Bedrock fracture intrinsic parameter quantitative determination method and system based on all-angle domain amplitude and phase joint inversion
By using a combined amplitude and phase inversion method across the entire angular domain, the problem of multiple solutions in the quantitative determination of bedrock fracture aperture by ground-penetrating radar was solved, achieving high-precision fracture parameter inversion, which is suitable for the determination of bedrock fracture parameters under complex geological conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-08
- Publication Date
- 2026-03-31
AI Technical Summary
Existing technologies for quantitatively determining bedrock fracture aperture using ground-penetrating radar suffer from insufficient information utilization, reliance on amplitude information leading to severe ambiguity, inaccurate system effect correction, and difficulty in accurately inverting fracture parameters under complex geological conditions.
A method combining amplitude and phase inversion across the entire angular domain is adopted. Data is acquired through a common center point mode. Combining Fresnel equations and thin-layer interferometry theory, an objective function constraining amplitude and phase is constructed. A global optimization algorithm is used to simultaneously invert fracture aperture, dielectric constant of infill material, and orientation parameters for system effect correction.
It achieves high-precision, low-multiplicity quantitative determination of fracture parameters, adapts to complex geological conditions, reduces reliance on prior information about the properties of infill materials, and improves the accuracy and applicability of inversion.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of geophysical exploration technology, specifically relating to a method and system for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain. Background Technology
[0002] Bedrock fissures, as discontinuous structures within rock masses, directly affect the engineering stability of the rock mass, the occurrence and migration paths of groundwater resources, and are closely related to the formation of various geological hazards. Among numerous fissure parameters, fissure aperture, i.e., the vertical distance between the two walls of a fissure, is one of the core indicators for rock mass quality evaluation and hydrogeological analysis.
[0003] Currently, the traditional method for obtaining fracture aperture parameters is mainly drilling, such as borehole core sampling and observation, and borehole television imaging. However, these methods are invasive exploration methods, which are not only costly and time-consuming, but also their results are limited to a local area around the borehole, making it difficult to provide continuous and comprehensive information on the spatial distribution and parameter changes of fractures over a large area.
[0004] Ground penetrating radar (GPR), a high-resolution, efficient, and non-destructive geophysical exploration technology, has been widely used to detect the location, extension, and orientation of bedrock fractures due to its sensitivity to differences in the electrical properties of the medium. Its working principle is that when the high-frequency electromagnetic waves emitted by the GPR propagate to the fracture interface, the significant difference in dielectric constant between the fracture filling material (such as air, water, or mud) and the surrounding rock results in effective electromagnetic wave reflection.
[0005] While GPR has achieved success in qualitative imaging of fractures, existing techniques still face significant challenges in quantitatively extracting fracture aperture from GPR data. One approach in existing techniques is based on co-offset profile data, estimating aperture through the spectral characteristics of the reflected wave or single amplitude information. However, this approach inherently suffers from severe ambiguity. Under near-perpendicular incidence conditions, the amplitude of the reflected signal is a combined response to multiple factors, including fracture aperture, dielectric constant of the filling material, and interface roughness. For example, a fracture with a small aperture but filled with a high-dielectric-constant material (such as water) may produce indistinguishable reflection amplitudes from a fracture with a large aperture but filled with a low-dielectric-constant material (such as air). This leads to non-unique inversion results and often requires prior assumptions about the type of fracture filling material, which is often difficult to obtain accurately in practical engineering, thus severely limiting the accuracy and reliability of quantitative estimation.
[0006] To overcome the aforementioned multiple-solution problem, another technique involves introducing amplitude variation with offset / angle (AVO / AVA) analysis. This technique uses common center point (CMP) data to provide more constraint information by utilizing the variation of reflected amplitude with incident angle. However, existing GPR-AVA techniques still face bottlenecks in practical applications: First, they rely primarily on amplitude information while neglecting the phase variation with angle (PVA) pattern, which also contains information about medium parameters, leading to insufficient information utilization. Second, the non-ideal radiation pattern of GPR antennas and the coupling effect between the antenna and the ground surface can cause severe distortion of signal amplitude and phase at long offsets (large angles), and existing correction methods are often overly simplistic, making it difficult to accurately isolate these systematic interferences. This directly weakens the reliability of AVA analysis, hindering its application from the laboratory to complex field environments. The root causes of the above technical problems are: (1) insufficient information utilization, relying only on amplitude information; (2) inaccurate system effect correction, affecting data quality; and (3) insufficient inversion constraints, leading to severe ambiguity. Therefore, there is an urgent need in this field for a new method for quantitative determination of bedrock fracture aperture that can fully utilize GPR wavefield information, effectively suppress inversion ambiguity, and adapt to actual working conditions. Summary of the Invention
[0007] To address the shortcomings and problems of current methods for determining fracture aperture, this invention provides a method and system for quantitatively determining intrinsic parameters of bedrock fractures using ground-penetrating radar based on the joint inversion of amplitude and phase across the entire angular domain.
[0008] This invention provides a method for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain, comprising the following steps: S1. In the surface area where bedrock fissures are known to exist, set up measuring points along the survey line perpendicular to the general direction of the fissures, and use a pre-calibrated shielded ground-penetrating radar antenna system to collect data in the common center point mode to obtain CMP gathers. S2. Preprocess and correct for system effects on the acquired CMP gathers, and convert the offset to the incident angle to obtain angular domain data; S3. Extract the peak amplitude A of the reflected wave corresponding to each incident angle from the angle domain data. ) and peak phase P( ); S4. Establish a theoretical model for slit reflection based on Fresnel equations and thin-layer interference theory to calculate the theoretical reflection coefficient, which includes amplitude and phase. d is the fracture aperture. The dielectric constant of the filler is Let be the dielectric constant of the surrounding rock. It is the angle of inclination. It is the azimuth angle; S5. Construct the objective function that combines amplitude and phase constraints.
[0009]
[0010]
[0011] In the formula: For amplitude residuals; The weighting factor for the amplitude residual function; For phase residuals; This is the weighting factor for the phase residual function; A global optimization algorithm was used to perform multi-parameter synchronous inversion to obtain the fracture aperture d and the medium constant ε of the filling material. fill Inclination angle α and azimuth angle β.
[0012] The above-mentioned method for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full-angle domain, in step S1, fixes the geometric center of the transmitting and receiving antennas at the measuring point, and symmetrically increases the spacing between the transmitting and receiving antennas in steps of 0.03-0.08 meters to obtain a gather containing at least 15 offsets. The initial offset is set to 0.1-0.3 meters, and the maximum offset is 2-4 meters. The incident angle corresponding to the offset range covers 0° to 65°.
[0013] The above-mentioned method for quantitative determination of intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain includes preprocessing of the CMP gather in step S2, including zero-time correction, geometric diffusion correction and medium absorption attenuation correction, to maintain the amplitude and phase characteristics of the signal.
[0014] The above-mentioned method for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain, the method for correcting the system effect of the CMP gather in step S2 is as follows: the antenna system is calibrated in advance in an anechoic chamber to obtain its full waveform response function to the reflection of a standard metal plate at different transmit and receive distances, and the preprocessed CMP gather is corrected using the full waveform response function to obtain the corrected CMP gather.
[0015] The above-mentioned method for quantitative determination of intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain uses the full waveform response function to correct the preprocessed CMP gather. Specifically, it uses a deconvolution operation to divide the spectrum of the measured signal by the spectrum of the system response function, and then performs an inverse Fourier transform to obtain the corrected time-domain waveform.
[0016] The above-mentioned method for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain, wherein the method for acquiring angular domain data in step S2 is as follows: Velocity analysis is performed on the reflection phase axis of the target fracture in the corrected CMP concentrator to obtain the electromagnetic wave velocity v of the overlying granite in the fracture. rock The crack depth z is calculated based on the zero offset two-way travel time t0 of the same phase axis. ; Then the offset x of each gather is converted into the angle of incidence. , .
[0017] The above-mentioned method for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain, in step S4, the theoretical reflection model is constructed based on the three-layer medium reflection theory, combined with Fresnel equations and thin-layer interference effects. For a given incident angle θ, the Fresnel reflection coefficients r1 and r2 of TE and TM waves are first calculated, and then the multiple reflection interference effects within the thin layer are considered to obtain the total reflection coefficient. The calculation formula is as follows:
[0018] In the formula: r1 is the Fresnel reflection coefficient of the rock-fill interface, r2 is the Fresnel reflection coefficient of the filler-rock interface; β fill For the phase delay within the filler, The angle of transmission is determined by Snell's law.
[0019] The aforementioned method for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain uses a global optimization algorithm, such as a particle swarm optimization algorithm, a genetic algorithm, or a simulated annealing algorithm.
[0020] The aforementioned method for quantitatively determining intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase across the entire angular domain employs a particle swarm optimization algorithm as the global optimization inversion algorithm, setting the parameter search space as follows: fracture aperture d ∈ [0.1 mm, 20 mm]; dielectric constant ε of the filling material. fill ∈ [1, 81], covering common filling materials such as air, soil, and water; tilt angle α ∈ [0°, 30°]; azimuth angle β ∈ [0°, 360°].
[0021] This invention also provides a quantitative determination system for intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain, comprising: The data acquisition module includes a transceiver antenna unit and a displacement control unit, used to acquire ground-penetrating radar data in a common center point mode. The displacement control unit is used to precisely control the antenna spacing to increase symmetrically in steps of 0.03-0.08 meters. The data preprocessing module is used to perform zero-time correction, geometric diffusion correction, and medium absorption attenuation correction on the acquired data; The system correction module stores a pre-calibrated full waveform response function of the antenna system, which is used to eliminate system effects through frequency domain deconvolution; Angle domain conversion module is used to convert offset data into incident angle data; The feature extraction module is used to extract amplitude variation data and phase variation data from angle domain data; The inversion calculation module includes a forward model unit and an optimization algorithm unit. The forward model unit constructs a theoretical model based on Fresnel equations and thin-layer interferometry theory. The optimization algorithm unit uses a global optimization algorithm to minimize the joint objective function. The results output module is used to output the fracture aperture, dielectric constant of the filling material, and occurrence parameters.
[0022] Compared with the prior art, the beneficial effects of the present invention are: the method of the present invention has high inversion accuracy and weak ambiguity. By combining amplitude and phase constraints, complementary information is formed, which effectively suppresses the ambiguity of inversion. Even when the properties of the filling material are unknown, the crack aperture and the dielectric constant of the filling material can be accurately and synchronously solved.
[0023] This invention uses the full waveform response function of the antenna system for system effect correction. Compared with the simplified model, it can more accurately isolate the influence of antenna and coupling effects, ensure data quality, and provide a solid data foundation for high-precision inversion. By using the properties of the fracture filling material as the parameters to be inverted rather than preset conditions, it avoids the strong dependence of traditional methods on prior information, has a wider range of applications, and can cope with more complex actual geological conditions.
[0024] This invention can simultaneously measure and invert the geometric parameters (aperture, orientation) and physical parameters (dielectric constant of the filling material) of the fracture, achieving multi-dimensional comprehensive characterization and moving from single-parameter estimation to multi-parameter comprehensive analysis. Attached Figure Description
[0025] Figure 1 This is a schematic diagram of the technical process for quantitatively determining the intrinsic parameters of bedrock fractures according to the present invention. Figure 2 This is a schematic diagram illustrating the principle of data acquisition using the Common Center Point (CMP) mode in the method of this invention; Figure 3 This is a schematic diagram of the amplitude-phase joint inversion principle in the method of the present invention. Detailed Implementation
[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.
[0027] Example 1: This example provides a method for quantitatively determining bedrock fracture aperture using ground-penetrating radar based on joint inversion of amplitude and phase across the entire angular domain. Figure 1 As shown, the method mainly includes the following contents.
[0028] First, in a surface area where bedrock fissures are known to exist, measuring points are laid out along a survey line roughly perpendicular to the direction of the fissures. The 100-1000MHz (e.g., 500MHz) antenna system is pre-calibrated in an anechoic chamber to obtain its full waveform response function to the reflection from a standard metal plate at different transmit / receive distances. The full waveform response function of the antenna system is obtained through the following steps: (a) In a controlled experimental environment, the ground-penetrating radar antenna system is placed in a standard test site; (b) Using a standard metal reflector as the reflector, record the response waveforms at different transmit / receive distances and azimuth angles; (c) Perform frequency domain analysis on the response waveform and establish a system response function library.
[0029] A shielded ground-penetrating radar antenna system with a pre-calibrated center frequency of 500 MHz was used for data acquisition in common center point (CMP) mode. The geometric center of the transmitting and receiving antennas was fixed at the measurement point, and the spacing between the transmitting and receiving antennas was increased symmetrically in steps of 0.03-0.08 meters to obtain a gather containing at least 15 offsets, the offset range corresponding to an incident angle covering 0° to 55°~65°.
[0030] As an example, such as Figure 2 As shown, the specific operation is as follows: the geometric center of the transmitting and receiving antennas is fixed at the measurement point, the initial offset is set to 0.2 meters, and then the distance between the transmitting and receiving antennas is increased symmetrically in steps of 0.05 meters until the maximum offset reaches 3 meters. For each offset, 256 superimposed samples are performed to improve the signal-to-noise ratio, and finally a CMP gather with high signal-to-noise ratio and wide angle range is obtained.
[0031] The acquired CMP gathers undergo amplitude-preserving and phase-preserving preprocessing, including: a) Zero-time correction accurately determines the arrival time of direct waves, ensuring the consistency of the time base; b) Geometric diffusion correction compensates for the signal amplitude multiplied by the propagation time t, eliminating the spherical diffusion effect; c) Medium absorption attenuation correction: The amplitude is compensated by exponential gain based on the attenuation coefficient of the surrounding rock medium.
[0032] Then, system effect correction is performed on the preprocessed CMP gather. The correction is achieved using the full waveform response function of the standard metal plate reflection at different transmit / receive distances, obtained by pre-calibrating the antenna system. The corrected CMP gather is obtained through frequency domain deconvolution. Specifically, the spectrum of the measured signal is divided by the spectrum of the system response function, followed by an inverse Fourier transform to obtain the corrected time-domain waveform. This operation minimizes the non-uniform effects of antenna radiation pattern, inter-antenna coupling, and antenna-ground coupling on the amplitude and phase of signals at different offsets.
[0033] Velocity analysis was performed on the reflection phase axis of the target fracture in the corrected CMP trace concentration to obtain the electromagnetic wave velocity v of the overlying granite. rock The value is 0.12 m / ns, and the crack depth z is calculated based on the zero offset two-way travel time t0 (50 ns) of the in-phase axis.
[0034] The offset x of each gather is then converted into the angle of incidence.
[0035] ; Finally, extract each angle from the flattened angle domain set. The corresponding peak amplitude A(θ) and peak phase P(θ) of the reflected wave are used to obtain the measured AVA and PVA data sequences.
[0036] Then, a thin-layer reflection theoretical model incorporating attitude parameters is constructed. In this embodiment, based on the reflection theory of a three-layer medium (surrounding rock-fill material-surrounding rock), and combined with Fresnel's equations and thin-layer interference effects, a forward model R is constructed that can calculate the theoretical reflection coefficient (including amplitude and phase). theory (θ, d, ε) fill , ε rock , α, β), ε fill pass Calculation yields (ε is calculated) rock ≈ 6.25), d, ε rock α and β are the parameters to be inverted.
[0037] The core equation of this theoretical model is: For a given incident angle θ, first calculate the Fresnel reflection coefficients r1 (rock-fill interface) and r2 (fill-rock interface) for TE and TM waves, respectively. Then, considering the multiple reflection interference effect within the thin layer, obtain the total reflection coefficient:
[0038] In the formula: For the phase delay within the filler, The angle of transmission is determined by Snell's law.
[0039] Then, as Figure 3 As shown, the objective function for constructing the joint amplitude and phase constraints includes: (1) Construct the amplitude residual function,
[0040] (2) Construct the phase residual function,
[0041] (3) Construct the objective function of joint amplitude and phase constraints
[0042] In the formula: The weighting factor for the amplitude residual function. This is the weighting factor for the phase residual function.
[0043] Weighting coefficient w amp and w phase The weighting coefficients are adaptively adjusted during the inversion iteration process based on the data signal-to-noise ratio or information entropy; as an example, the initial value of the weighting coefficients is set to w. amp = 0.4~0.6,w phase = 0.4~0.6.
[0044] A global optimization inversion algorithm is used for multi-parameter synchronous inversion, outputting the fracture aperture d and the medium constant ε of the filling material. fill Inclination angle α and azimuth angle β.
[0045] As a feasible example, Particle Swarm Optimization (PSO) is used as the global optimization inversion algorithm. The parameter search space is defined as follows: Crack aperture d ∈ [0.1 mm, 20 mm]; dielectric constant ε of the filler fill ∈ [1, 81] (covered with common fillers such as air, soil, and water); tilt angle α ∈ [0°, 30°]; azimuth angle β ∈ [0°, 360°]; PSO algorithm parameter settings: 50 particles, maximum number of iterations 200, inertia weight 0.7, learning factors c1=c2=1.5. The algorithm converges after 200 iterations, yielding the result that makes E... total The smallest set of optimal solutions. The optimal solution is located in the concave region where the objective function value is minimized. This region has a clear boundary, indicating that the uniqueness of the inverted solution is good.
[0046] The output results are: fracture aperture d = 5.1 mm, dielectric constant of the filler ε fill = 79.5, tilt angle α = 8°, azimuth angle β = 95°.
[0047] The results indicate that the aperture of the target fracture is approximately 5.1 mm, and its internal filling material is water (theoretical water ε). r ≈81), and the fissures exhibit a nearly horizontal, gently dipping angle.
[0048] Example 2: This example provides a system for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain, including: The data acquisition module includes a transceiver antenna unit and a displacement control unit, used to acquire ground-penetrating radar data in a common center point mode. The displacement control unit is used to precisely control the antenna spacing to increase symmetrically in steps of 0.03-0.08 meters. The data preprocessing module is used to perform zero-time correction, geometric diffusion correction, and medium absorption attenuation correction on the acquired data; The system correction module stores a pre-calibrated full waveform response function of the antenna system, which is used to eliminate system effects through frequency domain deconvolution; Angle domain conversion module is used to convert offset data into incident angle data; The feature extraction module is used to extract amplitude variation data and phase variation data from angle domain data; The inversion calculation module includes a forward model unit and an optimization algorithm unit. The forward model unit constructs a theoretical reflection coefficient calculation model based on Fresnel equations and thin-layer interferometry theory. The optimization algorithm unit uses a global optimization algorithm to minimize the joint objective function. The theoretical reflection coefficient calculation model is as follows:
[0049] In the formula: r1 is the Fresnel reflection coefficient of the rock-fill interface, r2 is the Fresnel reflection coefficient of the filler-rock interface; β fill For the phase delay within the filler, The angle of transmission is determined by Snell's law.
[0050] The joint objective function is the objective function that combines amplitude and phase constraints.
[0051]
[0052]
[0053] In the formula: For amplitude residuals; The weighting factor for the amplitude residual function; For phase residuals; This is the weighting factor for the phase residual function.
[0054] The results output module is used to output the fracture aperture, dielectric constant of the filling material, and occurrence parameters.
[0055] The above description is only a preferred embodiment of the present invention and does not limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for quantitatively determining the intrinsic parameters of bedrock fractures based on the joint inversion of amplitude and phase in the full angular domain, characterized in that: Includes the following steps: S1. In the surface area where bedrock fissures are known to exist, set up measuring points along the survey line perpendicular to the general direction of the fissures, and use a pre-calibrated shielded ground-penetrating radar antenna system to collect data in the common center point mode to obtain CMP gathers. S2. Preprocess and correct for system effects on the acquired CMP gathers, and convert the offset to the incident angle to obtain angular domain data; S3. Extract the peak amplitude A of the reflected wave corresponding to each incident angle from the angle domain data. ) and peak phase P( ); S4. Establish a theoretical model for slit reflection based on Fresnel equations and thin-layer interference theory to calculate the theoretical reflection coefficient, which includes amplitude and phase. d is the fracture aperture. The dielectric constant of the filler is Let be the dielectric constant of the surrounding rock. It is the angle of inclination. It is the azimuth angle; S5. Construct the objective function that combines amplitude and phase constraints. ; ; ; In the formula: For amplitude residuals; The weighting factor for the amplitude residual function; For phase residuals; This is the weighting factor for the phase residual function; A global optimization algorithm was used to perform multi-parameter synchronous inversion to obtain the fracture aperture d and the medium constant ε of the filling material. fill Inclination angle α and azimuth angle β.
2. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain as described in claim 1, characterized in that: In step S1, the geometric center of the fixed transceiver antenna is determined at the measuring point, and the distance between the transceiver antennas is symmetrically increased in steps of 0.03-0.08 meters to obtain a gather containing at least 15 offsets. The initial offset is set to 0.1-0.3 meters, and the maximum offset is 2-4 meters. The incident angle corresponding to the offset range covers 0° to 65°.
3. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain as described in claim 1, characterized in that: Step S2 involves preprocessing the CMP gather, including zero-time correction, geometric diffusion correction, and dielectric absorption attenuation correction, to maintain the amplitude and phase characteristics of the signal.
4. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain as described in claim 1, characterized in that: The method for correcting the system effect of the CMP gather in step S2 is as follows: the antenna system is calibrated in the anechoic chamber beforehand to obtain its full waveform response function to the reflection of the standard metal plate at different transmit and receive distances. The full waveform response function is then used to correct the preprocessed CMP gather to obtain the corrected CMP gather.
5. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain, as described in claim 4, is characterized in that: The preprocessed CMP gather is corrected using the full waveform response function. Specifically, this is achieved by deconvolution, dividing the spectrum of the measured signal by the spectrum of the system response function, and then performing an inverse Fourier transform to obtain the corrected time-domain waveform.
6. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain as described in claim 1, characterized in that: The method for obtaining angle domain data in step S2 is as follows: Velocity analysis is performed on the reflection phase axis of the target fracture in the corrected CMP concentrator to obtain the electromagnetic wave velocity v of the overlying granite on the fracture. rock The crack depth z is calculated based on the zero offset two-way travel time t0 of the same phase axis. ; Then the offset x of each gather is converted into the angle of incidence. , 。 7. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain as described in claim 1, characterized in that: In step S4, the theoretical reflection model is constructed based on the three-layer medium reflection theory, combined with Fresnel equations and thin-layer interference effects. For a given incident angle θ, the Fresnel reflection coefficients r1 and r2 of the TE wave and TM wave are first calculated. Then, considering the multiple reflection interference effects within the thin layer, the total reflection coefficient is obtained. The calculation formula is as follows: ; In the formula: r1 is the Fresnel reflection coefficient of the rock-fill interface, r2 is the Fresnel reflection coefficient of the filler-rock interface; β fill For the phase delay within the filler, The angle of transmission is determined by Snell's law.
8. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain according to claim 1, characterized in that: The global optimization algorithm is a particle swarm optimization algorithm, a genetic algorithm, or a simulated annealing algorithm.
9. The method for quantitative determination of intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain, as described in claim 7, is characterized in that: Particle swarm optimization (PSO) was used as the global optimization inversion algorithm, with the following parameters defined in the search space: fracture aperture d ∈ [0.1 mm, 20 mm]; dielectric constant of the filler ε. fill ∈ [1, 81], covering common filling materials such as air, soil, and water; tilt angle α ∈ [0°, 30°]; azimuth angle β ∈ [0°, 360°].
10. A quantitative determination system for intrinsic parameters of bedrock fractures based on joint inversion of amplitude and phase in the full angular domain, characterized in that: include: The data acquisition module includes a transceiver antenna unit and a displacement control unit, used to acquire ground-penetrating radar data in a common center point mode. The displacement control unit is used to precisely control the antenna spacing to increase symmetrically in steps of 0.03-0.08 meters. The data preprocessing module is used to perform zero-time correction, geometric diffusion correction, and medium absorption attenuation correction on the acquired data; The system correction module stores a pre-calibrated full waveform response function of the antenna system, which is used to eliminate system effects through frequency domain deconvolution; Angle domain conversion module is used to convert offset data into incident angle data; The feature extraction module is used to extract amplitude variation data and phase variation data from angle domain data; The inversion calculation module includes a forward model unit and an optimization algorithm unit. The forward model unit constructs a theoretical model based on Fresnel equations and thin-layer interferometry theory. The optimization algorithm unit uses a global optimization algorithm to minimize the joint objective function. The results output module is used to output the fracture aperture, dielectric constant of the filling material, and occurrence parameters.
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