical axis based on the correspondence between coordinates and reflectivity in the detection domain.

[0085] Preferably, the equivalent dielectric constant between the transmitting antenna and the underground target is a first constant, and the equivalent dielectric constant of the area where the underground target is located is a second constant, and the first constant and the second constant are different.

[0086] Preferably, the calculation module 302 is specifically configured to calculate the equivalent dielectric constant based on the depth-soil dielectric constant data by using a fitting method and a numerical integration method.

[0087] The ground penetrating radar imaging system provided by the embodiments of the present application can be understood with reference to the corresponding content of the method embodiment part described above, which will not be repeated here.

[0088] As shown in Figure 4 As shown in Figure 4 is a possible logical structure schematic diagram of the computing device provided by the embodiments of the present application. The computing device 40 includes a processor 401, a communication interface 402, a memory 403, and a bus 404, and the processor 401, the communication interface 402, and the memory 403 are connected to each other through the bus 404. In the embodiments of the present application, the processor 401 is configured to control and manage the actions of the computing device 40, for example, the processor 401 is configured to execute Figure 1 the steps in the embodiments and / or other processes for the technologies described herein. The communication interface 402 is configured to support the communication of the computing device 40. The memory 403 is configured to store the program code and data of the computing device 40.

[0089] The processor 401 can be a central processing unit, a general processor, a digital signal processor, an application specific integrated circuit, a field programmable gate array, or other programmable logic device, a transistor logic device, a hardware component, or any combination thereof. It can implement or execute the various exemplary logical blocks, modules, and circuits described in combination with the disclosure. The processor can also be a combination of computing functions, such as one or more microprocessor combinations, digital signal processor and microprocessor combinations, etc. The bus 404 can be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of representation, Figure 4 only one thick line is used in the figure, but it does not mean that there is only one bus or only one type of bus.

[0090] In another embodiment of the present application, a computer readable storage medium is also provided, which includes instructions, when the instructions are run on a computer, the computer executes the above Figure 1The method described in the embodiments.

[0091] Those skilled in the art can understand that the units of the examples described in combination with the embodiments disclosed in the present application can be realized in electronic hardware, computer software or a combination of both. In order to clearly illustrate the interchangeability of hardware and software, the components of the examples have been described in general terms in the above description. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0092] Those skilled in the art can clearly understand that, for the convenience and brevity of the description, the specific working processes of the above-described system, device and unit can refer to the corresponding processes in the foregoing method embodiments, which will not be repeated here.

[0093] In several embodiments provided by the embodiments of the present application, it should be understood that the disclosed system, device and method can be implemented in other ways. For example, the device embodiments described above are only schematic, for example, the division of the units is only a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some interface, device or unit, and can be electrical, mechanical or other forms.

[0094] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, that is, they can be located in one place, or can be distributed on a plurality of network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiments.

[0095] In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or software functional unit.

[0096] If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application or all or part of the technical solutions that essentially contribute to the prior art can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk, and various media that can store program codes.

[0097] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope of the claims and the description of the present application.

Claims

1. A ground-penetrating radar imaging method, characterized in that, The method includes: Acquire the scattered signal of the underground target, as well as the depth-soil dielectric constant data of the detection field where the underground target is located. The scattered signal includes the echo signal generated by the underground target based on the detection electromagnetic wave signal transmitted by the transmitting antenna. Based on the depth-soil dielectric constant data, the equivalent dielectric constant is calculated; Based on the assumption that the underground target is located vertically below the transmitting antenna, and the equivalent dielectric constant, a linear operator is constructed to map the reflectivity function to the scattered signal; wherein, the reflectivity function is used to quantify the influence of the difference in electromagnetic properties between the underground target and the soil medium in the detection domain on the reflection of electromagnetic waves, and the linear operator is used to describe the mapping from the reflectivity function to the scattered signal; The reflectivity function is inverted using a regularized inversion algorithm based on the linear operator and the scattering signal. Based on the reflectivity function, a ground-penetrating radar profile is generated.

2. The method according to claim 1, characterized in that, The construction of a linear operator from the reflectivity function to the scattered signal, based on the assumption that the underground target is located vertically below the transmitting antenna and the equivalent dielectric constant, includes: The detection domain is divided into M non-overlapping grid cells; The scattered signal is represented by a discrete matrix using the grid cell as the unit, resulting in a first matrix corresponding to the scattered signal; each element in the first matrix corresponds to one grid cell. Based on the first matrix, the third matrix corresponding to the linear operator is calculated.

3. The method according to claim 2, characterized in that, The step of inverting the reflectivity function using a regularized inversion algorithm, based on the linear operator and the scattering signal, includes: Singular value decomposition is performed on the third matrix to obtain the singular spectrum of the linear operator; The reflectivity function is obtained by inverting the singular value decomposition method using the truncated singular value decomposition method, based on the singular spectrum of the linear operator and the second matrix corresponding to the scattering signal.

4. The method according to claim 3, characterized in that, The formula for calculating the reflectivity function obtained by the truncated singular value decomposition inversion method includes: ； in, The reflectivity function is obtained through inversion, where x and z are the horizontal displacement and depth displacement, respectively. The truncation exponent is n, where n is the index of the singular value. It is a scattered signal. These are the singular values ​​in the singular spectrum, the orthogonal normalized basis of the data space, and the orthogonal normalized basis of the unknown space, respectively.

5. The method according to claims 1-4, characterized in that, The process of generating a ground-penetrating radar profile based on the reflectivity function includes: Based on the reflectivity function, the equivalent dielectric constant, and the electromagnetic wave propagation time, establish the correspondence between the coordinates and reflectivity in the detection domain; Based on the correspondence between coordinates and reflectivity in the detection domain, the ground-penetrating radar profile is generated.

6. The method according to any one of claims 1-4, characterized in that, The equivalent dielectric constant between the transmitting antenna and the underground target is a first constant, and the equivalent nodal constant of the region where the underground target is located is a second constant. The first constant and the second constant are different.

7. The method according to any one of claims 1-4, characterized in that, The calculation of the equivalent dielectric constant based on the depth-soil dielectric constant data includes: The equivalent dielectric constant is calculated based on the depth-soil dielectric constant data using fitting and numerical integration methods.

8. A ground-penetrating radar imaging system, characterized in that, The system, applied to the method of any one of claims 1-7, comprises: The acquisition module is used to acquire the scattering signal of the underground target and the depth-soil dielectric constant data of the detection field where the underground target is located. The scattering signal is the echo signal generated by the underground target based on the detection electromagnetic wave signal sent by the transmitting antenna. The calculation module is used to calculate the equivalent dielectric constant based on the depth-soil dielectric constant data; A construction module is used to construct a linear operator from the reflectivity function to the scattered signal based on the assumption that the underground target is located vertically below the transmitting antenna and the equivalent dielectric constant; wherein, the reflectivity function is used to quantify the influence of the difference in electromagnetic properties between the underground target and the soil medium in the detection domain on the reflection of electromagnetic waves, and the linear operator is used to describe the mapping from the reflectivity function to the scattered signal; The inversion module is used to invert the reflectivity function based on the linear operator and the scattering signal using a regularized inversion algorithm; The generation module is used to generate a ground-penetrating radar profile based on the reflectivity function.

9. A computing device, characterized in that, include: Memory, used to store programs; A processor for loading the program to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the method of any one of claims 1-7.

Images