Method and device for reconstructing a groundwater flow field

Abstract

This disclosure provides a method and apparatus for reconstructing groundwater flow fields. The method includes setting N interpolation points in a permeability coefficient weighted map of the area to be reconstructed, where N is a natural number greater than or equal to 1; acquiring several pre-set known hydraulic head points in the area to be reconstructed; converting the N interpolation points into N calculated hydraulic head points based on the permeability coefficient weighted map and the known hydraulic head points; and fitting all calculated hydraulic head points and known hydraulic head points to obtain groundwater flow field data for the area to be reconstructed. This disclosure maps neighboring hydraulic head points to a virtual two-dimensional hydraulic coordinate system near the interpolation points under the combined constraints of weighted shortest path distance and path direction, and determines the hydraulic head value of the interpolation points through local hydraulic head plane fitting. This method retains the characterization of the hydraulic connectivity of heterogeneous media by the shortest path distance, and reflects the hydraulic head variation trend near the interpolation points through local plane parameters.

Description

Technical Field

[0001] This disclosure relates to the field of geological field reconstruction technology, and in particular to a method and apparatus for reconstructing groundwater flow fields. Background Technology

[0002] This section is intended to provide background or context for the embodiments of this disclosure as set forth in the claims. The description herein is not intended to be a prior art simply because it is included in this section.

[0003] Groundwater head field is an important basic data for characterizing the occurrence state, flow direction and hydraulic gradient distribution of groundwater. Its spatial distribution results directly affect groundwater flow field analysis, pollutant migration prediction, engineering precipitation evaluation and water resource development and utilization decisions.

[0004] Currently, commonly used spatial interpolation methods for hydraulic head fields primarily reconstruct the flow using the Euclidean distance between the interpolation point and the hydraulic head point. However, for heterogeneous aquifers, groundwater flow is not only controlled by the geometric distance between observation points but is also significantly influenced by factors such as the spatial distribution of permeability coefficients, low-permeability interlayers or water-blocking regions, high-permeability dominant channels, and geological structural boundaries. Under these conditions, the Euclidean distance between two points cannot accurately reflect their hydraulic connectivity. Especially when low-permeability areas exist within the study area, the actual groundwater flow path often exhibits bypassing or preferential connectivity along high-permeability areas. Traditional interpolation methods tend to directly correlate observation points on both sides of low-permeability areas based on geometric distance, leading to distortion when isohyetal lines cross low-permeability areas.

[0005] Therefore, given the limited head data from observation wells, incomplete boundary conditions, and significant aquifer heterogeneity, there is an urgent need for a head field interpolation method that can comprehensively consider permeability coefficient zoning, hydraulic connectivity paths, path directions, and local head variation trends. This method should avoid relying solely on Euclidean distance or simple distance-weighted averaging, and should transform the blocking effect of low-permeability regions and the dominant connectivity effect of high-permeability regions into distance and direction constraints in the interpolation calculation. This would allow for a more reasonable reconstruction of the groundwater head field in heterogeneous aquifers and provide a reliable foundation for subsequent velocity field calculations and groundwater flow field analysis. Summary of the Invention

[0006] In view of this, the purpose of this disclosure is to propose a method and apparatus for reconstructing groundwater flow fields, which at least partially solves one of the technical problems in the related art.

[0007] To achieve the above objectives, a first aspect of the exemplary embodiments of this disclosure provides a method for reconstructing a groundwater flow field, comprising:

[0008] N interpolation points are set in the permeability coefficient weighted map of the area to be reconstructed; where N is a natural number greater than or equal to 1; several known hydraulic head points are obtained in the area to be reconstructed; based on the permeability coefficient weighted map and the several known hydraulic head points, the N interpolation points are converted into N calculated hydraulic head points; and all calculated hydraulic head points and known hydraulic head points are fitted to obtain the groundwater flow field data of the area to be reconstructed.

[0009] Based on the same inventive concept, a second aspect of the exemplary embodiments of this disclosure provides an apparatus for reconstructing groundwater flow fields, comprising: An interpolation point configuration module is configured to set N interpolation points in the permeability coefficient weighted map of the area to be reconstructed; where N is a natural number greater than or equal to 1; a module configured to acquire hydraulic head data of a number of pre-set known hydraulic head points in the area to be reconstructed; a module configured to convert the N interpolation points into N calculated hydraulic head points based on the permeability coefficient weighted map and the number of known hydraulic head points; and a fitting module configured to fit all the calculated hydraulic head points and the known hydraulic head points to obtain the groundwater flow field data of the area to be reconstructed.

[0010] Based on the same inventive concept, a third aspect of the exemplary embodiments of this disclosure provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method as described in the first aspect.

[0011] Based on the same inventive concept, a fourth aspect of the exemplary embodiments of this disclosure provides a non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform the method as described in the first aspect.

[0012] Based on the same inventive concept, a fifth aspect of the exemplary embodiments of this disclosure provides a computer program product including computer program instructions that, when run on a computer, cause the computer to perform the method as described in the first aspect.

[0013] As can be seen from the above, the technical solution provided in this disclosure differs from the traditional distance-weighted average interpolation method. This disclosure does not directly represent the hydraulic head at the interpolation point as the distance-weighted average of neighboring hydraulic head points. Instead, it maps neighboring hydraulic head points to a virtual two-dimensional hydraulic coordinate system near the interpolation point under the combined constraints of weighted shortest path distance and path direction, and determines the hydraulic head value at the interpolation point through local hydraulic head plane fitting. This method retains the characterization of the hydraulic connectivity of heterogeneous media by the shortest path distance, and also reflects the trend of hydraulic head variation near the interpolation point through local plane parameters. This allows for a better construction of a groundwater field structure that is identical to the real-world situation. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in this disclosure or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a schematic flowchart of the groundwater field reconstruction method according to an embodiment of the present disclosure; Figure 2 This is a flowchart illustrating the method for initially obtaining the calculated head point according to an embodiment of the present disclosure; Figure 3 This is a flowchart illustrating the method for obtaining the intermediate head point according to an embodiment of the present disclosure; Figure 4 This is a schematic diagram of an embodiment of groundwater field reconstruction according to the present disclosure; Figure 5 This is a schematic diagram of a triangular mesh node segmentation structure according to an embodiment of the present disclosure; Figure 6 This is a contour map of the seepage head distribution in an embodiment of this disclosure; Figure 7 This publication contains a cross-sectional view of the city's hydrogeological structure and boundary conditions; Figure 8 This is a schematic diagram of the structure of the groundwater field reconstruction device according to an embodiment of the present disclosure; Figure 9 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present disclosure. Detailed Implementation

[0016] It is understood that before using the technical solutions disclosed in the various embodiments of this application, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in this application in an appropriate manner in accordance with relevant laws and regulations, and user authorization should be obtained.

[0017] For example, upon receiving a user's active request, a prompt message is sent to the user to explicitly inform them that the requested operation will require the acquisition and use of the user's personal information. This allows the user to independently choose whether to provide personal information to the software or hardware, such as the electronic device, application, server, or storage medium performing the operations of this application's technical solution, based on the prompt message.

[0018] As an optional but non-limiting implementation, in response to a user's active request, sending a prompt message to the user can be done via a pop-up window, where the prompt message can be presented in text format. Furthermore, the pop-up window can also include a selection control allowing the user to choose "agree" or "disagree" to provide personal information to the electronic device.

[0019] It is understood that the above notification and user authorization process are merely illustrative and do not constitute a limitation on the implementation of this application. Other methods that comply with relevant laws and regulations may also be applied to the implementation of this application.

[0020] It is understood that the data involved in this technical solution (including but not limited to the data itself, the acquisition or use of the data) shall comply with the requirements of relevant laws, regulations and related provisions.

[0021] To make the objectives, technical solutions, and advantages of this disclosure clearer, the principles and spirit of this disclosure will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are provided merely to enable those skilled in the art to better understand and implement this disclosure, and are not intended to limit the scope of this disclosure in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of this disclosure to those skilled in the art.

[0022] In this article, it is important to understand that any number of elements in the accompanying figures is for illustrative purposes and not for limitation, and any naming is for distinction only and has no limiting meaning.

[0023] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this disclosure should have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains. The terms "first," "second," and similar words used in the embodiments of this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly. The article "a" or "an" preceding an element does not exclude the existence of multiple such elements.

[0024] The principles and spirit of this disclosure will be explained in detail below with reference to several representative embodiments. Invention Overview As described in the background section, groundwater head field is crucial fundamental data for characterizing groundwater occurrence, flow direction, and hydraulic gradient distribution. Its spatial distribution directly impacts groundwater flow field analysis, pollutant migration prediction, engineering precipitation evaluation, and water resource development and utilization decisions. In actual hydrogeological surveys, head data typically originates from a limited number of observation wells or monitoring wells, and the limited number and uneven spatial distribution of observation points are common problems. Therefore, how to reasonably reconstruct the continuous head field of the study area based on limited observation well head data is a key issue in groundwater numerical analysis and hydrogeological interpretation.

[0026] In related technologies, commonly used spatial interpolation methods for head fields mainly include the Kriging method, the inverse distance weighted method, and the discrete smooth interpolation method.

[0027] Kriging, based on spatial autocorrelation theory, uses a variogram to characterize the spatial structure of observed data and determines interpolation weights under unbiased estimation conditions, thus reflecting spatial variation patterns at the regional scale well.

[0028] The inverse distance weighting method is based on the principle of distance decay, which holds that the closer the observation point is to the point to be estimated, the greater its influence. It has the advantages of high computational efficiency and simple implementation.

[0029] Discrete smooth interpolation constructs a global optimization model through least squares and smoothness constraints, which maintains the continuity and smoothness of the interpolation field while fitting known observations, and is suitable for spatial field reconstruction under certain complex conditions.

[0030] However, for heterogeneous aquifers, groundwater flow is not only controlled by the geometric distance between observation points, but also significantly influenced by factors such as the spatial distribution of permeability coefficients, low-permeability interlayers or water-blocking areas, high-permeability dominant channels, and geological structural boundaries. Under these conditions, the Euclidean distance between two points cannot accurately reflect their hydraulic connectivity. Especially when low-permeability areas exist in the study area, the actual groundwater flow path often exhibits bypassing or preferential connectivity along high-permeability areas. Traditional interpolation methods tend to directly correlate observation points on both sides of low-permeability areas based on geometric distance, leading to distortion when isohyetal lines cross low-permeability areas.

[0031] Furthermore, while the inverse distance-weighted interpolation method can reflect the influence of local distances, it is essentially a distance-weighted average, and the interpolation results are usually limited to the range of nearby observations. This can easily lead to a significant local "bullseye effect" near the observation point, and it is difficult to express the trend of head changes along the main flow direction. Although the Kriging method can use spatial correlation structures for estimation, its variogram is usually based on the statistical distance relationship between observation points. When the number of observation wells is small or the heterogeneous structure is complex, the fitting stability and directional expressive ability of the variogram are limited. Discrete smoothing interpolation can improve the problems of local abrupt changes and meaningless oscillations, but its smoothing constraint can easily weaken the hydraulic differences caused by geological structures such as low-permeability areas and dominant seepage channels, making it difficult to fully reflect the actual hydraulic connectivity characteristics in heterogeneous media.

[0032] To address the aforementioned issues, this disclosure provides a scheme for reconstructing groundwater flow fields, specifically including: setting N interpolation points in a permeability coefficient weighted map of the area to be reconstructed; where N is a natural number greater than or equal to 1; obtaining several pre-set known hydraulic head points in the area to be reconstructed; converting the N interpolation points into N calculated hydraulic head points based on the permeability coefficient weighted map and the several known hydraulic head points; and fitting all calculated hydraulic head points and known hydraulic head points to obtain groundwater flow field data for the area to be reconstructed. The technical solution provided in this disclosure differs from the traditional distance-weighted average interpolation method. This disclosure does not directly represent the hydraulic head of the interpolation point as the distance-weighted average of neighboring hydraulic head points. Instead, it maps the neighboring hydraulic head points to a virtual two-dimensional hydraulic coordinate system near the interpolation point under the constraints of weighted shortest path distance and path direction, and determines the hydraulic head value of the interpolation point through local hydraulic head plane fitting. This method retains the characterization of the hydraulic connectivity of the heterogeneous medium by the shortest path distance and reflects the hydraulic head variation trend near the interpolation point through local plane parameters. To better construct a groundwater field structure that is identical to the actual situation.

[0033] After introducing the basic principles of this disclosure, various non-limiting embodiments of this disclosure will be described in detail below.

[0034] Exemplary methods specifically refer to Figure 1 This disclosure discloses a method for reconstructing groundwater flow fields, comprising: Step 101: Set N interpolation points in the permeability coefficient weighted map of the region to be reconstructed; where N is a natural number greater than or equal to 1.

[0035] Step 102: Obtain several known head points that have been pre-set in the region to be reconstructed.

[0036] Step 103: Based on the permeability coefficient weighted map and several known head points, convert the N interpolation points into N head calculation points.

[0037] And in step 104, all calculated hydraulic head points and known hydraulic head points are fitted together to obtain the groundwater flow field data of the area to be reconstructed.

[0038] Specifically, in step 101, the permeability coefficient weighted map of the region to be reconstructed can be obtained in the following way: In one specific embodiment, a study area can be defined. for Let the set of grid nodes be Let the set of units be The permeability coefficient of the k-th unit is... Let the set of known head points be... Let the set of points to be interpolated be... .in, Indicates a known head point. Indicates the point to be interpolated. Indicates the first The water head values ​​at known water head points. Using the above variables, those skilled in the art can understand how to construct the mesh of the region to be reconstructed; this disclosure will not elaborate further. This mesh can be a triangular mesh. See [link to details]. Figure 5 , Figure 5 A possible structural diagram of triangular mesh node segmentation is shown.

[0039] After mesh generation, the mesh is converted into a permeability coefficient weighted graph. The weighted graph is constructed using mesh nodes as graph nodes and cell edges as graph edges. This weighted graph can be expressed by formula (1): (1) in, For a set of graph nodes, Let be the set of edges in the graph.

[0040] The vertices of the triangle are several known water head points pre-set in the region to be reconstructed.

[0041] specifically refer to Figure 2 The specific implementation method of step 103 is as follows: Step 201: Based on the permeability coefficient weighted map, calculate the first weighted shortest path data between the remaining interpolation points and all known head points.

[0042] Specifically, a predetermined number of path nodes are selected on the weighted shortest path, and the direction of the weighted shortest path is obtained by linearly fitting the path nodes. Specifically, in obtaining the shortest path... Then, from the point to be interpolated Depart, select the first path Nodes:

[0043] in, , This represents the number of path nodes used for orientation fitting.

[0044] By performing linear fitting using the selected path nodes, the interpolation point can be obtained. Point to a known point Local path direction unit vector:

[0045] in, , The path direction unit vectors are respectively in direction and Components in direction.

[0046] This direction represents the direction of the hydraulic influence of a known head point on the interpolation point. In other words, the shortest path distance describes the "strength of the influence," while the path direction describes "the direction from which the influence originates." When the number of nodes on the shortest path is insufficient to match the preset number of nodes for the direction, the actual usable nodes along the path are used for direction calculation.

[0047] Specifically, step 201 may include: Calculate the weight value of the graph edges for each cell in the penetration weighted graph. Specifically, calculate the weight value of the graph edges for each cell in the penetration weighted graph.

[0048] For any graph edge Its geometric length is ,in, , These are the two nodes at the two ends of the edge.

[0049] The equivalent permeability coefficient of the edge is determined based on the permeability coefficient of the adjacent unit. Specifically, if the edge is shared by two units, the larger of the permeability coefficients of the two adjacent units is taken as the equivalent permeability coefficient of the edge. This step can be expressed by formula (2): (2) in, , These are the permeability coefficients of the two units sharing this edge.

[0050] Furthermore, the graph edge weights are defined using formula (3): (3) in, Indicates groundwater along the edge of the map The path cost of hydraulic connectivity. The lower limit threshold of the permeability coefficient is used to prevent the denominator from becoming zero or the edge weight from increasing abnormally due to an excessively small permeability coefficient.

[0051] From formula (3), those skilled in the art can know that: the larger the edge length of the graph, the greater the path cost; the smaller the permeability coefficient of the graph edge, the greater the path cost. Therefore, low-permeability areas are represented as high-cost areas in the weighted graph, and high-permeability areas are represented as low-cost areas.

[0052] By using the graph edge weights as constraints, the weighted shortest path distance between the remaining interpolation points and all known head points is calculated. In a specific embodiment, the calculation step can be implemented using Dijkstra's algorithm. Specifically, for any interpolation point... and the currently known head points The weighted shortest path between the two can be calculated using Dijkstra's algorithm.

[0053] Let from arrive One of the paths is ,in .

[0054] The weighted length of this path can be expressed as formula (4): (4) but and The weighted shortest path distance between them can be expressed as formula (5): (5) in, Indicates the point to be interpolated With known head points The hydraulic connectivity distance between them. This distance is not a standard Euclidean distance, but a weighted distance that takes into account the blocking effect of grid edge length and permeability coefficient.

[0055] The corresponding shortest path can be expressed as formula (6): (6) A second preset number of path nodes are selected based on the distance of the weighted shortest path, and the direction of the weighted shortest path is obtained by linearly fitting these path nodes. Specifically, in obtaining the shortest path... Then, from the point to be interpolated Depart, select the first path There are 10 nodes. This step can be expressed as formula (7): (7) in, , The number of path nodes used for direction fitting is the second preset number. This disclosure does not specify how the second preset number should be selected; those skilled in the art can choose an appropriate second preset number based on their own business needs using suitable methods.

[0056] By performing linear fitting using the selected path nodes, the interpolation point can be obtained. Point to a known point Local path direction unit vector .in, , The path direction unit vectors are respectively in direction and Components in direction.

[0057] This direction represents the direction of the hydraulic influence of the known head point on the interpolation point. In other words, the shortest path distance describes the strength of the influence of the known head point on the interpolation point, and the path direction describes the direction from which this influence originates. When the number of nodes in the shortest path is insufficient to match the preset number of nodes for the direction, the actual usable nodes in the path are used for direction calculation.

[0058] Step 202: Based on the first weighted shortest path data and the first preset selection rule, select the target interpolation point from the N interpolation points, and transform the first weighted shortest path data into first fitted coordinate data. The first preset selection rule includes selecting the interpolation point with the smallest sum of the mean and variance of the distances between the interpolation point and the known head points. Specifically, in each round of recursive calculation, calculate the mean and variance of the weighted shortest path distances from each remaining interpolation point to its neighboring constraint points, and construct an interpolation priority index based on the mean and variance. Select the interpolation point with the smallest priority index as the current priority interpolation point. For the current priority interpolation point, further combine its weighted shortest path distance and path direction with those of its neighboring constraint points to map the neighboring constraint points to a virtual two-dimensional hydraulic coordinate system, and perform local head plane fitting.

[0059] Specifically, step 202 may include: Based on the weighted shortest path data, the optimal interpolation point is obtained according to preset rules. In one possible implementation, this step may include: Based on the weighted shortest path data, a third preset number of interpolation points are extracted. Specifically, for any given interpolation point... From the currently known set of water head points Choose the one closest to its weighted shortest path. Each point is used as the set of nearest constraint points. .in, Indicates the first The set of currently known head points during round recursion. Initially, It only includes the original observation well head points; as the recursion proceeds, nodes that have completed interpolation are also added to the current set of known points.

[0060] Calculate the mean and variance of the distance to the points to be interpolated. Specifically, for the points to be interpolated... , its arrival The weighted shortest path distance between the nearest constraint points is: .in, .

[0061] Then, the distance mean and distance variance are calculated. The distance mean can be expressed by formula (8), and the distance variance can be expressed by formula (9): (8) (9) in, This represents the average hydraulic connectivity distance from the point to be interpolated to the nearest constraint point. This indicates the degree of dispersion of the distance distribution between neighboring constraint points.

[0062] Based on the mean distance and the variance distance, the priority of all the third preset number of interpolation points is calculated. Specifically, an interpolation priority function for the interpolation points is defined, which can be expressed by formula (10): (10) in, Points to be interpolated Priority indicators This is the variance adjustment coefficient, used to coordinate the influence of the mean and variance terms in priority determination. When the distance has been normalized, it can be taken as... .

[0063] In each round of recursive calculation, select The smallest interpolation point is taken as the current priority interpolation point, and the step of selecting the priority interpolation point can be expressed by formula (11): (11) in, For the first The set of points that have not yet been interpolated during round recursion.

[0064] And the highest priority interpolation point is selected as the origin to construct the hydraulic coordinate system.

[0065] The above steps prioritize calculating interpolation points that are close to the current known head point and have a relatively even distribution of distances to neighboring constraint points. A smaller mean indicates that the point is strongly constrained by the known point; a smaller variance indicates that the distances to neighboring points involved in the calculation are relatively evenly distributed, and not controlled by a single nearby point. Therefore, this step allows the interpolation process to gradually advance from the reliable region to the unknown region.

[0066] A virtual two-dimensional hydraulic coordinate system is constructed using the optimal interpolation point as the origin, and the weighted shortest path data of the neighboring constraint points of all the optimal interpolation points in the virtual two-dimensional hydraulic coordinate system are transformed into the fitted coordinates. Specifically, the current priority interpolation point is determined. Then, this point is used as the local coordinate origin. Regarding its first neighboring constraint points The weighted shortest path distance and path direction unit vector Nearby constraint points Mapped to In a virtual two-dimensional hydraulic coordinate system with the origin as the origin, it can be specifically represented by formulas (12) and (13): (12) (13) This yields local fitting samples near the constraint points. .in, For the first The coordinates of the nearest constraint points in the virtual hydraulic coordinate system This is the head value at that point. Because... It is a unit vector, therefore .

[0067] The above formula shows that the distance from a point in the virtual coordinate system to the origin is equal to the weighted shortest path distance. In other words, this disclosure does not directly use the real coordinates of neighboring points for plane fitting, but rather uses the shortest path distance plus the path direction to reconstruct the local position of neighboring points relative to the point to be interpolated.

[0068] The purpose of this step is to convert the information on flow around, hindrance, and dominant connectivity paths in a heterogeneous medium into two-dimensional coordinates required for local plane fitting.

[0069] Step 203: Based on the first fitted coordinate data, fit the local head plane using the weighted least squares method to transform the target interpolation point into a calculated head point.

[0070] Specifically, in one possible implementation, this step may include: Based on the fitted coordinate data, the residuals between the point to be interpolated and the nearest constraint points are constructed. Specifically, for neighboring constraint points Residuals can be established .

[0071] Based on the distance of the weighted shortest path, the parameters of the local head plane expression are calculated using the weighted least squares method. And based on the residuals and the parameters, the weighted residual objective function is constructed. Specifically, to give higher weight to neighboring constraint points closer to the current priority interpolation point in local plane fitting, this invention uses the weighted least squares method to solve for the local head plane parameters.

[0072] The weight can be defined by formula (14): (14) in, To prevent distance thresholds with a denominator of zero. When At that time, adopt Use it in place of the denominator for calculation. Because Therefore, the weight can also be understood as the reciprocal of the weighted shortest path distance. Thus, the weighted least squares objective function can be expressed as formulas (15) and (16): (15) Right now: (16) The objective function represents fitting the local head plane near the current interpolation point by means of neighboring constraint points, while using the inverse of the shortest path distance as a weight, so that points that are closer to the current point and have stronger connectivity have a greater impact on the fitting result.

[0073] Based on the known head point vectors, the solution to the weighted residual objective function is obtained through matrix calculations. Specifically, the above problem is written in matrix form. Construct the design matrix (17): (17) Water head vector matrix (18): (18) Weight matrix (19): (19) The weighted least squares problem can then be expressed as formula (20): (20) The solution to formula (20) can be expressed as formula (21): (twenty one) when When approaching singularity, generalized inverse or regularized least squares methods can be used to solve the problem to ensure the stability of local plane parameters.

[0074] Based on the solution of the weighted residual objective function, the head data of the optimal interpolation point is calculated. The optimal interpolation point from which the head data is obtained is then transformed into the calculated head point. Specifically, since the current priority interpolation point... Set as the origin of the virtual local coordinate system Substitute it into the local water head plane. Thus, we obtain formula (22): (twenty two) therefore That is, the local head plane intercept c obtained by fitting is the head value of the current priority interpolation point.

[0075] Step 204: In response to the number of obtained calculated head points being less than a first preset number, the above steps are repeated until the number of obtained calculated head points is greater than or equal to the first preset number; wherein the first preset number is less than N. Wherein, after obtaining a sufficient number of calculated head points, the method of this disclosure no longer obtains calculated head points based on known head points, but rather converts the remaining interpolation points into calculated head points based on the calculated head points for which head data has already been obtained. Because of... Figure 5 As shown in the mesh partitioning structure, the distance between the known calculated head point and the remaining interpolation point is smaller than the distance between the known head point and the interpolation point, thus the accuracy of the obtained results will be higher.

[0076] In one specific embodiment, the first preset number can be 30. Once 30 or more calculation head points have been obtained, the known head points are no longer used to calculate the head data of the remaining interpolation points. Instead, the already obtained calculation head points are used to calculate the head data of the remaining interpolation points.

[0077] specifically refer to Figure 3 Therefore, after converting at least a first preset number of interpolation points into calculation head points, the method included in this disclosure further includes: Step 301: In response to the number of calculated head points being greater than or equal to a first preset number, based on the permeability coefficient weighted map, calculate the second weighted shortest path data between the remaining interpolation points and all calculated head points. The specific implementation method for this step can be found in step 301.

[0078] Step 302: Based on the second weighted shortest path data and the second preset selection rule, select the target interpolation point from the remaining interpolation points, and transform the second weighted shortest path data into second fitted coordinate data. The second preset selection rule includes selecting the interpolation point with the smallest sum of the mean and variance of the distances from the calculated head points. Specifically, in each round of recursive calculation, calculate the mean and variance of the weighted shortest path distances from each remaining interpolation point to its neighboring constraint points, and construct an interpolation priority index based on the mean and variance. Select the interpolation point with the smallest priority index as the current priority interpolation point. For the current priority interpolation point, further combine its weighted shortest path distance and path direction with those of its neighboring constraint points to map the neighboring constraint points to a virtual two-dimensional hydraulic coordinate system, and perform local head plane fitting. The specific implementation method for this step can be found in step 202.

[0079] Step 303: Based on the second fitted coordinate data, fit the local head plane using the weighted least squares method to transform the target interpolation point into a head calculation point. The specific implementation method for this step can be found in step 203.

[0080] And in step 304, in response to the number of remaining interpolation points being greater than or equal to 1, the above steps are repeated until the number of interpolation points is less than 1.

[0081] For details, please refer to Figure 4 As shown in one possible embodiment, the technical solution of this disclosure uses the study area boundary, observation well locations, and permeability coefficient partition boundaries as constraints to perform grid subdivision of the study area and generate a computational grid. Input data includes grid node coordinates, element node connection relationships, element permeability coefficients, and known head data from the observation wells.

[0082] Specifically, after all the points to be interpolated have been converted into calculation head points, the current priority interpolation point... In a virtual two-dimensional hydraulic coordinate system, a local head plane is constructed (23): (twenty three) in, Indicates virtual Local head change rate in the direction, Indicates virtual Local head change rate in the direction, This represents the head value of the local head plane at the origin.

[0083] When the current priority interpolation point is completed After the head is calculated, the point is removed from the set of points to be interpolated and added to the current set of known points (24) and (25): (twenty four) (25) The original wellhead point remains fixed throughout the calculation process; the recursively obtained interpolation points are used as extended known points to continue participating in the selection of neighboring constraint points and local plane fitting for subsequent unknown points.

[0084] Repeat the steps for processing the remaining points to be interpolated until all unknown points have completed head interpolation. At this point, the hydraulic head values ​​of all grid nodes in the study area are obtained. After obtaining the hydraulic head values ​​of all grid nodes, the hydraulic gradient can be calculated based on the linear distribution of hydraulic head within the unit, and the groundwater velocity field can be calculated according to Darcy's law (26): (26) in, This represents the Darcy velocity vector within the cell. The permeability coefficient of this unit. This represents the head gradient within the unit.

[0085] Using the method of this invention, in the vicinity of low-permeability regions, the connection between the interpolation point and the observation well is no longer determined solely by the geometric straight-line distance, but rather by the permeability coefficient-weighted shortest path. Simultaneously, local head plane fitting can express the trend of head slope changes near the current point. Therefore, this method can reduce the distortion of isohead lines caused by traditional inverse distance-weighted interpolation directly crossing low-permeability regions and reduce the local bullseye effect near the observation well.

[0086] Using the methods included in this disclosure, the final groundwater flow field is as follows: Figure 6 and Figure 7 shown. Specifically, Figure 6 A hydrogeological conceptual profile is shown, illustrating the stratigraphic structure, permeability coefficient, and boundary constant head conditions of the model. Figure 7 The figures show contour maps of groundwater head obtained from numerical simulation, demonstrating the spatial distribution of groundwater head across the entire model area. Both figures comprehensively present the groundwater seepage modeling of strata containing weakly permeable interlayers. The left profile represents the modeling input conditions, while the right contour map shows the calculated hydraulic head field results.

[0087] Using the groundwater flow field reconstruction method based on weighted distance and least squares provided by this invention, the groundwater head field and velocity field of the study area can be obtained after calculating the above-mentioned heterogeneous aquifer flow model. The calculation results show that, under the condition of weakly permeable areas, this method can characterize the hydraulic connectivity between different nodes using permeability coefficient-weighted shortest path distance. This means that the connection between the interpolation point and the known head point is no longer determined solely by the Euclidean straight-line distance, but is jointly controlled by the medium's permeability and the available paths. For nodes near low-permeability areas, the shortest path distance can reflect the hindering effect of the weakly permeable zone on groundwater movement, causing the reconstruction results to show a trend of bypassing low-permeability areas and preferentially connecting along relatively high-permeability areas.

[0088] Furthermore, this method constructs a virtual two-dimensional hydraulic coordinate system by incorporating the shortest path direction, and uses a weighted least squares method to fit the local head plane within this local coordinate system. This ensures that the head reconstruction results are not only influenced by the distance to nearby known points but also reflect the local head slope variation trend. The hydraulic gradient and Darcy velocity field, further calculated from the reconstructed head field, clearly reflect the overall trend of groundwater movement from the high-head boundary to the low-head boundary, and exhibit reasonable flow characteristics around the groundwater near the weakly permeable area. Compared to the traditional interpolation method that only uses Euclidean distance for weighted averaging, this method can reduce the distortion of isohead lines caused by the direct correlation of head points on both sides of the low-permeability zone and reduce the local bullseye effect that easily occurs in traditional inverse distance interpolation.

[0089] In summary, the groundwater flow field reconstruction method based on weighted distance and least squares provided by this invention can incorporate permeability coefficient zoning, hydraulic connectivity paths, path directions, and local head variation trends into the head field reconstruction process, even under conditions of limited wellhead head data and significant spatial differences in aquifer permeability coefficients. This method does not rely on complete boundary conditions, source-sink terms, and storage parameters, and can quickly obtain a physically plausible groundwater head field. Furthermore, it can calculate the groundwater velocity field based on Darcy's law, providing an effective technical means for groundwater flow field analysis, engineering evaluation, and hydrogeological interpretation under heterogeneous aquifer conditions.

[0090] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0091] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0092] Exemplary device Based on the same inventive concept, corresponding to any of the above-described embodiments, this disclosure also provides an apparatus for reconstructing groundwater flow fields.

[0093] refer to Figure 8 The device for reconstructing groundwater flow field includes: An interpolation point configuration module is configured to set N interpolation points in the permeability coefficient weighted map of the area to be reconstructed; where N is a natural number greater than or equal to 1; a module configured to acquire hydraulic head data of a number of pre-set known hydraulic head points in the area to be reconstructed; a module configured to convert the N interpolation points into N calculated hydraulic head points based on the permeability coefficient weighted map and the number of known hydraulic head points; and a fitting module configured to fit all the calculated hydraulic head points and the known hydraulic head points to obtain the groundwater flow field data of the area to be reconstructed.

[0094] For ease of description, the above apparatus is described in terms of its functions, divided into various modules. Of course, in implementing this disclosure, the functions of each module can be implemented in one or more software and / or hardware.

[0095] The apparatus of the above embodiments is used to implement the corresponding method for reconstructing groundwater flow field in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0096] Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this disclosure also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for reconstructing groundwater flow fields as described in any of the above embodiments.

[0097] Figure 9This embodiment illustrates a more specific hardware structure of an electronic device, which may include a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, memory 1020, input / output interface 1030, and communication interface 1040 are interconnected internally via the bus 1050.

[0098] The processor 1010 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0099] The memory 1020 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program code is stored in the memory 1020 and is called and executed by the processor 1010.

[0100] The input / output interface 1030 is used to connect input / output modules to realize information input and output. The input / output modules can be configured as components in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touch screens, microphones, various sensors, etc., and output devices may include displays, speakers, vibrators, indicator lights, etc.

[0101] The communication interface 1040 is used to connect a communication module (not shown in the figure) to enable communication between this device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0102] Bus 1050 includes a pathway for transmitting information between various components of the device, such as processor 1010, memory 1020, input / output interface 1030, and communication interface 1040.

[0103] It should be noted that although the above-described device only shows the processor 1010, memory 1020, input / output interface 1030, communication interface 1040, and bus 1050, in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the embodiments of this specification, and not necessarily all the components shown in the figures.

[0104] The electronic devices described above are used to implement the corresponding methods for reconstructing groundwater flow fields in any of the foregoing embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0105] The memory 1620 stores machine-readable instructions executable by the processor 1610. When the electronic device is running, the processor 1610 communicates with the memory 1620 via the bus 1630, causing the processor 1610 to execute the following instructions during operation: Set N interpolation points in the permeability coefficient weighted map of the region to be reconstructed; where N is a natural number greater than or equal to 1. Obtain several pre-defined known head points in the region to be reconstructed; Based on the permeability coefficient weighted plot and several known head points, the N interpolation points are converted into N head calculation points; and All calculated hydraulic head points and known hydraulic head points are fitted together to obtain the groundwater flow field data of the area to be reconstructed.

[0106] Through the above method, the technical solution included in this disclosure maps nearby hydraulic head points to a virtual two-dimensional hydraulic coordinate system near the interpolation point under the joint constraints of weighted shortest path distance and path direction, and determines the hydraulic head value of the interpolation point through local hydraulic head plane fitting. This method retains the characterization of the hydraulic connectivity of heterogeneous media by the shortest path distance, and reflects the hydraulic head variation trend near the interpolation point through local plane parameters, thereby better constructing a groundwater field structure that is similar to the real situation.

[0107] Exemplary program product Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this disclosure also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the method for reconstructing groundwater flow fields as described in any of the above embodiments.

[0108] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0109] The aforementioned non-transitory computer-readable storage media can be any available medium or data storage device that a computer can access, including but not limited to magnetic storage (e.g., floppy disks, hard disks, magnetic tapes, magneto-optical disks (MOs), etc.), optical storage (e.g., CDs, DVDs, BDs, HVDs, etc.), and semiconductor storage (e.g., ROMs, EPROMs, EEPROMs, non-volatile memory (NAND flash), solid-state drives (SSDs)).

[0110] The computer instructions stored in the storage medium of the above embodiments are used to cause the computer to execute the method for reconstructing the groundwater flow field as described in any of the embodiments in the exemplary method section above, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0111] Based on the same inventive concept, corresponding to the method for reconstructing groundwater flow fields described in any of the above embodiments, this disclosure also provides a computer program product, which includes computer program instructions. In some embodiments, the computer program instructions can be executed by one or more processors of a computer to cause the computer and / or the processor to perform the method for reconstructing groundwater flow fields. Corresponding to the execution entity for each step in each embodiment of the method for reconstructing groundwater flow fields, the processor executing the corresponding step can belong to the corresponding execution entity.

[0112] The computer program product of the above embodiments is used to cause the computer and / or the processor to execute the method for reconstructing groundwater flow field as described in any of the above embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0113] Those skilled in the art will recognize that embodiments of this disclosure can be implemented as a system, method, or computer program product. Therefore, this disclosure can be implemented as entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, this disclosure can also be implemented as a computer program product contained in one or more computer-readable media, which includes computer-readable program code.

[0114] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example,, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (not exhaustive) of a computer-readable storage medium may include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0115] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of sending, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0116] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0117] Computer program code for performing the operations of this disclosure can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0118] It should be understood that each block of a flowchart and / or block diagram, as well as combinations of blocks in a flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device to produce a machine that, when executed by a computer or other programmable data processing device, creates means for implementing the functions / operations specified in the blocks of the flowchart and / or block diagram.

[0119] These computer program instructions may also be stored in a computer-readable medium that enables a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable medium produce a product comprising an instruction apparatus that implements the functions / operations specified in the boxes of a flowchart and / or block diagram.

[0120] Computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, such that the instructions that execute on the computer or other programmable apparatus can provide a process for implementing the functions / operations specified in the boxes of a flowchart and / or block diagram.

[0121] Furthermore, although the operations of the methods of this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that these operations must be performed in that specific order, or that all of the operations shown must be performed to achieve the desired result. Rather, the steps depicted in the flowcharts may be executed in a different order. Additionally or alternatively, certain steps may be omitted, multiple steps may be combined into one step, and / or one step may be broken down into multiple steps.

[0122] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. Each block in a flowchart or block diagram may represent a module, segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0123] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to the embodiments of this application, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0124] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this application (including the claims) is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this application as described above, which are not provided in the details for the sake of brevity.

[0125] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this application, the well-known power / ground connections to integrated circuit (IC) chips and other components may or may not be shown in the provided drawings. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this application, and this also takes into account the fact that the details of the implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this application will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of this application, it will be apparent to those skilled in the art that the embodiments of this application can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0126] Although this application has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0127] The embodiments of this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this application should be included within the protection scope of this application.

[0128] While the spirit and principles of this disclosure have been described with reference to several specific embodiments, it should be understood that this disclosure is not limited to the disclosed specific embodiments, and the division of aspects does not imply that features in these aspects cannot be combined for benefit; such division is merely for convenience of expression. This disclosure is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. The scope of the appended claims is to be interpreted in the broadest sense, thereby encompassing all such modifications and equivalent structures and functions.

Claims

1. A method for reconstructing groundwater flow fields, comprising: Set N interpolation points in the permeability coefficient weighted map of the region to be reconstructed; where N is a natural number greater than or equal to 1. Obtain several pre-set known head points in the region to be reconstructed; Based on the permeability coefficient weighted plot and the known head points, the N interpolation points are converted into N head calculation points; and All the calculated hydraulic head points and the known hydraulic head points are fitted together to obtain the groundwater flow field data of the area to be reconstructed.

2. The method according to claim 1, wherein, The step of converting the N interpolation points into N calculation head points based on the permeability coefficient weighted graph and the several known head points includes: Based on the permeability coefficient weighted graph, calculate the first weighted shortest path data between the remaining interpolation points and all known head points; Based on the first weighted shortest path data and the first preset selection rule, a target interpolation point is selected from the N interpolation points, and the first weighted shortest path data is transformed into first fitted coordinate data; wherein, the first preset selection rule includes selecting the interpolation point with the smallest sum of the mean and variance of the distance between the interpolation point and the known head point; Based on the first fitted coordinate data, the local head plane is fitted using the weighted least squares method to transform the target interpolation point into a calculated head point. In response to the number of calculated head points being less than a first preset number, the above steps are repeated until the number of calculated head points is greater than or equal to the first preset number; wherein the first preset number is less than N.

3. The method according to claim 2, wherein, The method further includes: In response to the number of calculated head points being greater than or equal to the first preset number, based on the permeability coefficient weighted map, the second weighted shortest path data between the remaining interpolation points and all the calculated head points is calculated; Based on the second weighted shortest path data and the second preset selection rule, a target interpolation point is selected from the remaining interpolation points, and the second weighted shortest path data is transformed into second fitted coordinate data; wherein, the second preset selection rule includes selecting the interpolation point and calculating the interpolation point with the smallest sum of the mean and variance of the distances from the head points; Based on the second fitted coordinate data, the local head plane is fitted using the weighted least squares method to transform the target interpolation point into a calculated head point; In response to the remaining number of interpolation points being greater than or equal to 1, the above steps are repeated until the number of interpolation points is less than 1.

4. The method according to claim 2, wherein, Based on the permeability coefficient weighted map, the weighted shortest path data between the remaining interpolation points and all known head points in the region to be reconstructed includes: Calculate the weight value of the graph edges for each cell in the penetration weighted graph; By using the graph edge weights as constraints, calculate the weighted shortest path distance between the remaining interpolation points and all known head points; and A second preset number of path nodes are selected based on the distance of the weighted shortest path, and the direction of the weighted shortest path is obtained by linearly fitting the path nodes.

5. The method according to claim 2, wherein, Based on the weighted shortest path data and preset selection rules, the target interpolation point is selected from the selected N interpolation points, and the weighted shortest path data is transformed into fitted coordinate data, including: Based on the weighted shortest path data, the optimal interpolation point is obtained according to preset rules; A virtual two-dimensional hydraulic coordinate system is constructed using the optimal interpolation point as the origin; and The weighted shortest path data of the neighboring constraint points of all the optimal interpolation points in the virtual two-dimensional hydraulic coordinate system are converted into the fitted coordinates.

6. The method according to claim 2, wherein, Based on the fitted coordinate data, the local head plane is fitted using the weighted least squares method to obtain the optimal interpolation point, which is then transformed into the head calculation point. Based on the fitted coordinate data, construct a weighted residual objective function; Based on the known head points, the solution to the weighted residual objective function is obtained through matrix calculations. Based on the solution of the weighted residual objective function, the head data of the optimal interpolation point is calculated; and The optimal interpolation point from which the head data is obtained is transformed into the calculated head point.

7. The method according to claim 5, wherein, Based on the weighted shortest path data and using preset rules, the optimal interpolation point is obtained as follows: Based on the weighted shortest path data, a third preset number of interpolation points are extracted; Calculate the mean and variance of the distances to the points to be interpolated; Based on the mean distance and the variance distance, calculate the priority of all the third preset number of interpolation points; and The point with the highest priority to be interpolated is selected as the origin for constructing the hydraulic coordinate system.

8. The method according to claim 6, wherein, Based on the fitted coordinate data, the weighted residual objective function is constructed as follows: Based on the fitted coordinate data, construct the residual between the point to be interpolated and the nearest constraint point; Based on the distance of the weighted shortest path, the parameters of the local head plane expression are calculated using the weighted least squares method; and Based on the residuals and the parameters, construct the weighted residual objective function.

9. An apparatus for reconstructing groundwater flow fields, comprising: The interpolation point configuration module is configured to set N interpolation points in the permeability coefficient weighted map of the region to be reconstructed; where N is a natural number greater than or equal to 1. The head data acquisition module is configured to acquire several pre-set known head points in the region to be reconstructed; The interpolation point conversion module is configured to convert the N interpolation points into N calculated head points based on the permeability coefficient weighted map and the several known head points; and The fitting module is configured to fit all the calculated hydraulic head points and the known hydraulic head points to obtain the groundwater flow field data of the area to be reconstructed.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method as claimed in any one of claims 1 to 8.

11. A non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform the method of any one of claims 1 to 8.

12. A computer program product comprising computer program instructions that, when executed on a computer, cause the computer to perform the method as described in any one of claims 1 to 8.

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