A method for modeling dielectric parameters of a perturbed heterogeneous formation

Abstract

The application relates to the field of tunnel advanced geological prediction and geological engineering detection technology, and provides a disturbed heterogeneous stratum dielectric parameter modeling method. The method constructs a uniform background dielectric constant basic model based on preset target stratum basic dielectric parameters, introduces a zero-mean two-dimensional random disturbance field, linearly superimposes the zero-mean two-dimensional random disturbance field and the basic model, obtains dielectric parameters of a non-uniform stratum medium, generates a one-dimensional random interface fluctuation function through Gauss filtering to determine the position of a soil-rock contact interface, divides soil layer and rock layer medium areas according to the interface, completes partition dielectric parameter assignment, and finally obtains a heterogeneous stratum dielectric distribution model. The application can simultaneously represent the spatial non-uniform distribution of dielectric parameters in the stratum and the rough fluctuation form of the soil-rock contact interface, the built model is closer to the real geological characteristics, the deviation between tunnel excavation face geological radar detection simulation and actual working conditions is effectively reduced, and the reliability and precision of the advanced geological prediction simulation are improved.

Description

Technical Field

[0001] This invention relates to the field of geological engineering and tunnel advanced geological prediction technology, specifically to a method for modeling dielectric parameters of disturbed heterogeneous strata. Background Technology

[0002] Existing models of formation dielectric parameters mostly adopt the homogeneous dielectric assumption, simplifying the formation into a medium with a uniform dielectric constant. This fails to reflect the spatial non-uniform distribution of dielectric parameters within the actual formation, resulting in a large deviation between the model and the actual formation. Consequently, the matching degree between the simulated waveforms of ground-penetrating radar and the measured data is low, affecting the accuracy of forecasts.

[0003] While some existing technologies attempt to simulate the morphology of soil-rock contact interfaces, they fail to generate randomly undulating interfaces that closely resemble geological realities through Gaussian filtering. This results in rigid interface depictions and an inability to flexibly adjust parameters such as smoothness and undulation amplitude, making it difficult to match the characteristics of real stratigraphic interfaces. Furthermore, existing technologies rarely combine random perturbation fields with uniform background models. Even when attempts are made, macroscopic mean constraints are not applied to the dielectric parameters after perturbation, leading to insufficient physical rationality of the models and a tendency to produce systematic simulation biases.

[0004] In addition, existing modeling lacks standardized parameter setting and zoning assignment rules, there are no standardized control methods for disturbance field parameters and interface control parameters, and the assignment of dielectric parameters of air layer and formation medium is chaotic, resulting in poor model standardization and stability.

[0005] Therefore, there is an urgent need for a perturbation-type heterogeneous stratum dielectric parameter modeling method to accurately characterize the dielectric non-uniformity of the stratum and the roughness of the interface, improve the accuracy and rationality of the model, and meet the high-precision simulation requirements of tunnel advanced geological radar detection. Summary of the Invention

[0006] In view of this, the present invention provides a perturbation-type heterogeneous stratum dielectric parameter modeling method to solve the problems in the existing tunnel face advanced ground radar detection simulation, which are that the stratum model cannot represent the non-uniform distribution of stratum dielectric parameters, the interface morphology is rigidly depicted and cannot be flexibly controlled, the model lacks physical rationality constraints, and the parameters and assignments are not standardized, which ultimately leads to large simulation deviations and insufficient detection simulation reliability.

[0007] First aspect This invention provides a method for modeling the dielectric parameters of perturbation-type heterogeneous strata, applied to a simulation scenario of advanced ground-penetrating radar detection at a tunnel face. The method includes: Based on the preset target formation dielectric parameters, a basic model of uniform background dielectric constant of the formation is constructed. Based on preset statistical characteristic parameters, a zero-mean two-dimensional random perturbation field is introduced into the basic model of the uniform background dielectric constant. The zero-mean two-dimensional random perturbation field is linearly superimposed onto the basic model of the dielectric constant of the uniform background to obtain the dielectric parameters of the non-uniform formation medium. Based on preset interface control parameters, a one-dimensional random interface fluctuation function is generated by Gaussian filtering to determine the spatial location of the soil-rock contact interface. Based on the one-dimensional random interface fluctuation function, the soil and rock layers are divided into medium regions. The corresponding dielectric parameters are assigned to each region after division, and the final dielectric parameter distribution model of the heterogeneous layer is obtained.

[0008] In one alternative implementation, the autocorrelation function of the zero-mean two-dimensional random perturbation field is an exponential kernel function or a Gaussian kernel function.

[0009] In one optional implementation, the preset statistical characteristic parameters include the standard deviation and spatial correlation length of the zero-mean two-dimensional random perturbation field. By adjusting the standard deviation and spatial correlation length, the spatial fluctuation characteristics of the formation dielectric parameters are controlled.

[0010] In one optional implementation, the step of generating a one-dimensional random interface fluctuation function based on preset interface control parameters using Gaussian filtering specifically includes: Based on a preset number of interface sampling points, a one-dimensional random noise sequence conforming to a standard normal distribution is generated; The one-dimensional random noise sequence is smoothed by convolution using a Gaussian convolution kernel with preset convolution kernel parameters. The smoothed noise sequence is normalized to limit the amplitude range of interface fluctuations; The preset stratigraphic reference depth is superimposed with the normalized noise sequence to generate a one-dimensional random interface undulation function.

[0011] In one optional implementation, the assignment of corresponding dielectric parameters to each partitioned region specifically involves: matching the vacuum dielectric constant to the air layer, and matching the dielectric parameters of the non-uniform formation medium after superimposing a zero-mean two-dimensional random perturbation field to the formation medium region.

[0012] In one optional implementation, the preset convolution kernel parameter is a Gaussian kernel standard deviation that matches the interface correlation length. By adjusting this interface correlation length, the smoothness of the contact interface between the soil and rock in the strata can be controlled.

[0013] In one alternative implementation, the amplitude of the undulation at the interface between the soil and rock is controlled by adjusting the normalized amplitude range of the interface undulation.

[0014] In one optional implementation, the one-dimensional random interface undulation function fluctuates up and down based on a preset formation reference depth, and the fluctuation amplitude does not exceed the interface undulation amplitude range defined by the normalization process.

[0015] In one alternative implementation, the dielectric parameters of the superimposed non-uniform formation medium maintain the macroscopic average dielectric constant consistent with the basic model of the dielectric constant of the uniform background.

[0016] Second aspect This invention provides a perturbation-type heterogeneous layer dielectric parameter modeling device, the device comprising: The basic modeling module is used to construct a basic model of the uniform background dielectric constant of the formation based on the preset target formation dielectric parameters. The perturbation field introduction module is used to introduce a zero-mean two-dimensional random perturbation field into the basic model of the uniform background dielectric constant based on preset statistical characteristic parameters. The dielectric parameter calculation module is used to linearly superimpose the zero-mean two-dimensional random perturbation field onto the basic model of the dielectric constant of the uniform background to obtain the dielectric parameters of the non-uniform formation medium. The interface generation module is used to generate a one-dimensional random interface fluctuation function based on preset interface control parameters and Gaussian filtering to determine the spatial location of the contact interface between the soil and rock in the strata. The partition assignment module is used to divide the soil and rock layer medium regions according to the one-dimensional random interface fluctuation function, assign corresponding dielectric parameters to each region after partitioning, and obtain the final heterogeneous layer dielectric parameter distribution model.

[0017] This invention constructs a uniform background dielectric constant basic model and introduces a zero-mean two-dimensional random perturbation field for linear parameter superposition, which can realistically reflect the spatial non-uniform distribution characteristics of dielectric parameters inside the formation medium. At the same time, relying on Gaussian filtering to generate a one-dimensional random interface undulation function, it can closely match the actual geological conditions to depict the rough undulation morphology of the soil-rock contact interface. Then, according to the divided regions, the dielectric parameters of the air layer and the formation medium are assigned, making the constructed formation dielectric distribution model more closely match the dielectric characteristics of the real formation. This effectively reduces the deviation between the simulation results of advanced ground-penetrating radar detection at the tunnel excavation face and the actual geological conditions, and improves the reliability and accuracy of the detection simulation. Attached Figure Description

[0018] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the overall process of a perturbation-type heterogeneous layer dielectric parameter modeling method according to an embodiment of the present invention; Figure 2 This is a detailed flowchart illustrating a perturbation-type heterogeneous layer dielectric parameter modeling method according to an embodiment of the present invention. Figure 3 This is a structural block diagram of a perturbation-type heterogeneous layer dielectric parameter modeling device according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention; Figure 5 This is a schematic diagram of a horizontal upper soft lower hard stratum model according to an embodiment of the present invention; Figure 6 This is a B-scan image of the contact surface interface horizontal soft upper and hard lower strata model (BrightnessScan ground radar two-dimensional cross-sectional scanning imaging image). Figure 7 This is a schematic diagram of a hard-over-soft stratum model with a horizontal contact surface interface according to an embodiment of the present invention. Figure 8 This is a scan image of the upper hard and lower soft stratum model B, which is the horizontal contact surface interface of this invention. Figure 9 This is a schematic diagram of a hard-over-soft stratum model with a non-horizontal contact surface interface according to an embodiment of the present invention. Figure 10 This is a scan image of model B of a non-horizontal upper hard and lower soft stratum in an embodiment of the present invention. Figure 11 This is a schematic diagram of a non-horizontal upper soft lower hard stratum model according to an embodiment of the present invention; Figure 12 This is a scan image of the upper soft and lower hard stratum model B, which shows that the contact surface interface is not horizontal according to an embodiment of the present invention. Figure 13 This is a schematic diagram of a heterogeneous model with a non-horizontal contact surface, featuring a hard upper surface and a soft lower surface, according to an embodiment of the present invention. Figure 14 This is a B-scan image of a heterogeneous model with a non-horizontal contact surface and a hard upper surface and a soft lower surface, according to an embodiment of the present invention. Figure 15 This is a schematic diagram of a heterogeneous model with a non-horizontal contact surface, soft on top and hard on the bottom, according to an embodiment of the present invention. Figure 16 This is a scan image of model B, a non-homogeneous model with a non-horizontal contact surface and a soft upper surface and a hard lower surface, according to an embodiment of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Example

[0021] According to an embodiment of the present invention, a method for modeling dielectric parameters of a perturbation-type heterogeneous layer is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0022] This embodiment provides a method for modeling the dielectric parameters of perturbation-type heterogeneous strata, applied to a simulation scenario of advanced ground-penetrating radar detection at a tunnel face. The execution entities are a geological numerical simulation computer, a tunnel advanced detection modeling system, and an electromagnetic detection simulation terminal. Figure 1 This is a flowchart of a perturbation-type heterogeneous layer dielectric parameter modeling method according to an embodiment of the present invention, such as... Figure 1 As shown, the process includes the following steps: Step S101: Based on the preset target formation dielectric parameters, construct a basic model of the uniform background dielectric constant of the formation.

[0023] Using the vacuum dielectric constant ε0 specified in the International System of Units (SI) as a fixed and universal calculation benchmark, the basic dielectric parameters of the target stratum are preset, and the complex relative dielectric constant of the uniform background is defined. The real and imaginary parts are separated to fully characterize the polarization capability and electromagnetic wave loss characteristics of the medium. Based on the basic conversion relationship of electromagnetics, the complex relative dielectric constant is converted into an initial value of the absolute dielectric constant that can be directly called in numerical simulation. Combined with the measured data of typical strata at the tunnel excavation face, the dielectric parameter values ​​of hard rock mass, soft rock mass and heterogeneous strata are determined, and a unified and stable macroscopic dielectric benchmark model of the strata is established to provide unified benchmark parameters for subsequent modeling.

[0024] Step S102: Based on preset statistical characteristic parameters, a zero-mean two-dimensional random perturbation field is introduced into the uniform background dielectric constant basic model.

[0025] Based on the physical characteristics of random fluctuations in dielectric parameters at the microscale of strata, statistical characteristic parameters of the perturbation field are preset, and a zero-mean two-dimensional random perturbation field is introduced. Two core statistical characteristic parameters, the standard deviation of the perturbation field and the spatial correlation length, are set to regulate the fluctuation amplitude and spatial correlation range of dielectric parameters, respectively. According to the spatial correlation characteristics of the strata, an exponential or Gaussian kernel function is selected as the autocorrelation function of the perturbation field to realize the quantitative definition of the non-uniformity of strata volume, providing a basis for subsequent characterization of dielectric parameter fluctuations.

[0026] Step S103: The zero-mean two-dimensional random perturbation field is linearly superimposed onto the basic model of the dielectric constant of the uniform background to obtain the dielectric parameters of the non-uniform formation medium.

[0027] Using the relative permittivity of a uniform background as a reference, a zero-mean two-dimensional random perturbation field is linearly superimposed to obtain the distribution of the relative permittivity of the medium. Then, through the basic electromagnetic conversion relationship between the absolute permittivity and the relative permittivity, the distribution of the absolute permittivity after superposition of perturbation is calculated. Without changing the macroscopic average permittivity of the medium, the precise characterization of the microscopic non-uniformity inside the formation is completed, and the basic dielectric parameters of the non-uniform formation medium are obtained.

[0028] Step S104: Based on preset interface control parameters, a one-dimensional random interface fluctuation function is generated by Gaussian filtering to determine the spatial location of the soil-rock contact interface.

[0029] Interface control parameters such as interface fluctuation amplitude and interface correlation length are preset to generate an initial random noise sequence that conforms to a standard normal distribution. The initial noise is smoothed using a Gaussian convolution kernel to make the interface shape continuous and natural. The smoothed noise sequence is normalized to limit the interface fluctuation amplitude to a reasonable range for engineering. The stratigraphic reference depth is superimposed with the normalized noise to obtain the final interface depth function and determine the interface fluctuation characteristic function. The root mean square height of the interface fluctuation is calculated to quantify the interface roughness and accurately determine the spatial location of the soil-rock contact interface.

[0030] Step S105: Divide the air layer and the formation medium region according to the one-dimensional random interface fluctuation function, assign corresponding dielectric parameters to each region after division, and obtain the final heterogeneous formation dielectric parameter distribution model.

[0031] The one-dimensional random interface undulation function is quantized to the numerical simulation grid scale to obtain the discretized soil-rock interface height. The top of the simulation region is a horizontal air layer, below which are the soil and rock layers. The random undulation interface is used to characterize the boundary morphology between the soil and rock layers, and their vertical distribution is determined based on specific geological conditions. The simulation region is divided according to the discretized soil-rock interface height, and corresponding dielectric parameters are assigned to the air layer, soil layer, and rock layer respectively. Based on this, the two-dimensional random volumetric perturbation and one-dimensional interface rough undulation characteristics are further integrated. Combining the partitioning assignment results, a complete absolute dielectric constant distribution model is constructed that simultaneously includes volumetric inhomogeneity and the soil-rock boundary undulation morphology, thus completing the dielectric parameter modeling of the perturbed heterogeneous strata.

[0032] The perturbation-type heterogeneous strata dielectric parameter modeling method provided in this embodiment ensures the overall stability and physical rationality of the strata dielectric parameters by constructing a macroscopically uniform background dielectric model. By introducing a flexibly adjustable two-dimensional random perturbation field, it can realistically simulate the dielectric parameter fluctuations at the microscopic scale of the strata, adapting to geological conditions with different degrees of heterogeneity. By generating interface undulation functions through Gaussian filtering random noise, it accurately restores the rough morphology of the natural soil-rock contact interface, solving the problem of rigid interfaces and inconsistencies with actual geology in traditional modeling. The final dielectric model maintains a consistent average dielectric constant at the macroscopic scale and exhibits random fluctuations and spatial correlation at the microscopic scale. It can directly provide physically reasonable and high-fidelity dielectric parameter support for numerical simulation and imaging analysis of electromagnetic detection systems such as ground-penetrating radar and TBM (Tunnel Boring Machine) advanced detection, improving the realism and reliability of advanced geological exploration simulation. Example

[0033] This embodiment details the implementation process of a perturbation-type heterogeneous stratum dielectric parameter modeling method. This method is applicable to simulation scenarios of advanced ground-penetrating radar detection at tunnel faces, enabling accurate characterization of stratum dielectric parameter heterogeneity and the rough morphology of the soil-rock interface. It provides dielectric parameter support for numerical simulation, imaging analysis, and related algorithm verification of electromagnetic detection systems. Those skilled in the art can completely reproduce the entire modeling process based on the detailed steps, parameter values, formula applications, and operational logic described in this embodiment without requiring additional technical information. The specific implementation process is as follows: Before executing the modeling method of this embodiment, the basic parameters required for modeling are obtained and input in advance, including the measured data of tunnel geological exploration, the parameters of numerical simulation grid, the dielectric reference parameters, and the configuration parameters of the target stratum working conditions.

[0034] Constructing a basic model of the dielectric constant against a uniform background in the formation. This step is fundamental to the entire modeling process. It is based on the physical characteristic that the dielectric properties of underground strata remain generally stable and without drastic fluctuations at a macroscopic observation scale. The purpose is to provide a unified benchmark parameter for subsequently introducing microscopic random disturbances and constructing the undulating morphology of the soil-rock interface, ensuring the stability and consistency of the subsequent modeling process. During implementation, the vacuum dielectric constant is first determined. As a fixed calculation benchmark for the entire modeling process, this parameter is a general physical constant in the fields of electromagnetics and electromagnetic detection. Its value remains fixed. Using this fixed benchmark can ensure that the calculation results of dielectric parameters are consistent and comparable under different engineering scenarios and geological conditions, and avoid systematic deviations in model calculations caused by fluctuations in the benchmark parameter.

[0035] Based on this, the complex relative permittivity of a uniform background is defined, and its expression is: ; This expression is a standard engineering representation of the electromagnetic properties of soil and rock media, conforming to the basic principles of electromagnetism. ε′ represents the real part of the complex relative permittivity, primarily used to characterize the polarization capability of the medium under alternating electromagnetic fields, reflecting the characteristics of charge migration and polarization deflection within the medium. Its value is related to factors such as the mineral composition and porosity of the medium. ε′′ represents the imaginary part of the complex relative permittivity, primarily used to characterize the absorption and loss characteristics of electromagnetic wave energy by the medium. Its value is closely related to the water content and conductivity of the medium. Using a complex permittivity parameter expression with separate real and imaginary parts can completely reflect all the core electromagnetic properties of the medium, providing a foundation for subsequent accurate simulation of the dielectric properties of the formation.

[0036] Based on the above expression for the complex relative permittivity, the initial value of the formation absolute permittivity is further calculated using the following formula: ; This formula strictly follows the basic electromagnetic conversion relationship between absolute permittivity and complex relative permittivity. Its function is to convert the relative permittivity parameters commonly used in engineering surveys into absolute permittivity parameters that can be directly identified and called by numerical simulation software, thereby achieving the adaptation of the basic model and the numerical simulation system.

[0037] Among them, the vacuum permittivity The internationally accepted standard values ​​in the field of electromagnetics are used; the real part of the complex relative permittivity. With the imaginary part The parameters can be determined based on actual engineering geological survey data, indoor geotechnical test results, or known empirical values ​​in related fields. Corresponding values ​​are adopted for different types of geological media to ensure that the model parameters are consistent with the actual geological conditions.

[0038] In this embodiment, the dielectric parameter values ​​for various lithologies are determined with reference to measured data of typical strata at the tunnel face. The relative dielectric constant of hard rock is set to 5, that of soft rock is set to 3, and the dielectric constant of heterogeneous strata fluctuates randomly within the range of 2 to 6. This range is determined because variations in mineral composition, water content, and porosity in actual strata can lead to corresponding changes in dielectric parameters. This setting ensures that the basic model remains consistent with actual geological conditions, avoiding distortion of simulation results due to parameter values ​​deviating from reality.

[0039] Based on a uniform background dielectric constant model, a zero-mean two-dimensional random perturbation field is introduced and parameters are superimposed. This step is based on the fact that, at the microscale, the dielectric parameters of underground media exhibit spatial random fluctuations due to factors such as uneven mineral particle distribution, local differences in water content, and irregular pore structure. The aim is to accurately characterize the non-uniformity of dielectric parameters within the strata, making the model more closely resemble the microstructure of real strata.

[0040] In this embodiment, the introduced two-dimensional random perturbation field is a zero-mean two-dimensional random perturbation field. The reason for using the zero-mean setting is to ensure that the disturbance only changes the local distribution pattern and local value of the dielectric parameter, without changing the overall macroscopic average dielectric value of the medium, thereby maintaining the physical stability of the model and ensuring that the model still conforms to the actual law of relatively stable formation dielectric properties on a macroscopic scale.

[0041] To achieve flexible control over the perturbation characteristics, two core statistical parameters of the perturbation field are set: standard deviation.

[0042] Spatial related length Among them, standard deviation Used to control the fluctuation range of dielectric parameters. The larger the value, the more intense the local fluctuations in the formation's dielectric parameters, making it suitable for simulating highly heterogeneous formations such as fractured zones and loose soil layers; spatial correlation length Used to regulate the spatial correlation range of disturbances The higher the value, the stronger the correlation between the dielectric properties of adjacent media, making it suitable for simulating geological conditions with relatively weak heterogeneity, such as intact rock masses and homogeneous strata. The two parameters are independent of each other and can be flexibly adjusted according to actual geological conditions, making them adaptable to most tunnel engineering geological scenarios, including soft soil, hard rock, and fault fracture zones.

[0043] The autocorrelation function of the perturbation field adopts two forms commonly used in the field of stochastic medium modeling, and can be selected according to the spatial correlation characteristics of the actual strata. The first type is the exponential kernel function, whose expression is: ; This first kernel function is suitable for strata with strong spatial correlation, such as loose deposits and fractured rock masses, and can accurately simulate the drastic fluctuations in dielectric parameters in such strata; the second type is a Gaussian kernel function, whose expression is... ; This kernel function is suitable for formations with smooth spatial correlations, such as intact hard rock masses and homogeneous strata, and can simulate the gentle fluctuations in dielectric parameters in such formations. In the formula, r represents the spatial distance between any two points within the formation medium; the introduction of this parameter accurately reflects the degree of correlation of dielectric parameters at different locations.

[0044] After introducing a perturbation field, the relative permittivity distribution of the medium can be written as: ; In the formula, For a uniform background relative permittivity, This is a zero-mean two-dimensional random perturbation field. The expression uses the relative permittivity of a uniform background as a reference, linearly superimposing the perturbation field, conforming to the principle of linear perturbation. It can characterize the dielectric parameter fluctuations at the microscale without changing the macroscopic average relative permittivity of the medium. The relative permittivity characterizes the inherent electromagnetic properties of the medium itself; its value is independent of the environmental reference and can directly reflect the differences in polarization characteristics of the formation medium, providing a basis for subsequent conversion of absolute dielectric parameters.

[0045] Based on the distribution of relative permittivity and according to the fundamental electromagnetic conversion relationship between absolute permittivity and relative permittivity, the absolute permittivity of the medium is: ; In the formula, Let be the vacuum permittivity. Substituting the relative permittivity distribution into this formula yields the complete expansion of the absolute permittivity. To simplify calculations, the above conversion formula can be used directly. The absolute permittivity is a parameter that numerical simulation software can directly recognize and call upon. This conversion process enables seamless adaptation between the model and the electromagnetic detection simulation system.

[0046] This superposition and conversion method is based on the principle of linear perturbation. The calculation process is simple and logically rigorous, and it can accurately characterize the microscopic dielectric inhomogeneity of the formation without destroying the macroscopic dielectric properties. After the model is built, the macroscopic average dielectric value of the medium (including relative and absolute dielectric) is consistent with the uniform background model, ensuring the physical rationality and engineering applicability of the model.

[0047] A one-dimensional random interface undulation function is constructed using a Gaussian filtering random noise generation method to simulate the rough morphology of the soil-rock interface. This step is based on the fact that the undulation morphology of the natural soil-rock interface conforms to the geological characteristics of Gaussian random distribution. By combining random noise with Gaussian filtering, a continuous, natural interface morphology that fits the actual geological conditions can be generated, solving the problem that traditionally manually set interface morphologies are rigid and do not match the actual geological interface.

[0048] During implementation, the soil-rock contact interface is first numerically defined. It is assumed that the interface exhibits a continuous and smooth distribution in the X direction, and the interface depth is represented by the function z(x), where x∈[1,…,N] are discrete grid points in the X direction, and N is the total number of interface sampling points. This definition method is fully compatible with the grid calculation rules of numerical simulation, ensuring that the constructed interface model can be directly imported into the numerical simulation system without additional format conversion.

[0049] Next, an initial random noise sequence of length N is generated, expressed as ε(x)∼N(0,1). This noise sequence conforms to a standard normal distribution with a mean of 0 and a variance of 1. This distribution is chosen because the undulations and variations in the surface of natural geological interfaces follow a Gaussian random distribution. Using an initial noise sequence generated from a standard normal distribution ensures the naturalness and authenticity of the interface morphology, avoiding abrupt changes and deviations from geological patterns caused by artificial settings.

[0050] To ensure a smooth and continuous interface morphology from the initial noise sequence, a Gaussian convolution kernel is needed to smooth the initial noise. The parameters of the Gaussian convolution kernel are set as follows: the kernel mean μ is set to N / 2, which ensures that the smoothed interface is symmetrical, without offset or distortion, conforming to the overall distribution characteristics of actual geological interfaces; the kernel standard deviation σ is related to the interface correlation length. The values ​​are equal, that is This setting allows for direct adjustment of interface smoothness by modifying the relevant lengths of the interface. The parameter association logic is clear, and the adjustment method is simple and intuitive, making it convenient for parameter adjustment in engineering applications.

[0051] Gaussian convolution kernel The specific expression is ; The initial random noise sequence With Gaussian convolution kernel Performing a convolution operation yields a smoothed noise sequence, the expression of which is: ; In the formula, ∗ represents the convolution operation symbol. The core function of convolution operation is to filter out sharp spikes and abrupt jumps in the initial random noise, making the noise sequence continuous and smooth, thereby generating a natural and smooth interface morphology, ensuring that the interface morphology conforms to the characteristics of the actual geological interface.

[0052] To ensure that the interface fluctuation amplitude conforms to the actual engineering range, the smoothed noise sequence is normalized, strictly limiting the noise amplitude to the interval [−A, A], where A is the preset interface fluctuation amplitude. The specific normalization formula is as follows: ; In the formula, This represents the maximum absolute value of the smoothed noise sequence. This normalization process scales the noise amplitude proportionally, limiting it to a preset range. This ensures that the interface undulations match the actual geological interface fluctuations, preventing interface morphology distortion due to abnormal noise amplitudes and improving the model's realism and engineering applicability.

[0053] After completing the normalization process, the preset stratigraphic reference depth will be... The interface depth function is obtained by superimposing it with the smoothed noise sequence. Its expression is ; This expression uses a reference depth Based on this, normalized random noise is superimposed. The core advantage of generating interface depth lies in: baseline depth. Theoretical average depth of the corresponding strata, noise term The random undulations of the interface relative to the reference depth, when combined, can accurately reconstruct the geometry of the real stratigraphic interface, with clear physical meaning; by adjusting the correlation length of the noise sequence... The smoothness of the interface can be controlled, and the fluctuation range of the interface can be controlled by adjusting the normalized amplitude A, so as to achieve flexible adaptation to different geological conditions and convenient parameter adjustment. The expression structure is simple, containing only two core parameters: reference depth and noise term, which is convenient for numerical simulation, while ensuring the reproducibility and engineering applicability of the model, and the calculation logic is concise.

[0054] The interface outline is described by a one-dimensional random function h(x), and its root mean square height is calculated using the following formula: ; In the formula, E is the mathematical expectation of the random variable. This parameter can accurately quantify the roughness of the interface, providing a quantitative basis for the evaluation of the interface morphology and the analysis of electromagnetic wave reflection characteristics, which facilitates the subsequent precise control and optimization of the interface morphology.

[0055] Among them, the interface undulation function h(x) is the undulation amount of the final interface depth z(x) relative to the reference depth That is, it satisfies , corresponding to the smoothed normalized noise sequence.

[0056] The correlation length is (that is, the interface correlation length described above). When numerically discretizing, the interface height needs to be quantized to the grid scale, and its expression is ; Among them is the initial plane position, and Δ is the spatial step. Then for each lateral position x, when y < s(x), the area is regarded as an air layer, and its dielectric constant takes ; when y > s(x), it is regarded as a dielectric region.

[0057] Therefore, the final absolute dielectric constant distribution can be written as: ; The dielectric parameter model of the perturbed heterogeneous formation constructed in this embodiment maintains the consistency of the average dielectric constant at the macroscopic scale, conforms to the actual law of the stability of the macroscopic dielectric characteristics of the formation; at the microscopic scale, it introduces random perturbations and spatial correlations, fitting the mesoscopic non-uniform characteristics of the real formation, and can provide physically reasonable and reliable-precision dielectric parameter support for the numerical simulation of electromagnetic detection systems, meeting the engineering application requirements of advanced geological detection of tunnel boring faces.

[0058] Embodiment 3 In this embodiment, a device for modeling dielectric parameters of a perturbed heterogeneous formation is further provided. This device is used to implement the above-mentioned embodiment and preferred implementation manner of the method for modeling dielectric parameters of a perturbed heterogeneous formation, and those that have been described will not be repeated. As used below, the term "module" can be a combination of software and / or hardware that can achieve a predetermined function. Although the devices described in the following embodiments are preferably implemented in software, implementation in hardware, or a combination of software and hardware is also possible and contemplated. As Figure 3 shown, it includes: A basic modeling module 301, which is used to construct a basic model of the dielectric constant of the formation's uniform background, define the complex relative dielectric constant with the vacuum dielectric constant as the fixed calculation reference, complete the conversion from relative dielectric constant to absolute dielectric constant, and determine the dielectric parameter values of hard rock masses, soft rock masses, and heterogeneous formations in combination with the measured data of the tunnel boring face formation.

[0059] A perturbation field introduction module 302, which is used to introduce a two-dimensional random perturbation field with zero mean, set the core statistical parameters of the standard deviation and spatial correlation length of the perturbation field, select an exponential or Gaussian kernel function according to the spatial correlation characteristics of the formation, and determine the autocorrelation function of the perturbation field.

[0060] The dielectric parameter calculation module 303 is used to linearly superimpose a zero-mean random perturbation field based on the relative permittivity of the uniform background, and calculate the distribution of the relative permittivity and absolute permittivity of the medium. Under the premise of keeping the macroscopic average permittivity unchanged, it characterizes the microscopic volumetric inhomogeneity of the formation.

[0061] The interface generation module 304 is used to generate a one-dimensional interface fluctuation function based on Gaussian filtered random noise, complete the initial noise smoothing and amplitude normalization processing, construct the interface depth function and interface fluctuation feature function, and calculate the root mean square height of the interface to quantize the roughness.

[0062] The partition assignment module 305 is used to quantize the interface undulation function to the numerical simulation grid scale, divide the air layer and formation medium region according to the interface height and perform partition dielectric assignment, integrate two-dimensional random disturbance and one-dimensional interface undulation characteristics, and construct the final complete heterogeneous formation dielectric constant distribution model.

[0063] Further functional descriptions of the above modules and units are the same as those in the corresponding embodiments described above, and will not be repeated here.

[0064] Example 4 In this embodiment, a perturbation-type non-homogeneous layer dielectric parameter modeling device is presented in the form of a functional unit. Here, a unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that execute one or more software or fixed programs, and / or other devices that can provide the above functions.

[0065] This invention also provides a computer device having the above-described features. Figure 4 The diagram shows a perturbation-type non-homogeneous layer dielectric parameter modeling device.

[0066] Please see Figure 4 , Figure 4 This is a schematic diagram of the structure of a computer device provided in an optional embodiment of the present invention, such as... Figure 4As shown, the computer device includes one or more processors 10, memory 20, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components communicate with each other via different buses and can be mounted on a common motherboard or otherwise installed as needed. The processors can process instructions executed within the computer device, including instructions stored in or on memory to display graphical information of a GUI on external input / output devices (such as display devices coupled to the interfaces). In some alternative implementations, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple computer devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 4 Take a processor 10 as an example.

[0067] Processor 10 may be a central processing unit, a network processor, or a combination thereof. Processor 10 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The programmable logic device may be a complex programmable logic device (CAMP), a field-programmable gate array (FPGA), a general-purpose array logic (GDA), or any combination thereof.

[0068] The memory 20 stores instructions executable by at least one processor 10 to cause the at least one processor 10 to perform the method shown in the above embodiments.

[0069] The memory 20 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the computer device. Furthermore, the memory 20 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some alternative embodiments, the memory 20 may optionally include memory remotely located relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0070] The memory 20 may include volatile memory, such as random access memory; the memory may also include non-volatile memory, such as flash memory, hard disk or solid-state drive; the memory 20 may also include a combination of the above types of memory.

[0071] The computer device also includes an input device 30 and an output device 40. The processor 10, memory 20, input device 30, and output device 40 can be connected via a bus or other means. Figure 4 Taking the example of a connection between China and Israel via a bus.

[0072] Input device 30 can receive input numerical or character information, and generate key signal inputs related to user settings and function control of the computer device, such as a touchscreen, keypad, mouse, trackpad, touchpad, joystick, one or more mouse buttons, trackball, joystick, etc. Output device 40 may include display devices, auxiliary lighting devices (e.g., LEDs), and haptic feedback devices (e.g., vibration motors). The aforementioned display devices include, but are not limited to, liquid crystal displays, light-emitting diodes, displays, and plasma displays. In some alternative embodiments, the display device may be a touchscreen.

[0073] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods shown in the above embodiments.

[0074] A portion of this application can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to this application through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0075] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for modeling the dielectric parameters of perturbation-type heterogeneous strata, applied to a simulation scenario of advanced ground-penetrating radar detection at a tunnel face, characterized in that... include: Based on the preset target formation dielectric parameters, a basic model of uniform background dielectric constant of the formation is constructed. Based on preset statistical characteristic parameters, a zero-mean two-dimensional random perturbation field is introduced into the basic model of the uniform background dielectric constant. The zero-mean two-dimensional random perturbation field is linearly superimposed onto the basic model of the dielectric constant of the uniform background to obtain the dielectric parameters of the non-uniform formation medium. Based on preset interface control parameters, a one-dimensional random interface fluctuation function is generated by Gaussian filtering to determine the spatial location of the soil-rock contact interface. Based on the one-dimensional random interface fluctuation function, the soil and rock layers are divided into medium regions. The corresponding dielectric parameters are assigned to each region after division, and the final dielectric parameter distribution model of the heterogeneous layer is obtained.

2. The method according to claim 1, characterized in that, The autocorrelation function of the zero-mean two-dimensional random perturbation field adopts an exponential kernel function or a Gaussian kernel function.

3. The method according to claim 2, characterized in that, The preset statistical characteristic parameters include the standard deviation and spatial correlation length of the zero-mean two-dimensional random perturbation field. By adjusting the standard deviation and spatial correlation length, the spatial fluctuation characteristics of the formation dielectric parameters are controlled.

4. The method according to claim 1, characterized in that, The method of generating a one-dimensional random interface fluctuation function based on preset interface control parameters and using Gaussian filtering specifically includes: Based on a preset number of interface sampling points, a one-dimensional random noise sequence conforming to a standard normal distribution is generated; The one-dimensional random noise sequence is smoothed by convolution using a Gaussian convolution kernel with preset convolution kernel parameters. The smoothed noise sequence is normalized to limit the amplitude range of interface fluctuations; The preset stratigraphic reference depth is superimposed with the normalized noise sequence to generate a one-dimensional random interface undulation function.

5. The method according to claim 1, characterized in that, The specific method for assigning corresponding dielectric parameters to each region after division is as follows: the air layer is matched with the vacuum dielectric constant, and the formation medium region is matched with the dielectric parameters of the non-uniform formation medium after superimposed zero-mean two-dimensional random perturbation field.

6. The method according to claim 4, characterized in that, The preset convolution kernel parameter is the standard deviation of the Gaussian kernel that matches the interface correlation length. By adjusting this interface correlation length, the smoothness of the contact interface between the soil and rock in the strata can be controlled.

7. The method according to claim 4, characterized in that, The amplitude of the interface fluctuations is controlled by adjusting the normalized amplitude range.

8. The method according to claim 4, characterized in that, The one-dimensional random interface undulation function fluctuates up and down based on a preset stratigraphic reference depth, and the fluctuation amplitude does not exceed the interface undulation amplitude range limited by the normalization process.

9. The method according to any one of claims 1 to 8, characterized in that, The dielectric parameters of the superimposed non-uniform formation medium maintain the same macroscopic average dielectric constant as the basic model of the dielectric constant of the uniform background.

10. A perturbation-type heterogeneous layer dielectric parameter modeling device, characterized in that, The device includes: The basic modeling module is used to construct a basic model of the uniform background dielectric constant of the formation based on the preset target formation dielectric parameters. The perturbation field introduction module is used to introduce a zero-mean two-dimensional random perturbation field into the basic model of the uniform background dielectric constant based on preset statistical characteristic parameters. The dielectric parameter calculation module is used to linearly superimpose the zero-mean two-dimensional random perturbation field onto the basic model of the dielectric constant of the uniform background to obtain the dielectric parameters of the non-uniform formation medium. The interface generation module is used to generate a one-dimensional random interface fluctuation function based on preset interface control parameters and Gaussian filtering to determine the spatial location of the contact interface between the soil and rock in the strata. The partition assignment module is used to divide the soil and rock layer medium regions according to the one-dimensional random interface fluctuation function, assign corresponding dielectric parameters to each region after partitioning, and obtain the final heterogeneous layer dielectric parameter distribution model.

Images