Two-dimensional stratum structure prediction method and system under limited borehole observation information condition

Abstract

This application discloses a two-dimensional stratigraphic structure prediction method and system under limited borehole observation information. The method first spatially discretizes the engineering geological profile of the target area to obtain several grid cells. Then, it constructs state variables for each grid cell, including feature vectors characterizing the engineering properties of the soil and labels representing the stratigraphic type. Subsequently, it establishes characteristic prototypes for various stratigraphic types based on the state variables of the borehole samples. Next, it constructs a stratigraphic classification model containing data consistency terms and spatial regularization terms. The former quantifies the matching degree between grid cells and stratigraphic types, while the latter achieves spatial continuity constraints by penalizing stratigraphic transitions between adjacent cells. Finally, it solves the model to obtain the two-dimensional stratigraphic structure prediction results. This application effectively solves the problems of spatial continuity and engineering rationality in stratigraphic prediction under limited borehole conditions, improving the stability of the prediction results.

Description

Technical Field

[0001] This application relates to the field of highway engineering surveying technology, specifically to a two-dimensional geological structure prediction method and system under limited borehole observation information. Background Technology

[0002] In the survey and design phase of highway engineering, the underground geological structure is a crucial foundation for subgrade stability analysis, foundation treatment scheme selection, and adverse geological risk assessment. The spatial distribution characteristics of the geological structure directly affect the safety and economy of the engineering scheme and are one of the indispensable key information in highway construction. Especially in urban roads, waterfront roads, and highway projects in soft soil areas, the complex geological structure and sensitive engineering conditions place higher demands on the accuracy of the understanding of the geological structure.

[0003] Constrained by factors such as terrain conditions, construction environment, and exploration costs, engineering exploration typically involves only a limited number of boreholes. The stratigraphic information obtained is spatially discrete and cannot fully reflect the continuous structural characteristics of the underground medium. However, highway engineering design and numerical analysis often require continuous and complete stratigraphic profiles as input conditions. This makes it a common and urgent problem in engineering practice to reasonably infer the stratigraphic structure under limited borehole observation information.

[0004] In practical engineering, the inference of stratigraphic structure often relies on manual interpretation of borehole data and empirical connection methods. These methods are applicable to relatively simple geological conditions, but their results are heavily influenced by the experience of the surveyors. In situations with frequent stratigraphic changes or strong spatial heterogeneity of parameters, problems such as unreasonable stratigraphic abrupt changes and unclear sequence relationships can easily arise. To improve the objectivity and stability of stratigraphic structure inference, some studies have introduced statistical interpolation and geostatistical methods to spatially extend borehole data. However, these methods typically focus on continuous variables, limiting their ability to handle discrete variables such as stratigraphic types, and they struggle to directly reflect stratigraphic sequence constraints.

[0005] In recent years, with the development of computational methods, stratigraphic division and identification methods based on multi-index joint analysis have gradually attracted attention. Related studies have improved the automation of stratigraphic identification by introducing engineering parameters such as water content, plasticity index, and liquidity index. However, in engineering applications, these methods often focus on the discrimination effect in the feature space, while giving insufficient consideration to the continuity and structural rationality of the predicted results in the physical space. This can easily lead to patchy or jagged distributions, affecting engineering interpretation and application. Summary of the Invention

[0006] The purpose of this application is to provide a two-dimensional stratigraphic structure prediction method and system under limited borehole observation information, which can improve the stability of the prediction results in spatial distribution and the engineering rationality.

[0007] The technical solution provided in this application is as follows:

[0008] In a first aspect, this application provides a two-dimensional formation structure prediction method under conditions of limited borehole observation information, comprising the following steps:

[0009] The engineering geological profile of the target area is spatially discretized, and the two-dimensional continuous spatial domain is divided into regular grids to obtain several grid cells. Each grid cell represents a finite spatial region within the profile.

[0010] Construct state variables for each grid cell, including feature vectors for characterizing the soil engineering properties of each grid cell and stratigraphic type labels for representing the stratigraphic type to which each grid cell belongs;

[0011] Based on the state variables corresponding to borehole samples, characteristic prototypes of various types of strata are established; whereby, the characteristic prototype refers to the typical characteristic vector of the corresponding type of strata.

[0012] A stratigraphic classification model is constructed based on the state variables of grid cells. The objective function of the stratigraphic classification model includes a data consistency term and a spatial regularization term. The data consistency term characterizes the degree of matching between each grid cell and different stratigraphic types based on the distance metric between the feature vectors of each grid cell and the feature prototypes of various types of stratigraphic types. The spatial regularization term penalizes stratigraphic transitions between adjacent grid cells to achieve spatial continuity constraints.

[0013] The objective function of the stratigraphic classification model is solved to obtain the stratigraphic type corresponding to each grid cell, i.e., the two-dimensional stratigraphic structure prediction result.

[0014] In one possible implementation, multiple physical indicators reflecting the state and composition characteristics of the soil and geometric indicators reflecting the spatial location are selected as stratigraphic discrimination features. For each grid cell, a multidimensional feature vector is constructed, where each dimension corresponds to a physical or geometric indicator.

[0015] In one possible implementation, when constructing the feature vector, all indicators are processed using a uniform scale, and a separate weighting coefficient is introduced for depth-related indicators to control their influence in the overall feature space. When different strata have significant overlap in stratigraphic discrimination features, the weighting coefficient is appropriately increased to enhance the sequence discrimination capability. When the information of depth-related indicators is too strong, causing the prediction results to tend to be stratified only by depth, the influence of depth-related indicators can be reduced by decreasing the weighting coefficient.

[0016] In one possible implementation, characteristic prototypes of various types of formations are established based on the state variables corresponding to borehole samples, including:

[0017] Let the first The feature set of borehole samples corresponding to the strata-like formation is Estimate the first by using sample statistics Characteristic prototypes of strata ,in, Indicates the first The feature vector of each grid cell Indicates the first Stratigraphic type of each grid cell , Let be the dimension of the eigenvector. Indicates the first Strata in the first Indicator values ​​on each feature dimension Indicates the first The grid cell in the first... Indicator values ​​on each feature dimension And a shared covariance matrix estimated from all borehole samples is introduced; It describes the overall correlation structure in the feature space.

[0018] In one possible implementation, the distance metric includes Euclidean distance and Mahalanobis distance, wherein:

[0019] When the different indices in the feature vector are preprocessed to have uniform dimensions and their correlation is less than the first preset threshold, the Euclidean distance metric is used, and the expression is: ,in Indicates the first Feature vectors of grid cells With the Characteristic prototypes of strata Distance metric (matching metric);

[0020] When the correlation between different indicators in the feature vector is greater than the second preset threshold or the variance difference is greater than the third preset threshold, Mahalanobis distance is used, and the expression is: When calculating the covariance matrix A small regularization term is introduced on the diagonal to avoid matrix singularity problems.

[0021] The first, second, and third preset thresholds can be determined based on experience.

[0022] In one possible implementation, the objective function of the model is:

[0023] ;

[0024] in, This is the set of stratigraphic type labels for all grid cells. The total number of grid cells. For data consistency items, their value is equal to the first... Feature vectors of grid cells and Distance metric value corresponding to the prototype of the stratigraphic type feature; and These are the vertical and horizontal continuity constraint strengths, respectively. and These represent the sets of vertically and horizontally adjacent grid cells, respectively. This is an indicator function, and it takes the value 1 when the stratigraphic types of adjacent units are inconsistent.

[0025] In one possible implementation, solving the objective function of the stratigraphic classification model includes: solving the objective function of the stratigraphic classification model using an iterative approximation solution strategy; the iterative approximation solution strategy specifically includes:

[0026] Initial solution construction: Based on the distance metric results, the stratigraphic type with the smallest corresponding distance metric value is selected as the initial stratigraphic type for each grid cell, resulting in an initial stratigraphic type label set. ;

[0027] Iterative Update: A conditional iterative model is used, based on the objective function, to update the stratigraphic type label of each grid cell point by point: for the... For each grid cell, the formation type label of the remaining grid cells is kept unchanged, and the local energy is selected. smallest As an updated stratigraphic type label, in and The first The vertical and horizontal neighbor sets of each grid cell;

[0028] Hard constraint processing for borehole samples: After each iteration, the formation type label of the grid cell corresponding to the borehole sample is forcibly restored to the actual formation type measured by the borehole to ensure that the borehole information is not interfered with by spatial regularization processing.

[0029] Determine if the iteration termination condition is met; terminate the iteration if it is met.

[0030] In some possible implementations, the iteration terminates when any of the following conditions are met:

[0031] (1) After a complete scan, the labels of all non-fixed grid cells were not updated;

[0032] (2) The change in the objective function value in two consecutive iterations satisfies , For the first The objective function value of the next iteration. This is the preset convergence threshold;

[0033] (3) Reach the preset maximum number of iterations .

[0034] Secondly, this application provides a two-dimensional formation structure prediction system under limited borehole observation information conditions, including: a memory and a processor;

[0035] The memory is used to store computer programs;

[0036] The processor is used to invoke the computer program to execute the method described above.

[0037] Thirdly, this application provides a computer-readable storage medium storing a computer program that, when run on an electronic device, causes the electronic device to perform the method described above.

[0038] Fourthly, this application provides a computer program product, including a computer program that, when run on an electronic device, causes the electronic device to perform the method described above.

[0039] The specific implementation methods of the second to fourth aspects of this application can refer to the implementation methods of the first aspect, and will not be elaborated here.

[0040] The two-dimensional formation structure prediction method and system under limited borehole observation information provided in this application have the following advantages:

[0041] This application achieves a unified expression of stratigraphic structure from continuous physical space to discrete inference problem by discretizing the research profile into a regular grid and using multi-index engineering parameters as feature descriptions. This effectively reduces the complexity of model solution and is suitable for stratigraphic structure prediction at the engineering scale.

[0042] The constructed multi-index feature space modeling method comprehensively considers soil physical indicators and spatial geometric indicators. Through scale unification, depth weighting, and reasonable distance measurement, it improves the stability and reliability of stratigraphic identification and solves the problem that a single index cannot accurately reflect the differences in stratigraphic types.

[0043] A stratigraphic classification model is constructed by introducing spatial continuity constraints and adopting anisotropic discrete Potts regularization, which not only ensures vertical sequence stability but also effectively weakens the jagged boundaries and isolated patches in the horizontal direction, avoiding problems such as unreasonable stratigraphic abrupt changes and unclear sequence relationships that are prone to occur in traditional methods.

[0044] The iterative approximate solution strategy adopted combines initial solution construction, iterative updates, and hard constraint processing of borehole samples to ensure that the prediction results not only conform to borehole observation information and meet spatial continuity requirements, but also have good convergence and engineering stability.

[0045] Engineering case studies demonstrate that the method presented in this application has a high accuracy rate in predicting results, and the overall stratigraphic structure is consistent with the engineering geological understanding. It can provide a reasonable stratigraphic structure reference for stratigraphic structure analysis and auxiliary interpretation during the highway engineering exploration stage, as well as for engineering design. Attached Figure Description

[0046] Figure 1 This is a flowchart of a method in one embodiment of this application.

[0047] Figure 2 This is a schematic diagram of the stratigraphic information and sample point distribution in the case analysis of this application.

[0048] Figure 3 This is a schematic diagram showing the water content distribution of sample points in the case analysis of this application.

[0049] Figure 4 This is a schematic diagram of the plasticity index distribution of sample points in the case analysis of this application.

[0050] Figure 5 This is a schematic diagram of the liquidity index distribution of sample points in the case analysis of this application.

[0051] Figure 6 This is a schematic diagram of the predicted stratigraphic results in the case analysis of this application.

[0052] Figure 7 This is a distribution chart showing the difference between the predicted results and the true values ​​in the case analysis of this application (where 0 indicates that the predicted results are consistent with the true values).

[0053] Figure 8 This is the energy curve (i.e., a schematic diagram of the optimization convergence process) in the case analysis of this application.

[0054] Figure 9 This is a schematic diagram of the characteristic field of water content w in the case analysis of this application.

[0055] Figure 10 This is a schematic diagram of the plasticity index Ip characteristic field in the case analysis of this application.

[0056] Figure 11 This is a schematic diagram of the liquid index IL characteristic field in the case analysis of this application.

[0057] Figure 12 This is a schematic diagram comparing the layer interface curves in the case analysis of this application.

[0058] Figure 13 This is a schematic diagram of the confusion matrix used in the case analysis of this application.

[0059] Figure 14 This is a diagram illustrating the stratification accuracy in the case analysis of this application. Detailed Implementation

[0060] To enable those skilled in the art to better understand the present application, the technical solution of the present application will be further described in detail below with reference to the embodiments and accompanying drawings.

[0061] This application focuses on the prediction of two-dimensional stratigraphic structure under highway engineering survey conditions, and constructs a stratigraphic classification model (stratigraphic structure prediction model) constrained by spatial regularization. This model, by regularly discretizing the cross-sectional space and using multi-index engineering parameters as feature descriptions, fully utilizes borehole observation information and introduces spatial continuity constraints reflecting stratigraphic depositional characteristics and sequence laws to make a holistic inference of the stratigraphic structure. This improves the stability and engineering rationality of the prediction results in spatial distribution. Engineering examples can verify the prediction effect and applicability of this application, and the research results can provide an effective auxiliary technical means for stratigraphic structure analysis in the highway engineering survey and design stages.

[0062] The present application will be further described in detail below with reference to the embodiments.

[0063] Example 1:

[0064] This application provides a two-dimensional formation structure prediction method under limited borehole observation information, including the following steps:

[0065] S1. Spatial domain discretization is performed on the engineering geological profile of the target area, dividing the two-dimensional continuous spatial domain into regular grids to obtain several grid units, each grid unit representing a finite spatial region within the profile.

[0066] The problem of two-dimensional stratigraphic structure prediction can be described as follows: under the condition of limited and unevenly distributed borehole information, how to reasonably infer the stratigraphic type at each location within a spatial profile so that the prediction results not only conform to the known observation information, but also satisfy the overall continuous characteristics of the stratigraphic structure in space.

[0067] From a modeling perspective, this problem falls under the category of spatial structure inference under conditions of incomplete information. Due to insufficient observational information, relying solely on borehole data for local interpolation or point-by-point classification can easily lead to unreasonable stratigraphic jumps or local noise structures in the prediction results, making it difficult to reflect the true sequence relations and spatial continuity of the strata. Therefore, it is necessary to introduce constraints that reflect the spatial continuity of the stratigraphy during the modeling process to reasonably limit the solution space.

[0068] Based on the above considerations, this application uniformly formulates the two-dimensional stratigraphic structure prediction problem as a discrete optimization problem with spatial continuity constraints. Within this framework, by comprehensively utilizing borehole observation information and spatial constraint mechanisms, stable inferences of the stratigraphic structure within the profile are achieved, laying the foundation for subsequent model construction and solution.

[0069] Subsurface strata exhibit a continuous spatial distribution, but in practical modeling and calculation, this continuous space needs to be transformed into a tractable discrete form. Therefore, this application takes engineering geological profiles as the research object, discretizing the two-dimensional continuous spatial domain into a regular grid, thereby achieving quantitative description and numerical modeling of the stratigraphic structure.

[0070] In some embodiments, the engineering geological profile can be divided into several equally spaced grid cells along both the horizontal and vertical directions, with each grid cell representing a finite spatial region within the profile. The stratigraphic properties within this region are expressed in an equivalent manner, thus approximating the continuous stratigraphic structure as a discrete structure composed of a finite number of grid cells. This approach significantly reduces the complexity of the model solution while preserving the overall spatial characteristics of the profile, making it suitable for stratigraphic structure prediction problems at the engineering scale.

[0071] S2. Construct state variables for each grid cell. The state variables include feature vectors for characterizing the soil engineering properties of each grid cell, and stratigraphic type labels for representing the stratigraphic type to which each grid cell belongs.

[0072] Within the discretized spatial domain, formation state variables are introduced to describe each grid cell. Let the first... The feature vector corresponding to each grid cell is This is used to characterize the engineering properties and spatial attributes of the soil at that location; discrete variables are also introduced. This indicates the stratigraphic type to which the grid cell belongs. Therefore, the stratigraphic structure within the entire profile can be represented as a distribution of a set of discrete stratigraphic type labels on a spatial grid.

[0073] The goal of two-dimensional stratigraphic structure prediction is to rationally determine the stratigraphic type label of each grid cell under the constraint of limited borehole observation information, so that the results maintain the consistency of borehole-revealed information while preserving the spatial continuity and sequence rationality of the structure. Through the above spatial domain discretization and state variable definition, the originally continuous and difficult-to-solve stratigraphic structure inference problem is transformed into a discrete inference problem with clear engineering implications, providing a unified expression framework for subsequent multi-index feature modeling and spatial constraint model construction.

[0074] In the process of two-dimensional stratigraphic structure prediction, a single engineering indicator is often insufficient to accurately reflect the differences in stratigraphic types. Different strata typically exhibit comprehensive differences in physical and mechanical properties, composition, and burial depth distribution, as shown by multiple indicators. Therefore, this application starts from multi-source exploration information and performs unified modeling of stratigraphic characteristics, namely, multi-indicator feature space modeling, to improve the stability and reliability of stratigraphic identification.

[0075] In selecting characteristic indicators, this application, combining experimental and observational data conventionally obtained in highway engineering surveys, selects multiple indicators capable of characterizing soil engineering properties as stratigraphic discrimination features, including physical indicators reflecting soil state and composition characteristics, and geometric indicators reflecting spatial location. For each grid cell, a feature vector is introduced. To express the feature indicators. Each component in the vector corresponds to a different physical or geometric index. In practical implementation, the feature vector can be composed of borehole test indices (such as water content, plasticity index, and liquidity index) and spatial location information (such as burial depth) to characterize the comprehensive engineering features of the soil at that location.

[0076] In some embodiments, considering the differences in dimensions and numerical ranges among various engineering indicators, direct joint modeling may lead to one indicator dominating distance calculations, thus affecting the stratigraphic discrimination results. Therefore, this application applies a unified scale to all indicators when constructing feature vectors and introduces a separate weighting coefficient for depth-related indicators.

[0077] In the model implementation, it is assumed that the last dimension of the feature vector is a depth-related feature, and a depth weight coefficient is introduced. Adjust it accordingly, namely:

[0078] (1)

[0079] in This is used to control the influence of depth information on the overall feature space. When there is significant overlap in engineering parameters between different strata, it is appropriate to increase the depth information. This helps enhance the ability to distinguish hierarchical order; when excessive depth information causes the prediction results to tend to be layered only according to depth, this can be addressed by reducing... Reduce its impact.

[0080] S3. Establish characteristic prototypes for various types of formations based on the state variables corresponding to borehole samples; where the characteristic prototype refers to the typical characteristic vector of the corresponding type of formation.

[0081] Borehole samples, as an important source of known stratigraphic information, can be regarded as representative observations of various stratigraphic categories in the feature space. Based on this, this application uses borehole sample-driven stratigraphic feature prototype modeling to characterize the distribution characteristics of different stratigraphic types in the feature space.

[0082] Let the first The feature set of borehole samples corresponding to the strata-like formation is Then, the characteristic prototype of this type of stratum can be estimated through sample statistical methods (such as mean calculation). Furthermore, considering the correlation between different characteristic indicators, a shared covariance matrix estimated from all borehole samples can be introduced. This is used to describe the overall correlation structure in the feature space. In this way, the originally discrete borehole observations are mapped to several class prototypes in the feature space, providing a reference for subsequent construction of distance-based stratigraphic discrimination models.

[0083] S4. Construct a stratigraphic classification model based on the state variables of grid cells. The objective function of the stratigraphic classification model includes a data consistency term and a spatial regularization term. The data consistency term characterizes the degree of matching between each grid cell and different stratigraphic types based on the distance metric between the feature vectors of each grid cell and the feature prototypes of various types of stratigraphic types. The spatial regularization term penalizes stratigraphic transitions between adjacent grid cells to achieve spatial continuity constraints.

[0084] After obtaining the characteristic prototypes of each stratigraphic category, the stratigraphic discrimination problem can be further formulated as: comparing the distances between the eigenvectors of the profile grid cells and the prototypes of each category, and evaluating their classification relationships accordingly. Given the ... The feature vector of each grid cell is Let the first The characteristic prototype of strata is ,in Let be the feature dimension.

[0085] In some embodiments, this application constructs data items using the following two commonly used distance metrics based on the statistical characteristics of the feature data and the sample size.

[0086] (1) Euclidean distance metric

[0087] When the different indices in the feature vector are preprocessed to have uniform dimensions and the correlation between them is weak (e.g., less than 0.3), the Euclidean distance can be used as a similarity measure in the feature space, and its expression is:

[0088] (2)

[0089] (2) Mahalanobis distance metric

[0090] When there is a significant correlation (e.g., greater than 0.5) between different indicators in the feature vector, or when the variance differences between different indicators are large (e.g., greater than 10), using Euclidean distance may underestimate or amplify the discriminative power of some features. In this case, Mahalanobis distance can be introduced to correct the feature space through the covariance structure. Its expression is:

[0091] (3)

[0092] in This is the feature covariance matrix estimated from the borehole samples. Covariance matrix for A symmetric matrix of order n, the nth order n in the matrix Line number Column elements Indicates the first The first characteristic indicator and the second The covariance of the first characteristic index (describing the first characteristic index) The first characteristic indicator and the second (the degree of correlation among individual feature indicators), diagonal elements Indicates the first The variance of each characteristic indicator. The calculation formula is: ;in, ; and The first The first sample The first indicator value and the first Individual indicator values, and The first The first indicator and the first The sample mean of each indicator, This represents the total number of borehole samples.

[0093] To ensure numerical stability, a small regularization term (e.g., ...) is introduced into the diagonal of the covariance matrix in actual calculations. The Mahalanobis distance is calculated based on the regularized covariance matrix, and the expression is adjusted as follows: ;in It is the identity matrix. The small regularization term does not change the core structure of the covariance matrix, does not affect the characterization of feature correlation, and can effectively avoid matrix singularity problems caused by the variance of some indicators approaching 0, thus ensuring computational stability.

[0094] In some embodiments, the Pearson correlation coefficient can be used to measure the degree of linear correlation between two feature indicators, with a value range of [-1, 1]. The calculation method is as follows: ;in, Indicates the first The first indicator and the first The correlation of individual indicators.

[0095] Variance variation is used to measure the difference in the magnitude of numerical fluctuations of different characteristic indicators. It can be calculated by dividing the maximum variance by the minimum variance. determination: ; ;in, For the first The sample variance of each characteristic indicator.

[0096] Through the multi-index feature space modeling described above, the problem of predicting two-dimensional stratigraphic structures is transformed from a complex structure inference problem in the original physical space into a category discrimination problem in the feature space. Furthermore, the spatial regularization constraint introduced on this basis further ensures the continuity of the discrimination results in spatial distribution and the engineering rationality.

[0097] Under highway engineering survey conditions, borehole data can provide clear stratigraphic information for some locations in the profile. However, in areas with large borehole spacing or insufficient control, relying solely on local feature information for point-by-point stratigraphic identification can easily lead to discontinuous boundaries or isolated anomalous units in the prediction results. Although such structures may be numerically valid, they are often difficult to correlate with engineering geological understanding.

[0098] To improve the stability and interpretability of the prediction results at spatial scales, this application introduces both data consistency constraints and spatial continuity constraints into the stratigraphic classification model: the former reflects the degree of support for stratigraphic types from borehole observations and multi-index features, while the latter reflects the spatial sequence relationships and continuity characteristics of the stratigraphic structure. Through the synergistic effect of these two constraints, a holistic inference of the stratigraphic structure within a two-dimensional profile is achieved.

[0099] Based on this, the problem of predicting two-dimensional stratigraphic structure is uniformly formulated as an optimization problem of a discrete stratigraphic type label field. By balancing data consistency and spatial continuity, a reasonable stratigraphic distribution result in an engineering sense can be obtained.

[0100] Suppose that the discretized research profile contains a total of The first grid cell, the... The feature vector corresponding to each unit is Its stratigraphic type is denoted as , Let this be the number of stratigraphic types. Define the set of stratigraphic type labels for all grid cells as follows: The objective function of the stratigraphic classification model can be expressed as:

[0101] (4)

[0102] The first term is the data consistency term, which is used to characterize the degree of matching between the feature vector and different stratigraphic types; the latter two terms are spatial continuity constraint terms (spatial regularization terms), which are applied to vertical and horizontal adjacent grid cell pairs, respectively. and These represent the sets of vertically and horizontally adjacent grid cells, respectively. (Symbols) This is an indicator function, and it takes the value 1 when the stratigraphic types of adjacent units are inconsistent.

[0103] The data consistency term models the feature distribution of each stratigraphic category based on borehole samples. By measuring the distance between the feature vector and the corresponding stratigraphic feature prototype, it reflects the degree to which local observation information supports stratigraphic discrimination. This term is the main source of data-driven information in the model, consistent with the aforementioned multi-index feature space modeling.

[0104] Spatial continuity constraints employ discrete Potts regularization to penalize stratigraphic transitions between adjacent grid cells. Let... The set of all vertically adjacent grid cell pairs. Given the set of all horizontally adjacent grid cell pairs, the spatial regularization term can be written as:

[0105] (5)

[0106] in and These represent the vertical and horizontal continuity constraint strengths, respectively. Considering the geological structure characteristics of highway engineering, the strength is typically taken as... , ,in This is a horizontally weakly canonical scaling parameter. In the vertical direction, a larger value... This helps to suppress unreasonable and frequent layer skipping, ensuring sequence stability; in the horizontal direction, it introduces smaller... This method effectively weakens jagged boundaries and isolated patches while avoiding excessive smoothing of actual lateral variations. This anisotropic constraint method aligns with common geological structure characteristics found in highway engineering.

[0107] This regularization form suppresses high-frequency oscillations caused by local noise during the overall optimization process by imposing a uniform transition cost on inconsistent labels of adjacent units, thereby guiding the model to tend to form a spatially coherent stratigraphic structure.

[0108] S5. Solve the objective function of the stratigraphic classification model to obtain the stratigraphic type corresponding to each grid cell, i.e., the two-dimensional stratigraphic structure prediction result.

[0109] The aforementioned stratigraphic classification model constrained by spatial regularization is a discrete variable optimization problem. Its objective function includes both data consistency and spatial continuity constraints, exhibiting an overall non-convex characteristic. Directly solving for the global optimum is computationally difficult and not necessary for engineering applications. Given that stratigraphic structure prediction prioritizes the stability and engineering feasibility of the results, this application employs an iterative approximate solution strategy to solve the model.

[0110] The core idea of ​​the model solution is to gradually update the formation state while maintaining the objective function at a progressively decreasing level, so that the prediction results meet the spatial continuity requirements while satisfying the constraints of observation information. The solution process follows the following principles: (1) Local update and overall coordination. In each iteration, the formation state of a single or local grid cell is updated, while considering its continuity relationship with adjacent cells to avoid isolated decision-making. (2) Energy reduction principle. Each state update is based on reducing or not increasing the objective function value, thereby ensuring the stable progress of the solution process.

[0111] Initial solution construction: To improve solution efficiency and enhance result stability, initial stratigraphic classification is first performed on each grid cell based solely on the data consistency term, without considering spatial regularization constraints. This initial result mainly reflects the support of borehole observations and multi-index characteristic information for stratigraphic types, and can be regarded as a data-driven preliminary stratigraphic structure.

[0112] A reasonable initial solution helps subsequent iterations quickly reach a stable state and reduces the risk of getting trapped in unreasonable local solutions.

[0113] Iterative update strategy: Based on the initial solution, a spatial regularization constraint is introduced, and iterative optimization is performed using an Iterated Conditional Modes (ICM) approach: The label is updated point-by-point in each iteration, for the ... Given a fixed set of labels for all other mesh elements, select the category that minimizes local energy:

[0114] (6)

[0115] in and Units The vertical and horizontal neighbor sets.

[0116] During the iterative update process, to ensure that the prediction results remain consistent with the known borehole information, the model applies hard constraints to the grid cells of the borehole sample points after each iteration, forcibly restoring their stratigraphic type labels to the actual stratigraphic type measured in the borehole. This approach ensures that borehole information always serves as a reliable constraint in the inference process, avoiding the erroneous smoothing or covering of known stratigraphic layers under spatial regularization. By continuously fixing the stratigraphic state of the borehole sample points during iteration, the model can fully utilize spatial continuity constraints while strictly meeting the consistency requirements of engineering exploration data.

[0117] Convergence and stability analysis: Although this model is a non-convex optimization problem, making it difficult to theoretically guarantee convergence to the global optimum, its solution process exhibits good stability in engineering applications, mainly reflected in the following aspects:

[0118] (1) Monotonicity of the objective function. Each state update is based on the criterion of not increasing the objective function value. Therefore, the objective function exhibits a non-increasing trend during the iteration process, which helps to ensure the convergence of the algorithm.

[0119] (2) Finite state space. The number of strata types is finite, and the size of the discrete state space is limited. Under the constraint of energy reduction, the iterative process cannot continue indefinitely and will eventually reach a stable state.

[0120] (3) Spatial consistency of results. Under reasonable initial conditions and parameter values, multiple runs of the model can usually obtain prediction results with similar spatial structures, indicating that the model has a certain robustness to initial disturbances.

[0121] Analysis of engineering stability and result reliability:

[0122] From an engineering application perspective, the stability of the model solution is reflected not only in mathematical convergence, but also in whether the prediction results conform to engineering experience and geological understanding. By introducing spatial regularization constraints, the model can effectively suppress unreasonable stratigraphic jumps in regions with sparse boreholes or fluctuating parameters, making the predicted profile exhibit a clear and continuous sequence structure.

[0123] Practice has shown that, under the premise of reasonable setting of regularization parameters, the model prediction results are not sensitive to local data disturbances and have good engineering stability, which can provide a reliable reference for highway engineering survey, analysis and design decisions.

[0124] Stopping Iteration Criteria: To balance computational efficiency and result accuracy, this application adopts one of the following stopping criteria as the termination condition in the ICM iterative solution: (1) Labels no longer change: After a complete scan, the labels of all non-fixed mesh elements are no longer updated; (2) Energy change threshold: The change in the objective function value between two consecutive iterations satisfies (3) Maximum number of iterations: reaching the preset upper limit This is used to limit the computation time in the worst-case scenario.

[0125] Regarding parameter selection, the main parameters of the model include: vertical regularization weights. Horizontal regularization weights (or proportion) ), and deep feature weight coefficients Based on the general characteristics of highway engineering profiles, the following approach can be adopted: (1) Horizontally weakly regular proportions. To suppress transverse serrated boundaries and isolated patches, .when When it degenerates into only vertical constraint, it is prone to lateral burrs; when If the value is too large, it may become overly smooth, masking the true transverse phase transition or the influence of local structures. (2) Vertical canonical strength Sections with sparse boreholes, large fluctuations in indicators, or stable stratigraphic sequences can be appropriately enlarged. To enhance sequence continuity; road sections with complex geological conditions and numerous interlayers / abrupt changes should reduce [the density of the road]. To avoid suppressing real transitions. (3) Depth weights When there is significant overlap in the geotechnical properties of adjacent layers, the appropriate increase can be made. Enhance hierarchical discriminant analysis; if the depth features are too strong, leading to stratification based solely on depth, then the hierarchy should be reduced. (4) Selection of distance metric: When the geotechnical indices are highly correlated (such as the correlation between water content and liquidity index), Mahalanobis distance is recommended, and numerical stability is enhanced by adding a covariance stabilizing term; when the indices are approximately independent or the sample size is small, Euclidean distance can be used to reduce estimation uncertainty.

[0126] The aforementioned stopping criteria and parameter recommendations enable the model to obtain stable and interpretable prediction results with fewer iterations at the general highway engineering profile scale, and can be adapted to the geological complexity and survey data conditions of different road sections by adjusting a few parameters.

[0127] Case Analysis:

[0128] A section along a road project was selected as a case study. The study area is located in the alluvial plain geomorphological unit, with relatively flat terrain, well-developed Quaternary overburden, and stratigraphic types mainly consisting of multi-layered sedimentary soils.

[0129] Two-dimensional stratigraphic profiles and borehole distribution in the study area are as follows: Figure 2 As shown, the research profile exhibits a relatively clear layered structure overall. Different strata are relatively stable in the vertical direction, but show some undulations in the horizontal direction. The borehole sample points are arranged along the road axis, with a large horizontal spacing and a relatively dense vertical sampling, which effectively reflects the variations in strata and soil parameters at different depths.

[0130] From the perspective of stratigraphic distribution, the stratigraphic interfaces are generally continuous in the horizontal direction, but not completely straight, reflecting the influence of changes in the sedimentary environment on the thickness and depth of strata in the alluvial plain area. This profile structure has a certain degree of complexity, while maintaining obvious sequence characteristics, and can serve as a typical engineering case for two-dimensional stratigraphic prediction methods.

[0131] The spatial distribution of geotechnical engineering parameters at the borehole point is as follows: Figures 3-5 As shown, these are the water content. w Plasticity index Ip and liquidity index IL Distribution characteristics within the profile. Each point in the figure corresponds to the measured parameter value of the borehole at a specific depth, and its spatial distribution is consistent with the borehole sampling location.

[0132] As can be seen from the figure, the water content w The plasticity index generally increases with burial depth, but within the same depth range, there is still some dispersion between different boreholes, reflecting the influence of local depositional conditions and soil property differences on the soil's water content. Ip The soil exhibits certain stratification characteristics in different strata, but its numerical distribution is not strictly zoned, reflecting the spatial heterogeneity of soil physical parameters in actual engineering. The spatial distribution of the liquidity index IL is relatively dispersed, with higher values ​​appearing in some deep locations, reflecting the engineering characteristics of local soft soil layers.

[0133] Prediction results and spatial structure analysis:

[0134] (1) Overall characteristics of stratigraphic prediction results:

[0135] Based on the aforementioned model, stratigraphic structure prediction was performed on the studied profile, and the results are as follows: Figure 6 As shown, the predicted profile exhibits a clear and continuous layered structure in its overall morphology. The strata are stably distributed vertically, with a clear sequence relationship, consistent with the basic judgment of the stratigraphic structure of this region in engineering geology. Furthermore, the prediction results also demonstrate a high accuracy rate of 95.64%.

[0136] From a spatial perspective, the stratigraphic interfaces exhibit some horizontal undulations, but the overall variation is gradual, without large-scale, unreasonable abrupt changes or fractures. This indicates that while utilizing borehole information, the model effectively constrains the spatial continuity of the strata, avoiding the generation of jagged or patchy non-engineering structures due to local data fluctuations. Furthermore, the borehole sample points in the prediction results are consistent with their corresponding stratigraphic type labels, demonstrating that the model strictly meets the constraints of the borehole-revealed information during the calculation process, providing a reliable foundation for subsequent results analysis.

[0137] To further analyze the spatial rationality of the prediction results, the model prediction results were compared with the actual strata, and the distribution of their differences is as follows: Figure 7 As shown in the figure, the areas of difference are mainly concentrated near the stratigraphic interfaces, while in the internal stratigraphic regions, the predicted height is consistent with the actual stratigraphic height.

[0138] This phenomenon indicates that the model has high discrimination stability within the strata. However, near the strata boundaries, due to some overlap in engineering parameters between different strata and limited borehole control, slight deviations in the prediction results at local locations are within a reasonable range. From an engineering perspective, these differences mostly occur in the strata boundary transition zone and have little impact on the overall representation of the stratigraphic structure and engineering applications.

[0139] Furthermore, the differential regions did not exhibit an irregular, scattered distribution, but rather a banded distribution along the layer boundaries, indicating that the model prediction error has a clear spatial structure characteristic rather than being dominated by random noise.

[0140] (2) Model optimization process and convergence characteristic analysis:

[0141] The changes in the objective function value during the model solution process are as follows: Figure 8 As shown, in the initial iteration phase, the objective function value decreases rapidly and then tends to stabilize, indicating that the model can complete the transition from the initial solution to the stable solution in a relatively small number of iterations.

[0142] This convergence process demonstrates the efficiency of the adopted solution strategy in engineering-scale problems. On the one hand, the data consistency term quickly guides the stratigraphic classification results toward a reasonable solution in the initial stage; on the other hand, the spatial regularization term gradually plays a role in subsequent iterations, correcting local discontinuous structures and making the prediction results more spatially smooth and stable.

[0143] Overall, the model optimization process did not exhibit significant oscillations or repeated bounces, indicating that the constructed objective function and solution strategy have good numerical stability and are suitable for practical engineering profile analysis.

[0144] (3) Correspondence between multi-index characteristic fields and stratigraphic structure:

[0145] Figures 9-11 The spatial distribution characteristics of water content (w), plasticity index (Ip), and liquidity index (IL) within the profile are presented. It can be seen that these engineering parameters generally exhibit a certain regularity with burial depth, but there are still obvious lateral differences within the same depth range, reflecting the spatial heterogeneity of soil engineering properties.

[0146] Comparative analysis of the characteristic fields and predicted stratigraphic structures reveals that different strata exhibit statistically significant differences in multiple index characteristics, but are not strictly zoned. For example, some adjacent strata have certain overlapping ranges in terms of water content or plasticity index, making stable partitioning difficult to achieve using only a single index. This also underscores the necessity of introducing multi-index joint modeling.

[0147] The model makes judgments by integrating multiple feature information and is supplemented by spatial continuity constraints, so that the predicted stratigraphic structure not only keeps in line with the overall trend of the feature field, but also avoids unreasonable stratification caused by fluctuations in a single index.

[0148] (4) Comparative analysis of the spatial morphology of the layer interface:

[0149] To visually assess the spatial morphology of the predicted stratigraphic interfaces, the interfaces of each layer were extracted and compared with a reference interface. The results are as follows: Figure 12 As shown, the overall trend of the prediction interface is highly consistent with that of the reference interface, and the fluctuations in the horizontal direction are basically the same.

[0150] In some local locations, there is a certain offset between the predicted interface and the reference interface, mainly concentrated in sections where the interface undulations are more pronounced. These deviations are often related to insufficient borehole control or transition zones of characteristic parameters, and fall within the range of uncertainties commonly encountered in engineering exploration. Overall, the predicted interface can effectively reflect variations in formation thickness and spatial continuity, meeting the engineering design requirements for continuous representation of the formation structure.

[0151] (5) Classification performance and hierarchical recognition difficulty analysis:

[0152] The overall performance of the model classification was evaluated using the confusion matrix and hierarchical accuracy statistics, and the results are as follows: Figure 13 and Figure 14 As shown in the diagram, the confusion matrix reveals that most samples are concentrated on the diagonal, indicating that the model has a high recognition accuracy for each stratum.

[0153] Further analysis of the stratification accuracy reveals that the difficulty of identifying different strata varies. Strata with stable sequences and prominent engineering parameter characteristics show higher accuracy, while strata in intermediate transitional positions with significant overlap in engineering parameters exhibit relatively lower accuracy. This result aligns with engineering experience and reflects the model's sensitivity to stratigraphic complexity.

[0154] Overall, the model maintains high accuracy while reasonably reflecting the difficulty of different formations in terms of engineering characteristics, and the prediction results have good credibility and engineering interpretability.

[0155] This application addresses the challenges of limited borehole quantity and incomplete spatial stratigraphic information in highway engineering surveys by constructing a two-dimensional stratigraphic structure prediction model that incorporates spatial regularization constraints. By discretizing the study profile into a regular grid and using multi-index engineering parameters as feature descriptions, a unified representation of stratigraphic structure from continuous physical space to discrete inference is achieved. Without relying on additional geological genetic assumptions, the model can fully utilize borehole information to make a comprehensive inference of the stratigraphic distribution within the profile.

[0156] During model construction, the combination of multi-index feature space discrimination and anisotropic spatial regularization constraints effectively mitigated the stratigraphic jumps and noise problems that easily arise in point-by-point classification. An iterative conditional mode was used for optimization during the solution process, and hard constraints were applied to the borehole sample points after each iteration to ensure that the prediction results remained consistent with known exploration information. Numerical results show that the model has good convergence and stability, and the predicted strata are spatially continuous with clear sequence relationships.

[0157] The results of engineering case studies further validated the applicability of the model in the geological profile analysis of actual highway engineering projects. The predicted stratigraphic structure was generally consistent with the engineering geological understanding, with errors mainly concentrated in the transition zones between strata and exhibiting clear spatial distribution characteristics. The study demonstrates that this model can serve as an effective technical means for stratigraphic structure analysis and auxiliary interpretation during the highway engineering exploration phase, providing a reasonable stratigraphic structure reference for engineering design.

[0158] Example 2:

[0159] This embodiment provides a two-dimensional formation structure prediction system under limited borehole observation information conditions, including: a memory and a processor;

[0160] The memory is used to store computer programs;

[0161] The processor is configured to invoke the computer program to execute the method as described in Embodiment 1.

[0162] Example 3:

[0163] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is run on an electronic device, it causes the electronic device to perform the method described in Embodiment 1.

[0164] Example 4:

[0165] This embodiment provides a computer program product, including a computer program that, when run on an electronic device, causes the electronic device to perform the method described in Embodiment 1.

[0166] The specific implementation of the system, electronic device, computer-readable storage medium, and computer program product provided in this application can be referred to the specific embodiments of the above methods, and will not be repeated here.

[0167] Obviously, those skilled in the art should understand that the various units or steps of this application described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device, or fabricating them separately as individual integrated circuit modules, or fabricating multiple modules or steps into a single integrated circuit module. Thus, this application is not limited to any particular combination of hardware and software.

[0168] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A two-dimensional formation structure prediction method under limited borehole observation information, characterized in that, Includes the following steps: The engineering geological profile of the target area is spatially discretized, and the two-dimensional continuous spatial domain is divided into regular grids to obtain several grid cells. Each grid cell represents a finite spatial region within the profile. Construct state variables for each grid cell, including feature vectors for characterizing the soil engineering properties of each grid cell and stratigraphic type labels for representing the stratigraphic type to which each grid cell belongs; Based on the state variables corresponding to borehole samples, characteristic prototypes of various types of strata are established, specifically including: Let the first The feature set of borehole samples corresponding to the strata-like formation is Estimate the first by using sample statistics Characteristic prototypes of strata ,in, Indicates the first The feature vector of each grid cell Indicates the first Stratigraphic type of each grid cell , Let be the dimension of the eigenvector. Indicates the first Strata in the first Indicator values ​​on each feature dimension Indicates the first The grid cell in the first... Indicator values ​​on each feature dimension And a shared covariance matrix estimated from all borehole samples is introduced; Describes the overall correlation structure in the feature space; A stratigraphic classification model is constructed based on the state variables of grid cells. The objective function of the stratigraphic classification model includes a data consistency term and a spatial regularization term. The data consistency term characterizes the degree of matching between each grid cell and different stratigraphic types based on the distance metric between the feature vectors of each grid cell and the feature prototypes of various stratigraphic types. The spatial regularization term penalizes stratigraphic transitions between adjacent grid cells to achieve spatial continuity constraints. The formula is as follows: ； in, This is the set of stratigraphic type labels for all grid cells. The total number of grid cells. For data consistency items, their value is equal to the first... Feature vectors of grid cells and Distance metric value corresponding to the prototype of the stratigraphic type feature; and These represent the vertical and horizontal continuity constraint strengths, respectively. ,in ; and These represent the sets of vertically and horizontally adjacent grid cells, respectively. For indicator functions, when Take 1 if there is a discrepancy; The objective function of the stratigraphic classification model is solved to obtain the stratigraphic type corresponding to each grid cell, i.e., the two-dimensional stratigraphic structure prediction result.

2. The method according to claim 1, characterized in that, Multiple physical indicators reflecting the state and composition characteristics of the soil, as well as geometric indicators reflecting the spatial location, are selected as stratigraphic discrimination features. For each grid cell, a multidimensional feature vector is constructed, where each dimension corresponds to a physical or geometric indicator.

3. The method according to claim 2, characterized in that, When constructing feature vectors, all indicators are processed using a uniform scale, and a separate weighting coefficient is introduced for depth-related indicators to control their influence in the overall feature space. When different strata overlap in their stratigraphic discrimination features, the weighting coefficient is increased to enhance the sequence discrimination capability. When the information of depth-related indicators is too strong, causing the prediction results to tend to be stratified only by depth, the influence of depth-related indicators is reduced by decreasing the weighting coefficient.

4. The method according to claim 1, characterized in that, The distance measurement methods include Euclidean distance measurement and Mahalanobis distance measurement, wherein: When the different indices in the feature vector are preprocessed to have uniform dimensions and their correlation is less than the first preset threshold, the Euclidean distance metric is used, and the expression is: ,in Indicates the first Feature vectors of grid cells With the Characteristic prototypes of strata Distance metric; When the correlation between different indicators in the feature vector is greater than the second preset threshold or the variance difference is greater than the third preset threshold, Mahalanobis distance is used, and the expression is: When calculating the covariance matrix A regularization term is introduced on the diagonal to avoid matrix singularity problems.

5. The method according to claim 1, characterized in that, Solving the objective function of the stratigraphic classification model includes: using an iterative approximation solution strategy to solve the objective function of the stratigraphic classification model; the iterative approximation solution strategy specifically includes: Initial solution construction: Based on the distance metric results, the stratigraphic type with the smallest corresponding distance metric value is selected as the initial stratigraphic type for each grid cell, resulting in an initial stratigraphic type label set. ; Iterative Update: A conditional iterative model is used, based on the objective function, to update the stratigraphic type label of each grid cell point by point: for the... For each grid cell, the formation type label of the remaining grid cells is kept unchanged, and the local energy is selected. smallest As an updated stratigraphic type label, in and The first The vertical and horizontal neighbor sets of each grid cell; Hard constraint processing for borehole samples: After each iteration, the formation type label of the grid cell corresponding to the borehole sample is forcibly restored to the actual formation type measured by the borehole to ensure that the borehole information is not interfered with by spatial regularization processing.

6. A two-dimensional formation structure prediction system under limited borehole observation information, characterized in that, include: Memory and processor; The memory is used to store computer programs; The processor is configured to invoke the computer program to perform the method as described in any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed on an electronic device, causes the electronic device to perform the method as described in any one of claims 1 to 5.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is run on an electronic device, the electronic device causes the electronic device to perform the method as described in any one of claims 1 to 5.

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