A method and system for three-dimensional modeling of a cover layer based on SEM-Kriging

Abstract

The application discloses a kind of based on SEM-Kriging's overburden three-dimensional modeling method, system, it is related to overburden three-dimensional modeling technical field, the method includes: extracting observable quantitative overburden thickness influence index as observation variable, and by each observation variable builds initial SEM structure equation model;To initial SEM structure equation model in turn carries out reliability test and validity test, obtains after adjustment corrected SEM structure model;Based on SEM structure model builds overburden thickness trend prediction model, and calculates thickness residual by overburden thickness trend prediction model and observation variable data;Thickness residual is compensated by interpolation using Kriging to the target residual of the overburden thickness;Using overburden thickness trend prediction model and target residual, the predicted thickness of the overburden in the study area is calculated and obtained, and three-dimensional modeling is carried out based on the predicted thickness of each spatial coordinate;Effectively improve the applicability of overburden thickness modeling under the condition of complex topography and non-uniform point.

Description

Technical Field

[0001] This invention relates to the field of 3D modeling technology for overlays, and more specifically, to a 3D modeling method and system for overlays based on SEM-Kriging. Background Technology

[0002] In the field of hydropower engineering, overburden layers are typically characterized by large areas, complex formations, and uneven spatial distribution. This directly impacts the construction of large-scale hydropower projects. Therefore, determining the thickness of overburden layers can effectively improve the economic efficiency and safety of hydropower construction, while also helping to reduce the impact of construction on the ecological environment. Currently, stratigraphic lithology modeling is widely used to visually reflect the spatial distribution characteristics of surface overburden layers. Based on the differences in core principles, stratigraphic lithology modeling methods can be divided into four categories: geological law modeling, numerical interpolation modeling, probabilistic statistical modeling, and machine learning modeling. Among them, geological law modeling mainly relies on the basic theories and laws of geology, combined with geological survey data and expert knowledge, to construct a model that conforms to geological logic. Traditional two-dimensional geological models mostly belong to geological law modeling, with representative methods including stratigraphic correlation modeling, sedimentary modeling, and structural geological modeling. Subsequently, with the application and promotion of mathematical statistics and probabilistic statistics methods, numerical interpolation three-dimensional modeling and probabilistic statistical three-dimensional modeling techniques have gradually increased. Representative methods include Kriging interpolation, sequential Gaussian simulation, inverse distance weighted interpolation, Monte Carlo simulation modeling, and Bayesian geological modeling. Among these, numerical interpolation modeling... While easy to implement and apply, it requires high-quality and quantity of data. Although probability and statistics can effectively handle the uncertainty and variability in geological data, the modeling is greatly affected by the rationality of the probability assumptions, and the computational resources and time costs are high. Therefore, with the development and application of machine learning technologies such as deep learning, data-driven machine learning methods have begun to be used for stratigraphic lithology modeling to reduce the influence of human subjectivity in the process. These methods can naturally handle nonlinear relationships, quickly learn and extract geological laws from a large amount of geological data, establish a mapping relationship between input data and stratigraphic lithology, and realize the prediction and classification of stratigraphic lithology. However, machine learning models are usually black box models with poor interpretability, which makes it difficult to intuitively explain their formation mechanism and geological significance.

[0003] Patent document CN117197378A discloses a method for three-dimensional geological modeling of overburden. The method described in this patent is highly dependent on the quality of hydropower engineering survey data. Uneven distribution or insufficient number of exploration points will directly affect the accuracy of three-dimensional geological modeling. Secondly, although polynomial models can fit the spatial distribution of overburden better than traditional linear interpolation methods, for deep overburden in mountainous areas with uncertainty and variability, polynomial models are based on simple function fitting, have low variable dimensionality, and lack geological interpretation significance. Therefore, they cannot capture the complex geological features and variation patterns in detail, making the modeling results prone to deviation and decreased accuracy in areas with sparse points or complex geological formations.

[0004] Therefore, this application is hereby submitted. Summary of the Invention

[0005] The purpose of this invention is to provide a SEM-Kriging-based three-dimensional modeling method and system for overburden layers, which effectively improves the geological interpretation and spatial representation capabilities of the model, reduces the dependence on standard profiles and regular point distributions, and achieves the effects of improving model interpretability, balancing prediction accuracy and spatial continuity. It also effectively improves the applicability of overburden thickness modeling under complex terrain and non-uniform point conditions.

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution:

[0007] Firstly, this application provides a SEM-Kriging-based 3D modeling method for overlay layers, including the following specific steps:

[0008] Based on the genesis and geological engineering characteristics of the overburden in the study area, we identified various latent variables that affect the thickness of the overburden and extracted multiple observable variables that quantify the thickness of the overburden from the latent variables. We then built an initial SEM structural equation model using the various latent variables and the corresponding multiple observable variables.

[0009] By using the previous observational variable data of the overburden in the study area, the reliability and validity of the initial SEM structural equation model were tested in sequence to obtain the adjusted and corrected SEM structural model.

[0010] A cover layer thickness trend prediction model was built based on the SEM structural model, and the thickness residual was calculated using the cover layer thickness trend prediction model and observed variable data.

[0011] Kriging is used to interpolate and compensate for the thickness residual to obtain the target residual of the cover layer thickness.

[0012] Using the overburden thickness trend prediction model and target residual, the predicted thickness of the overburden in the study area is calculated, and a three-dimensional model is performed based on the predicted thickness at each spatial coordinate.

[0013] Based on the above technical solution, the present invention can be further improved as follows.

[0014] Furthermore, the reliability tests mentioned above include the Cronbach's alpha test and the total correlation coefficient test.

[0015] Furthermore, the above validity test includes the following specific steps:

[0016] Calculate the KMO value for each observed variable and perform a Barlett's test of sphericity on each observed variable;

[0017] Exploratory factor analysis was conducted on observed variables whose KMO values ​​met the preset conditions and passed the Barlett test of sphericity.

[0018] The explanatory power of each observed variable under different factors in the exploratory factor analysis was extracted by orthogonal rotation, and observed variables whose explanatory power did not meet the pre-set model conditions were removed.

[0019] Furthermore, the adjusted and corrected SEM structural model includes topographic conditions, hydrological conditions, and tectonic conditions; among which:

[0020] The observed variables in topographic conditions include elevation data and slope data;

[0021] The observed variables in hydrological conditions include average annual rainfall and distance from the river system;

[0022] The observed variables in the structural conditions include the distance to the fault and the distance to the epicenter of historical earthquakes.

[0023] Furthermore, the aforementioned overburden thickness trend prediction model is as follows:

[0024] ,in:

[0025] ; ;

[0026] In the formula, These are the original values ​​of the observed variables; The average value of the raw data representing the thickness of the overburden layer; The standard deviation of the raw data representing the thickness of the overburden layer; The mean of the original data for the observed variable; The standard deviation of the raw data representing the observed variable. The index of the observed variable. This is the numbering of latent variables, which include topographic conditions, hydrological conditions, and tectonic conditions; It is a constant.

[0027] Furthermore, the aforementioned thickness residual is specifically as follows:

[0028] ;

[0029] In the formula, Indicates thickness residual, This represents the true value of the cover layer thickness from previous observational data. The value of the overburden thickness is obtained through the overburden thickness trend prediction model.

[0030] Secondly, this application provides a SEM-Kriging-based 3D overburden modeling system, applied to any of the SEM-Kriging-based 3D overburden modeling methods in the first aspect, comprising:

[0031] The observation variable extraction module is used to determine the various latent variables affecting the thickness of the overburden based on the genesis and geological engineering characteristics of the overburden in the study area, and to extract multiple observation variables that can be observed and quantified to determine the thickness of the overburden from the latent variables. The initial SEM structural equation model is then built using the various latent variables and the corresponding multiple observation variables.

[0032] The structural model calibration module is used to perform reliability and validity tests on the initial SEM structural equation model sequentially using the previous observation variable data of the cover layer in the study area, so as to obtain the adjusted and corrected SEM structural model.

[0033] The thickness residual calculation module is used to build a cover layer thickness trend prediction model based on the SEM structural model, and to calculate the thickness residual through the cover layer thickness trend prediction model and observed variable data.

[0034] The thickness residual compensation module is used to interpolate and compensate the thickness residual using Kriging to obtain the target residual of the cover layer thickness.

[0035] The 3D modeling module is used to calculate the predicted thickness of the overburden in the study area using the overburden thickness trend prediction model and the target residual, and to perform 3D modeling based on the predicted thickness at each spatial coordinate.

[0036] Furthermore, the aforementioned overburden thickness trend prediction model is as follows:

[0037] ,in:

[0038] ; ;

[0039] In the formula, These are the original values ​​of the observed variables; The average value of the raw data representing the thickness of the overburden layer; The standard deviation of the raw data representing the thickness of the overburden layer; The mean of the original data for the observed variable; The standard deviation of the raw data representing the observed variable. The index of the observed variable. This is the numbering of latent variables, which include topographic conditions, hydrological conditions, and tectonic conditions; It is a constant.

[0040] Thirdly, this application provides an electronic device, including: at least one processor, at least one memory, and a data bus;

[0041] In this system, the processor and memory communicate with each other via a data bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a SEM-Kriging-based 3D modeling method for overlays, as described in any of the first aspects.

[0042] Fourthly, this application provides a non-transitory computer-readable storage medium that stores computer instructions that cause a computer to execute a SEM-Kriging-based three-dimensional modeling method for overlays, as described in any of the first aspects.

[0043] Compared with the prior art, the present invention has at least the following beneficial effects:

[0044] 1. This invention introduces a structural equation model (SEM) to model the causal and progressive relationships of factors influencing overburden thickness, quantitatively explaining the mechanism of action of each factor index on overburden thickness, and clearly analyzing the interaction relationships between variables. This effectively improves the explanatory power of the overburden thickness prediction model for geological formation mechanisms, making the final prediction results more transparent and reliable.

[0045] 2. This invention couples SEM and Kriging, integrating the advantages of knowledge-driven and data-driven modeling. It constructs a predictive model for overburden thickness trends using the results of the SEM structural equation model, and then uses Kriging interpolation to compensate for the residuals. This fully utilizes the statistical relationships between factor indicators, improving the applicability of the model while effectively ensuring its prediction accuracy.

[0046] 3. This invention adopts a rasterized data structure throughout the modeling and prediction process. All input variables and final prediction results carry spatial coordinate information. Based on the ArcGIS platform, it not only facilitates spatial management and retrieval of data, but also, combined with Python, can directly support 3D visualization, realizing rapid spatial expression and intuitive presentation of overlay thickness, effectively improving the interactive experience and application efficiency of the model. Attached Figure Description

[0047] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0048] Figure 1 This is a flowchart of the modeling method in an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of the initial SEM structural equation model in an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of the SEM structure model after adjustment and correction in an embodiment of the present invention;

[0051] Figure 4 This is a diagram showing the SEM structural model result in Amos software in an embodiment of the present invention;

[0052] Figure 5 This is a schematic diagram of anisotropy analysis in the 0° direction in an embodiment of the present invention;

[0053] Figure 6 This is a schematic diagram of anisotropy analysis in the 45° direction in an embodiment of the present invention;

[0054] Figure 7 This is a schematic diagram of anisotropy analysis in the 90° direction in an embodiment of the present invention;

[0055] Figure 8 This is a schematic diagram of anisotropy analysis in the 135° direction in an embodiment of the present invention;

[0056] Figure 9 This is a thickness prediction diagram of the covering layer in an embodiment of the present invention;

[0057] Figure 10 This is a schematic diagram of a 3D model built using Python in an embodiment of the present invention. Detailed Implementation

[0058] 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, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0059] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0060] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0061] In the description of the embodiments of the present invention, "multiple" means at least two.

[0062] Example 1: To address the shortcomings of current models, such as poor geological interpretation and spatial representation capabilities, and high dependence on standard profiles and regular point distributions, this example provides a SEM-Kriging-based 3D overburden modeling method. Figure 1 As shown, the specific steps include the following:

[0063] S1. Based on the genesis and geological engineering characteristics of the overburden in the study area, we identified various latent variables that affect the thickness of the overburden and extracted multiple observable variables that quantify the thickness of the overburden from the latent variables. We then built an initial SEM structural equation model using the latent variables and the corresponding multiple observable variables.

[0064] By analyzing the formation and geological engineering characteristics of the overburden in the study area, observable and quantifiable indicators affecting overburden thickness were extracted as observation variables. Combined with existing research on the formation of overburden in the study area, the observation variables can be grouped according to their characteristics and influencing mechanisms, and classified into different groups of latent variables. An initial SEM structural equation model was built, which can classify the latent variables into topography (including NDVI, slope, aspect, and elevation), hydrology and climate (including average annual rainfall, distance from water system, average annual temperature, and topographic humidity), and geological structure (including distance from fault and distance from historical earthquake epicenters).

[0065] S2, using the previous observational variable data of the overburden in the study area, the initial SEM structural equation model is tested for reliability and validity in sequence to obtain the adjusted and corrected SEM structural model.

[0066] Specifically, the overburden thickness data from geological boreholes can be spatially digitized to obtain borehole location vector data containing overburden thickness attributes. Raster data of observed variables such as slope, aspect, rainfall, and temperature can be collected and organized. Based on the ArcGIS spatial platform, the raster size and spatial location of different data can be uniformly matched. 70% of the boreholes can be randomly sampled as training samples, while the remaining 30% serve as validation samples. Using the borehole location vectors as masks, information on all observed variables (overburden thickness, slope, aspect, temperature, etc.) for each borehole location can be extracted. To facilitate comparative analysis of different observed variable data and eliminate the different dimensions of the observed variable data, the Z-score method can be used to standardize the original observed variable data. The relevant parameters for data standardization are shown in Table 1.

[0067] Table 1

[0068]

[0069] When performing reliability and validity tests on the initial SEM structural equation model, the reliability tests include the Cronbach's alpha test and the total correlation coefficient test.

[0070] In this embodiment, a SEM structural equation model containing 10 observed variables was established. See [link to relevant documentation]. Figure 2 To ensure the consistency of the observed variables, before conducting exploratory factor analysis (EFA), we can use 430 training samples to calculate the Cronbach's coefficients of different observed variables using SPSS software and perform consistency tests. As shown in Table 2, the Cronbach's coefficient of geological structures is greater than 0.7, and the corrected total correlation coefficients are all greater than 0.5. It can be considered that the data of the two observed variables under geological structures have good measurement reliability.

[0071] Table 2

[0072]

[0073] Among them, the Cronbach's alpha coefficient for topography is much less than 0.6, indicating poor data reliability. For topography, the total correlation coefficient between vegetation cover (NDVI) and slope aspect is much less than 0.3. After deleting the above two observed variables, the Cronbach's alpha coefficient for topography increases to 0.683, so it should be deleted. Similarly, the Cronbach's alpha coefficient for hydrology and climate is also less than 0.6. The total correlation coefficient between annual average temperature and topographic humidity index (TWI) is much less than 0.3. After deleting the above two observed variables, the Cronbach's alpha coefficient for hydrology and climate increases to 0.947, so it should be deleted.

[0074] The above validity test includes the following specific steps:

[0075] S21, calculate the KMO value for each observed variable and perform a Barlett's test for sphericity on each observed variable.

[0076] Among them, the dimensionality reduction factor analysis function in SPSS software can be used to perform validity analysis on the observed variables after reliability analysis screening, so as to ensure the accuracy and usefulness of the SEM structural equation model. First, KMO and Barlett's test of sphericity were carried out on different observed variables under the latent variable used to explain the thickness of the overburden. The calculation showed that the KMO value was 0.654 > 0.5 (see Table 3), and the chi-square value of the Barlett's test of sphericity was 1240.335, with a significance of 0.000 < 0.001. That is, the scale data of the observed variable is suitable for exploratory factor analysis (validity test).

[0077] Table 3

[0078]

[0079] S22, conduct exploratory factor analysis on the observed variables whose KMO values ​​meet the preset conditions and pass the Barlett test of sphericity.

[0080] Among them, factor loading matrix and variance contribution rate analysis can be performed on the observed variable data to realize exploratory factor analysis of the observed variable data. Three types of factors were extracted through principal component analysis, as shown in Table 4. The cumulative variance contribution rate reached 84.48%, indicating that it can reflect the original observed variable data relatively fully.

[0081] Table 4

[0082]

[0083] S23 uses the orthogonal rotation method to extract the explanatory rates of each observed variable under different factors in the exploratory factor analysis, and removes observed variables whose explanatory rates do not meet the preset model conditions.

[0084] The orthogonal rotation method was used to extract the explanatory power of observed variables under different factors (latent variables). Observed variables with an absolute explanatory power greater than 0.5 can be classified under the same type of factor (latent variable). If the absolute explanatory power of the same observed variable is greater than 0.5 under both types of factors (latent variables), the observed variable should be classified under the factor (latent variable) with the larger explanatory power. According to the relevant validation analysis and SPSS calculation results, as shown in Table 5, it can be seen that the structure and factor variables in the initial SEM structural equation model constructed above have changed. Therefore, the modified model structure is as follows: Figure 3 As shown, it includes topographic conditions (including elevation and slope), hydrological conditions (including average annual rainfall and distance from water systems), and tectonic conditions (including distance from faults and distance from historical earthquake epicenters).

[0085] Table 5

[0086]

[0087] In Table 5 above, data with an absolute explanatory value below 0.5 are not shown. In summary, the Z-score method was used to standardize the original data, and there were no missing data. The skewness and kurtosis of the processed data conformed to a normal distribution, which met the requirements of the Amos software. The reliability and validity of the processed data were tested, and the initial model was adjusted and modified based on the test results.

[0088] S3. A cover layer thickness trend prediction model is built based on the SEM structural model, and the thickness residual is calculated through the cover layer thickness trend prediction model and observed variable data.

[0089] The modified model can be plotted in Amos software based on the modification results. The processed data can then be imported into the software, and the maximum likelihood method can be used to calculate the parameter estimates for the measurement and structural models. Figure 4 As shown, based on the indicators in the SEM structural equation model analysis results, the chi-square degrees of freedom (Chi / DF) of the above model is 1.923 < 2, indicating that it is not affected by the complexity of the model; the goodness-of-fit index (GFI) = 0.948 > 0.9, indicating that the model has strong explanatory power; the adjusted goodness-of-fit index (AGFI) = 0.904 > 0.9, also indicating that it is not affected by the complexity of the model; the root mean square error (RMSEA) = 0.105 > 0.08, and the standardized residuals are slightly greater than the evaluation index of 0.08. Considering that the model has been tested for reliability and validity, and that the causal relationship in the model structure is established under the guidance of existing research experience and results in the region, its small error is ignored, and no parameter correction is performed on the model.

[0090] Specifically, the path coefficients of the latent variables in the structural model and the factor loadings of the observed variables in the measurement model are shown in Table 6.

[0091] Table 6

[0092]

[0093] according to Figure 4The variable types and arrow directions indicate that intermediate latent variables such as topographic conditions, together with observed variables such as elevation and slope, form a reflective measurement model. These intermediate latent variables, in turn, form a recursive structure model with observed variables related to overburden thickness. The path coefficients for topographic, hydrological, and tectonic conditions in the observation model are -0.59, -0.42, and 0.07, respectively. Topographic and hydrological conditions have a strong negative impact on overburden formation, while tectonic conditions have a weak positive impact. Slope, distance from water systems, and distance from faults are the main observed variables for their respective latent variables. It can be seen that higher elevations, steeper slopes, greater distance from water systems, higher annual rainfall, and greater distance from faults or historical earthquake epicenters make overburden formation less likely, which aligns with actual conditions. The factor loadings in the measurement model indicate the degree to which each observed index is determined by its corresponding latent variable; larger values ​​indicate stronger correlations. For example, in this analysis, the factor loading of topographic conditions on elevation is 0.64, meaning that for every 1 standard deviation increase in topographic conditions, elevation increases by approximately 0.64 standard deviations.

[0094] Furthermore, in actual engineering situations, the interface between the overburden and bedrock should be a three-dimensional curved surface in space. However, the overburden thickness prediction formula constructed based on the SEM structural equation model is a multinomial linear regression equation, which is essentially a linear regression hyperplane. It represents an average trend of the surface overburden thickness in a high-dimensional parameter space. In a sense, the SEM structural equation model alone cannot fully describe the true surface morphology of the overburden in space, nor can it capture the nonlinear changes along different observation indicators. Therefore, we adopt the SEM-Kriging coupling method to construct a continuous surface of overburden thickness that conforms to the actual spatial distribution, rather than a simple high-dimensional hyperplane. First, based on the SEM structural equation model results, we analyze the complex causal relationships and hierarchical structure between variables to establish an overburden thickness trend model. Then, we calculate the residual between the actual overburden thickness and the trend model prediction, and perform Kriging interpolation on the residual to obtain the residual prediction for the study area. Finally, we superimpose the prediction with the trend model based on the spatially relevant location to obtain the final overburden thickness prediction. The overburden thickness trend prediction model is as follows:

[0095] ,in:

[0096] ; ;

[0097] In the formula, These are the original values ​​of the observed variables; The average value of the raw data representing the thickness of the overburden layer; The standard deviation of the raw data representing the thickness of the overburden layer; The mean of the original data for the observed variable; The standard deviation of the raw data representing the observed variable. The index of the observed variable. This is the numbering of latent variables, which include topographic conditions, hydrological conditions, and tectonic conditions; It is a constant.

[0098] The specific formula for the overburden thickness trend prediction model described above can be obtained as follows: From the perspective of the overburden formation process mechanism, the changes in observed variables are driven by latent variables. Therefore, the measurement model is a reflection model, and the reflection relationship of this model can be written in the following standardized form:

[0099] (1); where: These are the standardized values ​​of the observed variables; For standardized latent variables; For the factor loadings corresponding to the observed variables; This represents the residual term corresponding to the observed variable (random disturbances that the latent variable could not explain, with an expected value of 0). Indicates the latent variable number (i=1, 2, 3, ..., n); Number the observed variables (j=1, 2, 3, ..., m); it should be noted that the residual term here represents the fact that the latent variables cannot fully explain all the variation of the observed variables. Theoretically, the residual term is an independent random error with an expected value of 0. Therefore, the residual is a theoretical concept in the model and is used to explain the model error, but not for the numerical estimation of the latent variables. So when estimating the latent variables, only the standardized values ​​of the observed indicators and the standard factor loadings are used.

[0100] The above formula (1) reflects a clear model definition. However, since the latent variable L itself cannot be directly observed, the value of the latent variable must be estimated through observed variables and factor loadings. According to the maximum likelihood estimation and regression score method in statistics, the normalized variance weighted method (regression method) can be used to approximate the value of the latent variable. The formula is as follows:

[0101] (2); where: —Standardized latent variables; —Standardized values ​​of observed variables subordinate to latent variables; —Standardized factor loadings for the observed variables; —Observation variable number (i=1, 2, 3, ..., n); To simplify the expression, formula (2) can be simplified to:

[0102] (3); where: —Standardized values ​​of observed variables subordinate to latent variables; —Latent variables after formula simplification The corresponding coefficients of different observed variables j are determined by the factor loadings of the observed variables. Determined; the normalized variance weighting method aims to find an optimal set of weights. This makes the latent variable score When expressed as a linear combination of observed variables, it can reflect the common information in the observed variables to the greatest extent, that is, maximize the proportion of the common variance of the latent variables and the observed variables.

[0103] At the same time, based on the recursive architecture and latent variables in the structural model The path coefficient can be used to determine the trend of the standardized overburden thickness. Rewritten as a linear combination of latent variables:

[0104] (4); where: —Standardized value for cover layer thickness; —Path coefficients corresponding to latent variables; —Standardize latent variables; standardize the observed variables in formula (3). Substituting into formula (4), we get the following formula:

[0105] (5); where: —Standardized value for cover layer thickness; —Path coefficients corresponding to latent variables; —Latent variables after formula simplification The corresponding coefficients of different observed variables j are determined by the factor loadings of the observed variables. Determine; expand equation (5):

[0106] To further simplify:

[0107] (6); where: —by path coefficients A constant determined jointly by the factor loadings; —Standard values ​​of different observed variables under different latent variables in the model; —Latent variables after formula simplification The corresponding coefficients of different observed variables j are determined by the factor loadings of the observed variables. Sure.

[0108] At the same time, the standardization formula needs to be converted to the true scale. In the above, the original data is standardized using the Z-score method, and the formula is as follows:

[0109] (7); where: —Data standardization value, —Original data values, —Data corresponds to the mean. —The data corresponds to the standard deviation; Substituting the above standardization formula (7) into formula (6), we get the following formula:

[0110] (8); Expand and merge:

[0111] (9); After merging the constant terms, the final formula model for predicting the overburden thickness trend can be obtained:

[0112] .

[0113] Therefore, after obtaining the above After obtaining the specific expression form, the expression for the thickness residual can be obtained, as follows:

[0114] ;

[0115] In the formula, Indicates thickness residual, This represents the true value of the cover layer thickness from previous observational data. The value of the overburden thickness is obtained through the overburden thickness trend prediction model.

[0116] S4. Kriging is used to interpolate and compensate for the thickness residual to obtain the target residual of the coating layer thickness.

[0117] After obtaining the predicted value of the thickness residual of the training sample, the Kriging method can be used to interpolate the thickness residual of the training sample to obtain the target residual of the cover layer thickness of the entire study area.

[0118] Specifically, the Kriging method estimates the thickness residuals of the sample data and fits a semi-variogram model to reflect the spatial autocorrelation of "closer distances mean greater similarity." Then, neighborhood sample points are selected around each predicted location S0, and weights are obtained by solving a system of linear equations. Finally, a weighted average is used to give the predicted value of the thickness residuals in the study area. The Kriging random field model can be expressed as:

[0119] In the formula, This represents the thickness residual at spatial location S. The population mean is a constant but unknown. The spatially correlated random residuals with a mean of 0 are used to represent spatial autocorrelation; the Kriging prediction formula can be:

[0120] In the formula, To predict the location The thickness residual estimate at that location, i.e., the interpolation result; For the first Measured thickness residual values ​​at each sampling point location. The number of samples at the participating sampling points. For the first The weights corresponding to each sampling point are obtained by solving the semi-mutation function, which is theoretically defined as follows:

[0121] In the formula, Indicates spatial location and The semivariogram values ​​between For variance operators, This represents the difference in thickness residuals between two sampling points, providing a direct representation of spatial correlation.

[0122] S5. Using the overburden thickness trend prediction model and target residual, the predicted thickness of the overburden in the study area is calculated, and a three-dimensional model is performed based on the predicted thickness at each spatial coordinate.

[0123] Among them, the trend value of the overlay thickness is based on spatial relationships. and residual values Then the predicted thickness of the overburden layer in the study area can be obtained. , is represented as: Using 30% of the training sample points, the true and predicted thickness of the overburden layer were extracted. A comparative analysis was conducted to verify the prediction accuracy of the SEM-Kriging-based overburden layer thickness identification and extraction model. Finally, the predicted thickness was derived. In addition, with the digital elevation model (DEM) raster data of the study area, three-dimensional modeling of the overburden layer of the study area can be achieved based on Python.

[0124] The following tables (Tables 1-6) further illustrate the specific coefficients in the overburden thickness trend prediction model:

[0125] Table 6 shows that the Amos output provides the standardized factor loadings of the observed indicators. Since the measurement model is a response model, in this embodiment, the response relationship can be written as the following expression:

[0126] , , ,

[0127] In the formula, —Elevation standardization value; —Slope standardization value; —Standardized value of annual average rainfall; —Standardized value of distance from water system; —Standardized value of distance from fault; —Standardized distance from the epicenter of a historical earthquake.

[0128] Since the residual term represents the inability of the latent variable to fully explain all the variation of the observed variable, it is theoretically an independent random error with an expected value of 0. Therefore, the residual term is not considered in the subsequent estimation of latent variable values. Although the model definition is clear, since the latent variable L itself cannot be directly observed, the normalized variance weighted method (regression method) is used to estimate the latent variable value based on the observed variable and the corresponding factor loading. The model contains 3 mediating latent variables, and each latent variable has 2 observed variables. Therefore, according to formula (2), the latent variable can be written as:

[0129] ; ; ;

[0130] In the formula: —Standardized latent variables; —Standardized values ​​of observed variables subordinate to latent variables; —Standardized factor loadings for the observed variables; —Observation variable number (i=1, 2, 3, ..., n); can be further simplified to:

[0131] ; ; In the formula:

[0132] ; ;

[0133] ; ;

[0134] ; ;

[0135] Standardized cover layer trend prediction thickness It can be written as a linear combination of latent variables:

[0136] ;

[0137] In the formula: —Standardized values ​​for predicting the trend of overburden thickness; —Path coefficients corresponding to latent variables; —Standardize latent variables; transform observed variables Substituting into the above formula, we get the following formula:

[0138] ;

[0139] In the formula: —Standardized values ​​for predicting the trend of overburden thickness; —Path coefficients corresponding to latent variables; —Latent variables after formula simplification The corresponding coefficients of different observed variables j are determined by the factor loadings of the observed variables. Sure;

[0140] Expanding the above formula:

[0141] , further expressed as:

[0142] ;

[0143] in: ;

[0144] ;

[0145] ;

[0146] ;

[0147] ;

[0148] ;

[0149] In the formula: —by path coefficients A constant determined jointly by the factor loadings; —Standard values ​​of different observed variables under different latent variables in the model; inverse standardization of the above equation is performed using the Z-score standardization formula:

[0150] ;

[0151] After combining the constant terms, we get:

[0152] ;

[0153] In the formula: —Original values ​​of the observed indicators; where:

[0154]

[0155]

[0156]

[0157]

[0158] =446.073

[0159] in: ;

[0160] ;

[0161] ;

[0162] ;

[0163] ;

[0164] ;

[0165] In summary, the formula for predicting the overburden thickness trend in the study area is:

[0166] ;

[0167] In the formula: —Original values ​​of elevation observation indicators; —Original values ​​of slope observation indicators; —Original values ​​of annual average rainfall observation indicators; —Original values ​​of the distance to the water system observation index; —Original values ​​of the distance to the fault observation index; —Original values ​​of the observation index of distance from the epicenter of historical earthquakes.

[0168] Furthermore, after completing the formula for predicting the trend of overburden thickness... After the structure is constructed, the thickness residual of the overburden layer at the training sample points can be calculated using the raster calculator in ArcGIS based on the trend prediction formula. .

[0169] After obtaining the thickness residuals of the training samples, the variogram analysis function in the ArcGIS toolbox can be used to check whether the residuals have spatial structure. The residual prediction thickness can be set as the target variable, and search directions of 0°, 45°, 90°, and 135° can be set to analyze anisotropy. Figure 5 , Figure 6 , Figure 7 , Figure 8As shown, the results indicate that there are no significant changes in the four directions, and the shapes and spatial variation amplitudes of the graphs are highly similar, indicating that the residual data exhibits an isotropic spatial structure. Therefore, Ordinary Kriging is used to interpolate the predicted thickness of the residuals. Ordinary Kriging analysis is performed using the Geostatistics Wizard in the ArcGIS Toolbox. The residual calculation field in the training sample is selected, the exponential function is selected and set to non-anisotropic, and the maximum number of adjacent features is set to 15 and the minimum number of adjacent features is set to 2. Kriging interpolation of the residuals in the study area is obtained. It should be noted that the raster size and position should be consistent with the overburden thickness trend prediction layer during calculation. After the calculation is completed, the overburden thickness trend prediction layer and the overburden thickness residual prediction layer are overlaid using the ArcGIS Raster Calculator to finally obtain the target residual of the overburden thickness.

[0170] In the above analysis, based on the SEM structural equation model calculation results obtained from the training samples (after adjustment and correction), the overall model fit is relatively good and has strong interpretability. Furthermore, based on the points extracted from the remaining 30% of the validation samples, the predicted cover layer thickness was extracted and compared with the actual cover layer thickness. The calculated R² = 0.778 between the actual and predicted cover layer thickness values ​​for the validation sample points, indicating that the constructed cover layer thickness extraction model has strong predictive ability and high reliability. The established three-dimensional surface of the cover layer space basically conforms to the actual distribution and is suitable for regional cover layer thickness prediction and trend analysis. However, the root mean square error is relatively high due to some errors at certain sample points. After smoothing, the predicted cover layer thickness map was obtained, as shown below. Figure 9 As shown.

[0171] In the above, a thickness prediction map of the study area was extracted based on the SEM-Kriging method (see...). Figure 9 Finally, based on the spatial relationship between the digital elevation model (DEM) and the overburden thickness data of the study area, a 3D model of the terrain surface mesh and the overburden thickness columnar structure was implemented using Python. Figure 10 As shown.

[0172] Example 2: This application provides a SEM-Kriging-based 3D overlay modeling system, applied to the SEM-Kriging-based 3D overlay modeling method of Example 1, including:

[0173] The observation variable extraction module is used to determine the various latent variables affecting the thickness of the overburden based on the genesis and geological engineering characteristics of the overburden in the study area, and to extract multiple observation variables that can be observed and quantified to determine the thickness of the overburden from the latent variables. The initial SEM structural equation model is then built using the various latent variables and the corresponding multiple observation variables.

[0174] The structural model calibration module is used to perform reliability and validity tests on the initial SEM structural equation model sequentially using the previous observation variable data of the cover layer in the study area, so as to obtain the adjusted and corrected SEM structural model.

[0175] The thickness residual calculation module is used to build a cover layer thickness trend prediction model based on the SEM structural model, and to calculate the thickness residual through the cover layer thickness trend prediction model and observed variable data.

[0176] The thickness residual compensation module is used to interpolate and compensate the thickness residual using Kriging to obtain the target residual of the cover layer thickness.

[0177] The 3D modeling module is used to calculate the predicted thickness of the overburden in the study area using the overburden thickness trend prediction model and the target residual, and to perform 3D modeling based on the predicted thickness at each spatial coordinate.

[0178] The overburden thickness trend prediction model described above is as follows:

[0179] ,in:

[0180] ; ;

[0181] In the formula, These are the original values ​​of the observed variables; The average value of the raw data representing the thickness of the overburden layer; The standard deviation of the raw data representing the thickness of the overburden layer; The mean of the original data for the observed variable; The standard deviation of the raw data representing the observed variable. The index of the observed variable. This is the numbering of latent variables, which include topographic conditions, hydrological conditions, and tectonic conditions; It is a constant.

[0182] Example 3: This application provides an electronic device, including: at least one processor, at least one memory, and a data bus;

[0183] In this system, the processor and the memory communicate with each other via a data bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a SEM-Kriging-based three-dimensional modeling method for overlays, as described in Example 1.

[0184] Example 4: This application provides a non-transitory computer-readable storage medium that stores computer instructions that cause a computer to execute a SEM-Kriging-based 3D overlay modeling method according to Example 1.

[0185] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0186] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0187] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0188] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0189] Those skilled in the art will understand that all or part of the steps in the above facts and methods can be implemented by a program instructing related hardware. The program or the program described therein can be stored in a computer-readable storage medium. When the program is executed, it includes the following steps: at this time, the corresponding method steps are introduced. The storage medium can be ROM / RAM, magnetic disk, optical disk, etc.

[0190] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A three-dimensional modeling method for overlay layers based on SEM-Kriging, characterized in that, The specific steps include the following: Based on the genesis and geological engineering characteristics of the overburden in the study area, various latent variables affecting the thickness of the overburden were identified, and multiple observable variables that quantify the thickness of the overburden were extracted from the latent variables. An initial SEM structural equation model was built using each latent variable and the corresponding multiple observable variables. By using the previous observation data of the overburden in the study area, the initial SEM structural equation model was tested for reliability and validity in sequence to obtain the adjusted and corrected SEM structural model. A cover layer thickness trend prediction model was built based on the SEM structural model, and the thickness residual was calculated using the cover layer thickness trend prediction model and observed variable data. Kriging is used to interpolate and compensate for the thickness residual to obtain the target residual of the coating layer thickness; Using the overburden thickness trend prediction model and the target residual, the predicted thickness of the overburden in the study area is calculated, and a three-dimensional model is performed based on the predicted thickness at each spatial coordinate.

2. The SEM-Kriging-based 3D modeling method for overlay layers according to claim 1, characterized in that, The reliability tests include the Cronbach's alpha test and the total correlation coefficient test.

3. The SEM-Kriging-based 3D modeling method for overlay layers according to claim 1, characterized in that, The validity test includes the following specific steps: Calculate the KMO value for each of the observed variables and perform a Barlett test for sphericity on each of the observed variables; Exploratory factor analysis was conducted on the observed variables whose KMO values ​​met the preset conditions and passed the Barlett test of sphericity. The explanatory power of each observed variable under different factors in the exploratory factor analysis was extracted by orthogonal rotation, and observed variables whose explanatory power did not meet the pre-set model conditions were removed.

4. The SEM-Kriging-based 3D modeling method for overlay layers according to claim 1, characterized in that, The adjusted and corrected SEM structural model includes topographic conditions, hydrological conditions, and tectonic conditions; wherein: The observed variables in the terrain conditions include elevation data and slope data; The observed variables in the hydrological conditions include average annual rainfall and distance from the water system; The observed variables in the structural conditions include the distance to the fault and the distance to the epicenter of historical earthquakes.

5. A three-dimensional modeling method for overlay layers based on SEM-Kriging according to claim 4, characterized in that, The specific model for predicting the thickness trend of the overburden layer is as follows: ,in: ； ； In the formula, These are the original values ​​of the observed variables; The average value of the raw data representing the thickness of the overburden layer; The standard deviation of the raw data representing the thickness of the overburden layer; The mean of the original data for the observed variable; The standard deviation of the raw data representing the observed variable. The index of the observed variable. This is the numbering of latent variables, which include topographic conditions, hydrological conditions, and tectonic conditions; It is a constant.

6. The SEM-Kriging-based 3D modeling method for overlay layers according to claim 1, characterized in that, The thickness residual is specifically: ； In the formula, Indicates thickness residual, This represents the true value of the cover layer thickness from previous observational data. The value of the overburden thickness is obtained through the overburden thickness trend prediction model.

7. A 3D modeling system for overlay layers based on SEM-Kriging, characterized in that, include: The observation variable extraction module is used to determine various latent variables affecting the thickness of the overburden layer based on the genesis and geological engineering characteristics of the overburden layer in the study area, and to extract multiple observation variables that can be observed and quantified to determine the thickness of the overburden layer from the latent variables. An initial SEM structural equation model is built through each of the latent variables and the corresponding multiple observation variables. The structural model calibration module is used to perform reliability and validity tests on the initial SEM structural equation model sequentially using the previous observation variable data of the cover layer in the study area, so as to obtain the adjusted and corrected SEM structural model. The thickness residual calculation module is used to build a cover layer thickness trend prediction model based on the SEM structural model, and to calculate the thickness residual through the cover layer thickness trend prediction model and observed variable data. The thickness residual compensation module is used to interpolate and compensate the thickness residual using Kriging to obtain the target residual of the cover layer thickness. The 3D modeling module is used to calculate the predicted thickness of the overburden in the study area using the overburden thickness trend prediction model and the target residual, and to perform 3D modeling based on the predicted thickness at each spatial coordinate.

8. A SEM-Kriging-based 3D modeling system for overlay layers according to claim 7, characterized in that, The specific model for predicting the thickness trend of the overburden layer is as follows: ,in: ； ； In the formula, These are the original values ​​of the observed variables; The average value of the raw data representing the thickness of the overburden layer; The standard deviation of the raw data representing the thickness of the overburden layer; The mean of the original data for the observed variable; The standard deviation of the raw data representing the observed variable. The index of the observed variable. This is the numbering of latent variables, which include topographic conditions, hydrological conditions, and tectonic conditions; It is a constant.

9. An electronic device, characterized in that, include: At least one processor, at least one memory, and a data bus; The processor and the memory communicate with each other via the data bus. The memory stores program instructions that can be executed by the processor, which calls the program instructions to execute a SEM-Kriging-based 3D modeling method for overlays as described in any one of claims 1-6.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to execute the SEM-Kriging-based three-dimensional modeling method for overlays according to any one of claims 1-6.

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