CN-121978682-A - Three-dimensional ground penetrating radar dispersion medium discontinuous finite element forward modeling method, system and storage medium

CN121978682ACN 121978682 ACN121978682 ACN 121978682ACN-121978682-A

Abstract

The invention discloses a three-dimensional ground penetrating radar dispersion medium intermittent finite element forward modeling method, a system and a storage medium, wherein the method comprises the following steps of S1, establishing a forward modeling, and setting parameters at a boundary; S2, inputting parameters, setting excitation points and receiving points, S3, conducting grid subdivision on a three-dimensional dispersion medium model, S4, solving the numerical flux of 6 components of a three-dimensional electromagnetic field, S5, updating auxiliary field variables of a three-dimensional area, S6, updating electromagnetic field components of a whole area, S7, increasing time steps, repeating the steps until three-dimensional forward modeling of the current time step is completed, S8, repeating the steps until all excitation is completed, and S9, outputting data. The invention optimizes the three-dimensional full-area electromagnetic field evolution calculation logic and adapts to the multi-scale modeling requirement of a large-scale complex underground structure. The finally output three-dimensional radar profile can three-dimensionally present the depth, the morphology and the spatial distribution of an underground target, and the detection blind area is reduced.

Inventors

CHEN CHENG
FENG DESHAN
YANG MENG
LIU SHUO
TAO XIAO

Assignees

中国电建集团中南勘测设计研究院有限公司
中南大学

Dates

Publication Date: 20260505
Application Date: 20251216

Claims (10)

1. A three-dimensional ground penetrating radar dispersion medium discontinuous finite element forward modeling method is characterized by comprising the following steps: s1, establishing a forward model of a three-dimensional dispersion medium, and setting CFS-PML parameters at boundaries; s2, inputting physical property parameters of a dispersion medium, and setting positions of an excitation point and a receiving point; s3, meshing the three-dimensional dispersion medium model; s4, solving the numerical flux of 6 components of the three-dimensional electromagnetic field; s5, updating auxiliary field variables of the three-dimensional CFS-PML region; S6, updating electromagnetic field components of the whole area; s7, adding a time step, and repeating the steps S4-S6 until the three-dimensional forward modeling of the current time step is completed; S8, repeating the steps S4-S7 until all the excitation is completed; and S9, outputting data to form a radar profile of the three-dimensional dispersion medium.
2. The discontinuous finite element forward method of three-dimensional ground penetrating radar dispersion medium according to claim 1, wherein the physical property parameter of the dispersion medium is relative dielectric constant epsilon r , Where ε ∞ is the relative permittivity at infinity, Δεis the difference between the relative permittivity at static zero frequency and at infinity, τ is the relaxation time, j is the imaginary unit, ω is the angular frequency.
3. The method according to claim 1, wherein the numerical flux in step S4 is calculated by the following formula: fluxH x 、fluxH y 、fluxH z are the numerical fluxes of the magnetic fields in the x, y, z directions, respectively; fluxE x 、fluxE y 、fluxE z are the numerical fluxes of the electric fields in the x, y, z directions, respectively; Kappa e ,v h ,κ h ,v e is the numerical flux coefficient; n x ,n y and n z are projections of the tetrahedral normal vector in the x, y, z directions; h x ,H y ,H z is the component value of the magnetic field of the current unit in the x, y and z directions respectively; E x ,E y ,E z is the component value of the electric field of the current unit in the x, y and z directions respectively; the component values of the magnetic fields of adjacent units in the x, y and z directions are respectively; The component values of the electric fields of adjacent units in the x, y and z directions are respectively shown; HH and EE represent the normal component jump values of the magnetic and electric fields, respectively.
4. A three-dimensional ground penetrating radar dispersive medium discontinuous finite element forward modeling method according to claim 3, wherein the normal component jump values of the magnetic field and the electric field are calculated by the following formula:
5. The three-dimensional ground penetrating radar dispersive medium discontinuous finite element forward modeling method according to claim 1, wherein the auxiliary field variables comprise an electric field auxiliary variable P and a magnetic field auxiliary variable Q, the electric field auxiliary variable P comprises P x , the magnetic field auxiliary variable Q comprises Q x , and the P x and Q x are updated by the following formula: P x ＝ε ∞ [(σ y -σ x -α z )P x,1 -(α y +σ x )P x,2 -(α x +σ x )P x,3 ]+P x,4 +P x,5 +P x,6 ; Q x ＝μ[(σ y -σ x -α z )Q x,1 -(α y +σ x )Q x,2 -(α x +σ x )Q x,3 ]/ε 0 ; Wherein P x and Q x are the auxiliary field variables of the electric field component E x and the magnetic field component H x , respectively, ε ∞ is the relative dielectric constant at infinite frequency, σ x and σ y are the conductivities in the x-direction and y-direction in the CFS-PML layer, respectively, α x 、α y and α z are the complex frequency shift parameters in the x-direction, y-direction and z-direction in the CFS-PML layer, respectively, μ is the magnetic permeability, ε 0 is the dielectric constant under vacuum, P x,1 、P x,2 、P x,3 、P x,4 、P x,5 、P x,6 is the 6 auxiliary field variable components of the electric field component E x , respectively, and Q x,1 、Q x,2 、Q x,3 is the 3 auxiliary field variable components of the magnetic field component H x , respectively.
6. The method of three-dimensional ground penetrating radar dispersive medium discontinuous finite element forward modeling according to claim 1, wherein the electromagnetic field component of the full region is updated according to the following formula: Wherein, the Is the partial derivative, t is time, D k is the current tetrahedron, M is the mass matrix of the cell; S x 、S y and S z are unit rigid matrixes in the x direction, the y direction and the z direction respectively, wherein F is a boundary unit matrix; J z is a loaded excitation source; The vector is composed of values of the basis function at the unit node, the superscript T represents the transpose of the vector, dv represents the volume infinitesimal, delta epsilon is the difference between the relative dielectric constants at static zero frequency and infinite frequency, and sigma is the conductivity.
7. The method according to claim 1, wherein the CFS-PML parameters at the boundary include a maximum α max of complex frequency shift parameters at the CFS-PML outer boundary, a conductivity maximum σ max at the CFS-PML outer boundary, and a PML thickness d 0 , and wherein σ i and α i are obtained according to the following formula: Sigma i is the conductivity in the i direction in the CFS-PML layer, α i is the complex frequency shift parameter in the i direction in the CFS-PML layer, α max is the maximum value of the complex frequency shift parameter at the outer boundary of the CFS-PML layer, d i is the distance to the innermost i direction of the PML layer, d 0 is the PML thickness, σ max is the maximum value of the conductivity at the outer boundary of the CFS-PML layer, and m is the exponential order.
8. The method of discontinuous finite element forward modeling of a three dimensional ground penetrating radar dispersive medium of claim 7, wherein the maximum value of electrical conductivity σ max at the outer boundary of the CFS-PML is calculated by the formula σ max ＝-(m+1)ln(R 0 )/(2ηd 0 ε r Where m is an exponential order, R 0 is the expected reflection error, η is the wave impedance of the PML layer, ε r is the relative permittivity of the medium.
9. A three-dimensional ground penetrating radar dispersive medium discontinuous finite element forward modeling system, comprising: The modeling parameter setting module is used for building a forward model of the three-dimensional dispersion medium and setting CFS-PML parameters at the boundary; the input setting module is used for inputting physical property parameters of the dispersion medium and setting positions of the excitation point and the receiving point; the parameter calculation module is used for meshing the three-dimensional dispersion medium model; the numerical flux solving module is used for solving the numerical fluxes of 6 components of the three-dimensional electromagnetic field; the auxiliary field variable updating module is used for updating the auxiliary field variable of the three-dimensional CFS-PML region; the electromagnetic field component updating module is used for updating the electromagnetic field component of the whole area; the cyclic simulation module is used for adding time steps and completing three-dimensional forward modeling of the current time steps; the circulation excitation module is used for completing all excitation; And the output module is used for outputting data to form a radar profile of the three-dimensional dispersion medium.
10. A storage medium storing the computer program, wherein the computer program when executed by the processor implements the three-dimensional ground penetrating radar dispersive medium discontinuous finite element forward method of any one of claims 1 to 8.

Description

Three-dimensional ground penetrating radar dispersion medium discontinuous finite element forward modeling method, system and storage medium Technical Field The invention relates to the technical field of physical detection, in particular to a three-dimensional ground penetrating radar dispersion medium intermittent finite element forward modeling method. Background Ground Penetrating Radar (GPR) is widely applied to the fields of petroleum exploration, geological disaster early warning, cultural heritage protection and the like as a high-precision nondestructive exploration technology, and acquires underground material structure information by transmitting high-frequency electromagnetic waves and receiving reflected signals. Because electromagnetic wave propagation in the underground involves complex wave equation solving and multi-physical field coupling, and actual exploration faces the challenges of stratum absorption attenuation, random noise interference and the like, GPR forward modeling research has important significance for constructing a mapping relation between a ground electric model and radar response, optimizing a time shift data processing algorithm and breaking through inversion imaging technology. Compared with the two-dimensional GPR which can only provide a single survey line section and is easy to cause limitation of decision deviation, the three-dimensional GPR can display underground target characteristics in a three-dimensional way through intensive gridding acquisition and volume data reconstruction, so that detection dead zones are reduced, but the existing method has the problems of lower precision and imperfect influence consideration on boundaries. Disclosure of Invention The present invention aims to solve at least one of the technical problems existing in the prior art. Therefore, the invention provides a discontinuous finite element forward modeling method for a three-dimensional ground penetrating radar dispersion medium. In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: A discontinuous finite element forward modeling method for a three-dimensional ground penetrating radar dispersion medium comprises the following steps of S1, establishing a forward model of the three-dimensional dispersion medium, setting CFS-PML parameters at boundaries, S2, inputting physical parameters of the dispersion medium, setting excitation points and receiving points, S3, conducting grid subdivision on the three-dimensional dispersion medium model, S4, solving numerical flux of 6 components of a three-dimensional electromagnetic field, S5, updating auxiliary field variables of a three-dimensional CFS-PML area, S6, updating electromagnetic field components of a whole area, S7, increasing time steps, repeating the steps S4-S6 until three-dimensional forward modeling of the current time step is completed, S8, repeating the steps S4-S7 until all excitation is completed, and S9, outputting data to form a radar section of the three-dimensional dispersion medium. Further, the physical property parameter of the dispersion medium is relative dielectric constant epsilon r, Where ε ∞ is the relative permittivity at infinity, Δεis the difference between the relative permittivity at static zero frequency and at infinity, τ is the relaxation time, j is the imaginary unit, ω is the angular frequency. Further, the numerical flux in step S4 is obtained by calculation of the following formula: fluxH x、fluxHy、fluxHz are the numerical fluxes of the magnetic fields in the x, y, z directions, respectively; fluxE x、fluxEy、fluxEz are the numerical fluxes of the electric fields in the x, y, z directions, respectively; Kappa e,vh,κh,ve is the numerical flux coefficient; n x,ny and n z are projections of the tetrahedral normal vector in the x, y, z directions; h x,Hy,Hz is the component value of the magnetic field of the current unit in the x, y and z directions respectively; E x,Ey,Ez is the component value of the electric field of the current unit in the x, y and z directions respectively; the component values of the magnetic fields of adjacent units in the x, y and z directions are respectively; The component values of the electric fields of adjacent units in the x, y and z directions are respectively shown; HH and EE represent the normal component jump values of the magnetic and electric fields, respectively. Further, the normal component jump values of the magnetic field and the electric field can be obtained by calculation according to the following formula: Further, the auxiliary field variables include an electric field auxiliary variable P and a magnetic field auxiliary variable Q, the electric field auxiliary variable P includes P x, the magnetic field auxiliary variable Q includes Q x, and the P x and Q x are as follows The following formula is updated: Px＝ε∞[(σy-σx-αz)Px,1-(αy+σx)Px,2-(αx+σx)Px,3]+Px,4+Px,5+Px,6; Qx＝μ[(σy-σx-αz)Qx,1-(αy+σx)Qx,2-(αx+σx)Qx,3]/ε0; W