A geological body modeling method, device, equipment, medium and product

Abstract

The present application provides a kind of geologic body modeling method, device, equipment, medium and product.According to one example of the present application, the method can include: obtaining geologic data of a geologic body, the geologic data including topographic point cloud data and stratigraphic borehole data; generating a topographic surface according to the topographic point cloud data, and generating a stratigraphic surface according to the stratigraphic borehole data; constructing a geologic body model based on the topographic surface and the stratigraphic surface; discretizing the geologic body model to generate a discrete grid model, so that the discrete grid model has grid elements that can be directly used for numerical calculation and analysis, without the need for data conversion and processing in third-party software, while ensuring the accuracy of geologic body modeling, achieving visualization and computability of geologic body modeling.

Description

Technical Field

[0001] This application relates to the field of geological engineering technology, and in particular to a method, apparatus, equipment, medium and product for modeling geological bodies. Background Technology

[0002] As engineering technology develops towards intelligence, three-dimensional geological body modeling, as an important technical means for the expression and analysis of geological information, integrates spatial data processing, geological statistical analysis and computer graphics methods to realize the construction of three-dimensional models of geological structural information, thereby providing technical support for geological analysis, engineering applications and other work.

[0003] Geological modeling in related technologies focuses on the geometric construction of geological structures and can usually only output visualized three-dimensional models, which cannot directly support subsequent numerical calculation and analysis tasks such as geological hazard simulation and stability evaluation. Summary of the Invention

[0004] To overcome the problems existing in related technologies, this application provides a geological body modeling method, apparatus, equipment, medium, and product.

[0005] According to a first aspect of any embodiment of this application, a geological body modeling method is provided, the method comprising: Obtain geological data of the geological body, including topographic point cloud data and stratigraphic borehole data; A terrain surface is generated based on the terrain point cloud data, and a ground surface is generated based on the stratum borehole data; Based on the topographic surface and the ground stratum, a geological body model is constructed; The geological body model is discretized to generate a discrete mesh model.

[0006] According to a second aspect of any embodiment of this application, a geological body modeling apparatus is provided, the apparatus comprising: The acquisition module is used to acquire geological data of the geological body, including topographic point cloud data and stratigraphic borehole data; The generation module is used to generate a terrain surface based on the terrain point cloud data and to generate a ground surface based on the stratum borehole data. A construction module is used to construct a geological body model based on the topographic surface and the ground stratum; The discrete module is used to discretize the geological body model to generate a discrete mesh model.

[0007] According to a third aspect of any embodiment of this application, an electronic device is provided, comprising: processor; Memory used to store processor-executable instructions; The processor executes the executable instructions to implement the method as described in any of the embodiments of the first aspect above.

[0008] According to a fourth aspect of any embodiment of this application, a computer-readable storage medium is provided having computer instructions stored thereon that, when executed by a processor, implement the method described in any of the embodiments of the first aspect above.

[0009] According to a fifth aspect of any embodiment of this application, a computer program product is provided, having a computer program / instructions stored thereon, which, when executed by a processor, implement the method described in any embodiment of the first aspect above.

[0010] The technical solution provided in this application may include the following beneficial effects: As can be seen from the above embodiments, by acquiring geological data of the geological body, generating a topographic surface based on topographic point cloud data, and generating a ground surface based on stratum borehole data, a geological body model is constructed based on the topographic surface and ground surface. The geological body model is then discretized to generate a discrete mesh model, which enables the discrete mesh model to have mesh cells that can be directly used for numerical calculation and analysis without the need to import data into third-party software for data conversion and processing. This ensures the accuracy of geological body modeling while realizing the visualization and computability of geological body modeling.

[0011] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0012] The accompanying drawings, which are incorporated in and form part of this application, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0013] Figure 1 This is a flowchart illustrating a geological body modeling method according to an exemplary embodiment of this application; Figure 2 This is a schematic diagram illustrating a solid model constructed based on terrain surfaces according to an exemplary embodiment of this application; Figure 3 This is a schematic diagram of a geological body model embedded in a stratum according to an exemplary embodiment of this application; Figure 4 This is a schematic diagram illustrating a discrete mesh model generated using a local encryption method according to an exemplary embodiment of this application; Figure 5 This is a schematic diagram illustrating a discretization process based on grid partitioning and geological zoning according to an exemplary embodiment of this application; Figure 6 This is a schematic diagram of a sampling grid for terrain point cloud data according to an exemplary embodiment of this application; Figure 7 This is a schematic diagram of a terrain elevation matrix according to an exemplary embodiment of this application; Figure 8 This application is a schematic diagram illustrating a method for generating boundary dense point cloud data based on slope constraints according to an exemplary embodiment. Figure 9 This is a schematic diagram of a landslide surface according to an exemplary embodiment of this application; Figure 10 This is a flowchart illustrating another geological body modeling method according to an exemplary embodiment of this application; Figure 11 This is a schematic diagram illustrating a landslide geological body modeling according to an exemplary embodiment of this application; Figure 12 This is a schematic diagram of the structure of an electronic device according to an exemplary embodiment of this application; Figure 13 This is a block diagram of a geological body modeling apparatus according to an exemplary embodiment of this application. Detailed Implementation

[0014] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0015] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0016] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0017] Visual models output from geological body modeling typically aim to display the spatial morphology of geological bodies, and can only reproduce the outline and appearance of geological bodies. However, numerical computation and analysis tasks rely on discrete units to complete the solution calculations. Visual models cannot be used as computational models for numerical computation and analysis tasks, and cannot achieve the visualization and computability of geological body modeling.

[0018] To address the aforementioned problems, this application proposes a geological body modeling method, apparatus, equipment, medium, and product. The following embodiments are provided to further illustrate this application: Please see Figure 1 , Figure 1 This is a flowchart illustrating a geological body modeling method according to an exemplary embodiment of this application. The method can be applied to geological engineering applications such as 3D modeling systems and engineering numerical simulation platforms, and may include the following steps: Step S101: Obtain geological data of the geological body, including topographic point cloud data and stratigraphic borehole data.

[0019] In this step, topographic point cloud data of the geological body is obtained through methods such as ground-based 3D laser scanning and on-site measurement point acquisition. Topographic point cloud data can characterize the undulation morphology and spatial location information of the geological body's surface. Stratigraphic borehole data of the geological body is obtained through methods such as geological drilling and in-situ exploration. Stratigraphic borehole data can characterize the spatial distribution and interface location characteristics of underground strata.

[0020] Geological bodies are continuous geological structures distributed across the Earth's surface and subsurface, such as rock and soil bodies and layered strata, exhibiting continuous surface morphology and subsurface bedding. Topographic point cloud data is a discrete set of points reflecting the three-dimensional spatial location of the Earth's surface in the study area. Each point in the topographic point cloud data can contain both planar coordinates and elevation values.

[0021] Formation borehole data is discrete data reflecting the location of strata interfaces at different depths underground. It can include the planar coordinates and elevation values ​​of borehole locations. The elevation value is the coordinate value of a spatial point in the vertical direction (Z-axis direction), which can characterize the altitude or relative height of the point.

[0022] After obtaining the topographic point cloud data and stratigraphic borehole data of the geological body, the geological data, such as the topographic point cloud data and stratigraphic borehole data, can be stored in point cloud file format.

[0023] Step S102: Generate a terrain surface based on the terrain point cloud data, and generate a ground surface based on the stratum borehole data.

[0024] In this step, the acquired terrain point cloud data is preprocessed using methods such as data filtering and coordinate correction. Then, based on the preprocessed terrain point cloud data, a continuous and smooth spatial surface is constructed using methods such as spatial surface fitting and interpolation to obtain the terrain surface. The terrain surface is a parametric surface that characterizes the surface undulation of the study area.

[0025] For formation borehole data, spatial interpolation, surface reconstruction and other methods can be used to infer the morphology of the layering interface corresponding to different formations based on the spatial points of the formation reflected by the formation borehole data, and generate a ground surface that can restore the formation morphology. The ground surface is a parametric surface that represents the layered structure inside the study area.

[0026] Step S103: Construct a geological model based on topographic surfaces and ground planes.

[0027] In this step, spatial geometric information of topographic surfaces and ground planes is integrated through spatial surface splicing and topological fusion to achieve the fusion and construction of multiple geological interfaces, thereby creating a geological body model that reflects the stratigraphic spatial structure of the study area and has continuous topological relationships. The geological body model is a geometric carrier that carries the spatial morphology and internal structure of the geological body, and can reflect the surface morphology and stratigraphic spatial structure of the geological body.

[0028] In one embodiment, when constructing a geological body model, a solid model with bottom and side boundaries can be generated first, using the top surface as the top boundary. For example, the constructed top surface can be used as the top boundary and stretched vertically. A Boolean operation is then performed on the stretched solid model to remove redundant parts that exceed the preset study area, ensuring that the top boundary of the solid model completely fits the top surface, thus generating a closed solid model.

[0029] Please see Figure 2 , Figure 2 This diagram illustrates a method for constructing a solid model based on a terrain surface. The upper surface represents the completed terrain surface, the middle arrow indicates the vertical geometric stretching direction, the lower blue surface is the initial extension formed after vertical stretching of the terrain surface, and the middle black plane is the preset bottom boundary reference plane. A Boolean clipping operation is performed on the initial solid model formed by the stretching to remove redundant extensions below the reference plane. The terrain surface, bottom boundary, and side boundaries together form a closed solid model.

[0030] Next, the strata are embedded into the solid model to obtain the geological body model. For example, Boolean operations can be used to embed geological interfaces such as strata into the solid model, forming a shared boundary between the geological body model and the strata. The shared boundary is the boundary where the outer boundary of the geological body model coincides geometrically with the geological interfaces such as strata within it, or between different geological interfaces. As geometric dividing surfaces within the geological body model, geological interfaces such as strata can delineate underground stratigraphic space, establish spatial topological relationships between the strata and the geological body model, and reconstruct the layered distribution of the geological strata.

[0031] Please see Figure 3 , Figure 3 A schematic diagram of a geological body model embedded in a stratum is shown. The blue outline represents the solid model, and the brown surface represents the embedded stratum. The stratum and the solid model form a stable shared boundary, dividing the geological body model into different stratigraphic units. The green surface represents a landslide surface; the construction method and embedding process of the landslide surface will be described in detail in subsequent embodiments.

[0032] As described above, by generating a solid model with the top boundary of the terrain surface, the ground stratum is embedded into the solid model, so that the geological body model and the ground stratum form a shared boundary, ensuring the topological association between the geological body model and the internal ground stratum.

[0033] Step S104: Discretize the geological body model to generate a discrete mesh model.

[0034] In this step, the geological body model is transformed into a discrete mesh model through discretization methods such as unstructured mesh generation, providing a computational platform for subsequent numerical calculation and analysis tasks. The goal of discretization is to decompose the continuous entity into independent computational units, enabling the model to adapt to the solution logic of various numerical simulation algorithms while balancing mesh quality and computational efficiency.

[0035] Among them, the discrete mesh model is a discretized model composed of independent tetrahedral, hexahedral, and other mesh elements, and serves as the computational carrier for numerical calculation methods.

[0036] In one embodiment, unstructured mesh generation or similar methods can be used to first discretize and sample the curved boundaries of the geological body model to obtain continuous discrete lines. Then, based on the discrete lines, patch meshes of shapes such as triangles are generated to achieve two-dimensional discretization of the model surface. Finally, volume meshes of shapes such as tetrahedrons are generated based on the patch meshes to achieve polyhedral discretization from low-dimensional to high-dimensional, generating a discrete mesh model suitable for numerical computation.

[0037] During the discretization process, local refinement can be performed on target areas such as landslide bodies that are of particular interest, based on the accuracy requirements of numerical calculations. The mesh size of the area is set to be smaller than that of the non-target areas, thereby improving the numerical calculation accuracy of the target area while ensuring overall computational efficiency.

[0038] Please see Figure 4 , Figure 4 A schematic diagram of a discrete mesh model generated using a local refinement method is shown. For example, the landslide body of the geological body is approximately 310m long, 320m wide, and 145m high. The diagram exemplarily shows the discrete mesh model of this geological body after unstructured tetrahedral meshing.

[0039] The enlarged area on the left shows a locally refined grid of the target area, such as the landslide body. The grid cells in this area are smaller and more densely distributed. The enlarged area on the right shows the grid distribution at different geological interfaces. The total number of grid cells in the discrete grid model is approximately 347,089 tetrahedral cells, with the landslide body accounting for approximately 145,709 tetrahedral cells.

[0040] In another embodiment, the geological body model can be first meshed to generate multiple mesh cells. For example, geological interfaces such as strata within the geological body model can be ignored, and the complete geological body model can be meshed unstructured to generate multiple mesh cells.

[0041] Using the strata as the cutting plane, determine the geological zone to which each grid unit belongs in the geological body model. For example, using the strata inside the model as the cutting plane, determine the geological zone, such as landslide body, stratigraphic unit, or other geological unit, to which each grid unit belongs in the geological body model through spatial coordinate comparison and other methods.

[0042] Finally, each grid cell is assigned to its corresponding geological partition, establishing the correspondence between each grid cell and the geological partition, thus obtaining the discrete grid model.

[0043] Please see Figure 5 , Figure 5 This diagram illustrates a discretization process based on mesh generation and geological partitioning. The left side shows the tetrahedral mesh generation result of the complete geological body model without any cuts. This step ignores the geological interfaces within the model, generating unstructured tetrahedral mesh elements for the entire model. The middle section shows multiple geological partitions after the tetrahedral mesh has been partitioned according to geological interfaces such as strata, with each tetrahedral mesh element assigned to its corresponding geological partition.

[0044] The meshless particle model corresponding to the geological partitions on the right can generate one or more particles for each tetrahedral mesh cell through methods such as cell centroid sampling and regular mesh sampling, thus obtaining the particle model for each geological partition. The particle model can be directly used for subsequent meshless numerical calculations and analyses. The discrete mesh model has approximately 8803 meshes for the landslide body, approximately 116440 meshes for the upper strata, and approximately 82928 meshes for the lower strata.

[0045] As described above, by first dividing the overall geological model into multiple grid cells, and then using the ground plane as the cutting surface to determine the geological partition to which each grid cell belongs and assigning grid cells, a discrete grid model is obtained. This allows for the rapid completion of grid discretization of the geological model. Furthermore, the boundaries of the grid cells do not need to be strictly aligned with the ground plane, thus avoiding the generation of low-quality grid cells with distorted shapes in small areas with complex geological morphology, thereby ensuring the accuracy of subsequent numerical calculations.

[0046] The geological body modeling method in this embodiment acquires geological data of the geological body, generates a topographic surface based on topographic point cloud data, and generates a ground surface based on stratum borehole data. Based on the topographic surface and ground surface, a geological body model is constructed. The geological body model is then discretized to generate a discrete mesh model. The discretization process is integrated within the modeling process, enabling the discrete mesh model to have grid cells that can be directly used for numerical calculation and analysis without the need to import data into third-party software for data conversion and processing. This ensures the accuracy of geological body modeling while achieving visualization and computability of geological body modeling.

[0047] In the foregoing embodiments, it was introduced that topographic surfaces and ground planes were constructed based on topographic point cloud data and stratigraphic borehole data, respectively, to build a geological body model and generate a discrete mesh model adapted for numerical calculation, thereby realizing the visualization and computational capability of geological body modeling. In the following embodiments, the construction process of geological interfaces such as topographic surfaces, ground planes, and landslide surfaces of geological bodies will be described in more detail, and can be applied to any of the above embodiments.

[0048] In one embodiment, when generating a terrain surface based on terrain point cloud data, the terrain point cloud data can first be sparsified to generate a regularly distributed terrain elevation point matrix; then, a terrain surface is generated based on the terrain elevation point matrix. The planar positions of each point in the terrain elevation point matrix are evenly distributed, and each point contains a corresponding elevation value.

[0049] For example, voxel downsampling can be used to sparsify terrain point cloud data, dividing the three-dimensional space of the terrain point cloud data into multiple uniformly sized voxel units, selecting the centroid or average point in each voxel unit as a representative point, and eliminating redundant data in the terrain point cloud data, thereby reducing the amount of data processing while preserving the terrain undulation features.

[0050] Please see Figure 6 , Figure 6 A schematic diagram of a sampling grid for terrain point cloud data is shown. After obtaining the sparsed terrain point cloud data, a two-dimensional sampling grid with equal spacing can be constructed based on the spatial distribution range of the terrain point cloud data in the X and Y axes. This sampling grid can cover the distribution area of ​​the terrain point cloud data.

[0051] Please see Figure 7 , Figure 7 A schematic diagram of a terrain elevation point matrix is ​​shown. After constructing the sampling grid, the elevation value of each grid node can be spatially interpolated using methods such as radial basis function interpolation to obtain the elevation value of each grid node, i.e., the Z-axis coordinate, thus generating a regularly distributed terrain elevation point matrix. The planar positions of each point in the terrain elevation point matrix are regular, and the elevation information is complete, accurately reflecting the undulating shape of the land surface.

[0052] After generating the terrain elevation point matrix, a parametric surface can be constructed based on the terrain elevation point matrix to generate a terrain surface. For example, the B-spline surface construction method described in Formula 1 can be used to generate the terrain surface: Formula 1 in, The parameterized expression representing the generated terrain surface; , They are respectively direction, Direction Second-rate, B-spline basis functions; The first in the topographic elevation lattice Line 1 Column control points; , They are respectively direction, The node vectors in the directions are such that the generated terrain surface is defined by the node vectors in both directions.

[0053] As mentioned above, by converting dense terrain point cloud data into regularly distributed terrain elevation point lattices, and then generating terrain surfaces based on the terrain elevation point lattices, the computational overhead of surface fitting can be reduced, and the construction efficiency and smoothness of terrain surfaces can be improved.

[0054] In one embodiment, when generating a ground plane based on formation borehole data, the formation borehole data can first be used as interpolation constraint points to establish an interpolation function; within the spatial distribution range of the formation borehole data, a regularly distributed sampling grid is generated; then, the interpolation function is used to determine the elevation value of each grid node in the sampling grid, obtaining a formation elevation point matrix; finally, the ground plane is generated based on the formation elevation point matrix. The planar positions of each point in the formation elevation point matrix are uniformly distributed, and each point contains a corresponding elevation value.

[0055] For example, formation borehole data may include subsurface discrete point data and surface outcrop data. These data can be used as interpolation constraint points to establish an interpolation function. The interpolation function is a spatial mapping relationship constructed based on discrete constraint points, which can achieve a continuous mapping from plane coordinates to elevation values. It can be a radial basis function (RBF) interpolation model, a kriging interpolation model, etc.

[0056] For example, the following formula 2 can be used to establish the interpolation function through the construction method of the radial basis function interpolation model: Formula 2 in, This represents an interpolation function, whose input is the plane coordinates of any point in the plane. The output is the elevation value of that point; This represents the total number of interpolation constraint points; For the first The weight coefficients corresponding to each interpolation constraint point can be obtained by solving a system of linear equations. It is a radial basis kernel function; For the first The plane coordinates of the interpolation constraint points, and the measured elevation value corresponding to each interpolation constraint point. .

[0057] The interpolation function satisfies the interpolation condition. This means that the elevation values ​​of all constraint points are consistent with the measured elevation values, ensuring the reliability of the formation borehole data.

[0058] Within the spatial distribution range of formation borehole data, the coordinate values ​​of all interpolation constraint points in the X and Y axes can be counted first to determine the planar boundary range. Then, a regular two-dimensional sampling grid with equal spacing can be constructed within this range, with the planar coordinates of each grid node evenly distributed, covering the entire distribution area of ​​the interpolation constraint points.

[0059] By using the constructed interpolation function, the planar coordinates of each node in the sampling grid are substituted into the interpolation function to obtain the elevation value corresponding to each grid node, thereby generating a stratigraphic elevation matrix containing planar coordinates and corresponding elevation values. The stratigraphic elevation matrix completely covers the planar range of the geological body and can accurately reflect the undulation of the ground surface.

[0060] After generating the stratigraphic elevation lattice, the B-spline surface construction method can be used to construct a parametric surface based on the stratigraphic elevation lattice, generating a continuous and smooth stratigraphic surface.

[0061] As described above, by establishing an interpolation function using formation borehole data as interpolation constraint points, a sampling grid is generated within the distribution range of the formation borehole data. The formation elevation lattice is then calculated using the interpolation function, generating a formation plane that accurately reflects the deep morphology of the formation and improving the construction accuracy of the formation plane.

[0062] When the formation borehole data only includes subsurface discrete point data, the radial basis kernel function corresponding to the interpolation function can be the thin-plate spline (TPS) kernel function, as shown in Equation 3: Formula 3 in, The calculation result of the radial basis kernel function of the thin plate spline is represented by the basis function term for constructing the radial basis interpolation model; This represents the Euclidean spatial distance between any point to be interpolated and the discrete underground point data. , Let be the planar coordinates of any grid node to be interpolated. For the first The planar coordinates of the underground discrete points used as interpolation constraints.

[0063] In scenarios where borehole data only includes discrete underground points and lacks surface outcrop data, thin plate spline kernel functions can perform smooth surface extension and spatial extrapolation based on limited measurement point data, compensating for the insufficient coverage of measured points. At the same time, the continuous and smooth ground surface obtained by fitting the kernel function can restore the gentle and continuous distribution pattern of underground strata.

[0064] Within the spatial distribution range of the underground discrete point data, a regularly distributed sampling grid is generated. Then, an interpolation function is used to determine the elevation value of each grid node in the sampling grid, thus obtaining the stratigraphic elevation matrix. Finally, the ground surface is generated based on the stratigraphic elevation matrix.

[0065] Because the geological strata constructed solely based on discrete subsurface point data may be limited to the borehole distribution range, they cannot meet the boundary requirements for geological body modeling.

[0066] In one embodiment, when generating a ground plane based on a stratigraphic elevation lattice, the planar coordinates of the stratigraphic elevation lattice can first be scaled to generate an extended sampling grid; then, an interpolation function can be used to determine the elevation value of each grid node in the extended sampling grid to obtain an extended elevation lattice; finally, the ground plane is generated based on the stratigraphic elevation lattice and the extended elevation lattice.

[0067] The extended sampling grid is obtained by extending the planar coordinates of the original sampling grid outward. The extended elevation matrix is ​​a matrix obtained by reusing the constructed interpolation function to calculate the elevation of all nodes of the extended sampling grid. The extended elevation matrix can cover the extended area beyond the original borehole range, providing control point data for the extended area of ​​the ground plane.

[0068] For example, firstly, the planar coordinates of the stratigraphic elevation lattice in the X and Y axes are extracted. Then, a scaling transformation is performed on these planar coordinates to generate an extended sampling grid. The grid step size and node arrangement rules of the extended sampling grid remain consistent with the original sampling grid to ensure uniform grid distribution. For instance, the following formula 4 can be used to perform the scaling transformation on the planar coordinates: Formula 4 in, , These represent the planar coordinates of the grid nodes in the stratigraphic elevation lattice in the X and Y directions, respectively; , These represent the planar coordinates of the corresponding grid nodes within the expanded sampling grid in the X and Y directions, respectively, after scaling. , These represent the center reference coordinates of the grid nodes in the stratigraphic elevation lattice in the X and Y axes, respectively; , These represent the coordinate scaling factors in the X and Y axes, respectively.

[0069] By setting the scaling factor to a value greater than 1, the planar range can be extended outward from the center of the grid, resulting in a wider-coverage extended sampling grid without changing the grid density and arrangement rules.

[0070] Next, the interpolation function constructed above is reused. The planar coordinates of each grid node within the extended sampling grid are substituted into the interpolation function to calculate the elevation value corresponding to each grid node, thus obtaining the extended elevation matrix. The elevation values ​​of each point within the extended elevation matrix change continuously and smoothly, reflecting the stratigraphic interface morphology outside the measured point range. For example, the following formula 5 can be used to calculate the elevation value corresponding to each grid node within the extended sampling grid: Formula 5 in, , These are the planar coordinates of each grid node in the expanded sampling grid in the X and Y directions, respectively, after scaling transformation; Represents the interpolation function; This represents the elevation value corresponding to each grid node within the expanded sampling grid, calculated through interpolation. It involves the elevation values ​​of all grid nodes within the expanded sampling grid. The data are aggregated to form a complete extended elevation matrix.

[0071] Spatial point stitching and data fusion are performed between the stratigraphic elevation lattice and the extended elevation lattice. The fused elevation lattice serves as the control vertices, and a complete ground stratum is generated through methods such as B-spline surface construction. The internal region of the ground stratum closely matches the stratigraphic morphology reflected by the discrete underground measurement data, while the outer extended region covers the boundary range of the geological body model.

[0072] As described above, by first generating a stratigraphic elevation lattice within the distribution range of underground discrete point data, and then obtaining an extended sampling grid and the corresponding extended elevation lattice through scale transformation, the spatial range of the ground plane is extrapolated and expanded. This avoids the ground plane being limited to the borehole distribution range, thus failing to meet the boundary continuity requirements of geological body modeling. Furthermore, while ensuring the accuracy of the original region corresponding to the underground discrete point data, the surface morphology of the extended region and the original region maintains a consistent trend and geometric continuity.

[0073] In one embodiment, the geological body model may include a landslide geological body model. Since the landslide geological body model needs to accurately reflect the spatial morphology and distribution range of the sliding interface in order to realize subsequent numerical analysis tasks such as landslide stability evaluation and deformation evolution simulation, the acquired geological data may also include landslide point cloud data, which may include central point cloud data and boundary point cloud data.

[0074] Among them, the central point cloud data is discrete point cloud data distributed in the main area of ​​the landslide within the geological body, which can reflect the undulating shape of the main area of ​​the landslide. The boundary point cloud data is discrete point cloud data distributed in the edge area of ​​the landslide within the geological body, which can define and reflect the edge contour of the landslide and can be used as boundary constraint data of the landslide surface to control the morphological changes of the edge area.

[0075] By using boundary point cloud data as a slope constraint, the central point cloud data can be fused to generate a landslide surface. The landslide surface is a curved surface constructed by fusing the central and boundary point cloud data of the landslide, which can characterize the sliding surface between the landslide body and the strata.

[0076] For example, by using boundary condition constraint interpolation, surface fitting, etc., the spatial distribution range and edge slope variation characteristics of the landslide surface can be defined first using the landslide boundary point cloud data. Then, the central point cloud data can be used as morphological control points. The central dense point cloud data and the boundary dense point cloud data can be fused by radial basis function interpolation, parametric surface fitting, etc., and finally a landslide surface with a continuous overall shape can be generated.

[0077] When constructing a geological body model, a landslide geological body model can be built based on topographic surfaces, strata, and landslide surfaces. For example, by using methods such as surface embedding and topological relationship fusion, the generated landslide surface can be embedded as an internal structural surface into the model based on the solid model. This allows the landslide surface to form shared boundaries with the outer boundary of the solid model and with each stratum, thus dividing the internal space of the model into multiple independent geological zones such as landslide body units and multi-layer stratigraphic units, thereby constructing a landslide geological body model with spatial topological relationships.

[0078] Please continue reading. Figure 3 The green surface in the figure represents a landslide surface embedded within the geological model. This landslide surface is located within a stratigraphic unit above the ground surface, and its boundary smoothly connects to the side boundary of the solid model. The landslide surface divides the upper rock and soil mass into independent landslide units, reflecting the spatial superposition relationship between the landslide body and various strata, and providing a geometric basis for subsequent numerical calculations.

[0079] As mentioned above, by fusing the central point cloud data with the boundary point cloud data as a slope constraint to generate a landslide surface, and constructing a geological body model based on the topographic surface, ground surface and landslide surface, the geometric consistency of the landslide boundary area can be improved, the landslide surface morphology can be ensured to conform to the real geological features, and the modeling accuracy of the landslide geological body model can be improved.

[0080] In one embodiment, when generating the landslide surface, the central point cloud data can be interpolated first to generate central dense point cloud data; then, based on the spatial structure characteristics of multiple regions in the boundary point cloud data, the slope constraints corresponding to each region can be determined; next, based on the slope constraints corresponding to each region, boundary dense point cloud data extending towards the center of the landslide can be generated; finally, the landslide surface can be generated based on the central dense point cloud data and the boundary dense point cloud data.

[0081] Among them, the point distribution density of the dense point cloud data in the central part is greater than that of the point cloud data in the central part, and the point distribution density of the dense point cloud data at the boundary is greater than that of the point cloud data at the boundary.

[0082] For example, for the acquired point cloud data of the central part of the landslide, interpolation can be performed using methods such as radial basis function interpolation and thin plate spline interpolation to supplement the gaps between points in the central point cloud data of the landslide, thereby obtaining densely distributed point cloud data of the central part. The dense point cloud data of the central part can restore the undulation shape and detailed features of the main area of ​​the landslide surface.

[0083] For landslide boundary point cloud data, based on the spatial structural characteristics of the landslide within the geological body, the boundary point cloud data can be divided into multiple regions such as the rear boundary, lateral boundary, and leading boundary. Features such as slope dip angle and normal variation of the boundary point cloud data for each region can be extracted to determine the slope constraints for each region. Slope constraints can constrain the morphological change trend of the landslide surface edge region, ensuring that the generated landslide surface boundary conforms to the actual geological structure.

[0084] In one embodiment, multiple regions in the boundary point cloud data include a landslide back wall, a landslide side wall, and a landslide outlet; wherein the slope constraint of the landslide back wall is greater than the slope constraint of the landslide outlet, and / or the slope constraint of the landslide side wall is greater than the slope constraint of the landslide outlet.

[0085] Based on the spatial structural characteristics of areas such as the landslide back wall, landslide side wall, and landslide exit in the boundary point cloud data, differentiated slope constraints can be assigned to different regions. The landslide back wall corresponds to the rear edge region of the landslide body, which presents a steep morphology, and can be given a relatively large slope constraint. The landslide side wall corresponds to the two sides of the landslide body, which presents a steeply extending morphology, and can also be given a relatively large slope constraint. The landslide exit corresponds to the front edge region of the landslide body, which has relatively gentle terrain, and can be given a relatively small slope constraint value.

[0086] By assigning differentiated slope constraints, the generated landslide surface can conform to the geological morphology of the landslide back wall and side wall being relatively steep and the landslide exit being relatively gentle in the boundary area. It exhibits a variation trend that closely matches the real geological morphology in different boundary areas, further improving the modeling accuracy of the landslide geological body.

[0087] After determining the slope constraints for each region, the boundary point cloud data is used as the starting reference. Interpolation is then performed along the extension direction of the corresponding slope constraints towards the central region of the landslide. Continuously distributed dense boundary point cloud data is generated using methods such as Hermite interpolation. This dense boundary point cloud data can gradually extend inward along the boundary, achieving a smooth transition between the boundary region and the central region.

[0088] Please see Figure 8 , Figure 8A schematic diagram of generating boundary dense point cloud data based on slope constraints is shown. Curve 81 in the figure represents the landslide boundary, α and β represent the slope constraints corresponding to the back wall and the landslide exit, respectively, curve 82 is a Hermit spline curve constructed based on slope constraints, and the shaded area is the interpolation surface 83 of the central dense point cloud data.

[0089] For example, the initial tangent direction is determined based on the slope constraints corresponding to each boundary point of curve 81, so that the perpendicular plane of the normal passing through the boundary point intersects with the interpolation surface 83. Continuous intersection points on the interpolation surface 83 are selected as control points to construct curve 82. To ensure that the subsequently generated landslide surface can form a complete intersection with the terrain surface, a straight line can be extended upwards along the tangent direction of the spline curve to supplement the points in the generated landslide wall area.

[0090] By repeating the above process on all boundary points and performing dense sampling along the curve, it is possible to generate boundary dense point cloud data with consistent directionality and high density.

[0091] Finally, the dense point cloud data in the central area and the dense point cloud data at the boundary are spatially fused to form a control point set covering the entire landslide surface. Using methods such as Poisson surface reconstruction, the local voids and unevenness in the point cloud within the fused control point set are addressed. After surface reconstruction, a triangular mesh file in stereolithography (STL) format is generated. By extracting the corner coordinates of the triangular mesh, the fused point cloud in the control point set is converted into a smooth point cloud supporting B-spline interpolation. Finally, a continuous and smooth landslide surface is generated through parametric surface construction.

[0092] Please see Figure 9 , Figure 9 A schematic diagram of a landslide surface is shown. The landslide surface is generated by fusing dense point cloud data from the central area and dense point cloud data from the boundary area, followed by surface reconstruction and parametric surface optimization. The overall shape of the landslide surface is continuous and smooth, and it can completely cover the main area of ​​the landslide and the edge landslide wall area, restoring the spatial undulation characteristics and boundary morphology of the landslide interface.

[0093] As described above, by first interpolating the central point cloud data to generate central dense point cloud data, and then determining the corresponding slope constraints based on the spatial morphology of different regions in the boundary point cloud data, boundary dense point cloud data extending towards the center of the landslide is generated. This can optimize the point cloud density and morphological characteristics of the central and boundary regions of the landslide respectively. Based on the central and boundary dense point cloud data, a landslide surface that conforms to the morphology of the real landslide surface is generated, further improving the accuracy of geological body modeling.

[0094] To further introduce the modeling process of landslide geological bodies Figure 10 A flowchart of another geological body modeling method is shown. Combined with... Figure 11 The schematic diagram shown illustrates the complete modeling process of a landslide geological body, briefly describing the process from three levels: surface construction, volume construction, and mesh generation. For detailed implementation, please refer to the aforementioned embodiments. This method may include the following steps: Step S1001: Obtain topographic point cloud data, stratum borehole data, and landslide point cloud data of the geological body.

[0095] In this step, topographic point cloud data, stratigraphic borehole data, and landslide point cloud data of landslide geological bodies in the study area, such as the mining area, are collected through ground three-dimensional laser scanning and geological drilling mapping.

[0096] Step S1002: Perform sparsification processing on the terrain point cloud data to generate a terrain elevation point matrix.

[0097] In this step, voxel downsampling and other methods are used to sparsify the terrain point cloud data, and spatial interpolation calculations are performed in combination with regular sampling grids to generate a regularly distributed terrain elevation point array.

[0098] Step S1003: Generate a terrain surface based on the terrain elevation point matrix.

[0099] In this step, using topographic elevation lattice points as control points, a continuous and smooth parametric topographic surface is constructed through methods such as Poisson surface reconstruction, resulting in a topographic surface that reflects the undulating shape of the land surface. Figure 11 The terrain surface construction step based on dense point clouds.

[0100] Step S1004: Use the formation borehole data as interpolation constraint points to establish an interpolation function.

[0101] In this step, the subsurface discrete point data and surface outcrop data from the formation borehole data are used as interpolation constraint points to construct a radial basis function interpolation model, forming an interpolation function for fitting the ground plane, corresponding to... Figure 11 The RBF interpolation reconstruction step based on sparse point ground plane construction.

[0102] Step S1005: Generate a sampling grid within the spatial distribution range of the formation borehole data.

[0103] Step S1006: Use the interpolation function to determine the elevation value of each grid node in the sampling grid to obtain the stratum elevation matrix.

[0104] Step S1007: Generate the ground plane based on the stratigraphic elevation matrix.

[0105] In this step, using the stratigraphic elevation lattice as control points, a continuous and smooth ground plane is generated through parametric surface construction to reconstruct the spatial distribution of the subsurface stratigraphic interface. For scenarios where borehole data coverage is insufficient, the sampling range can be expanded through scale transformation to ensure that the ground plane completely covers the modeling boundary of the geological body.

[0106] Step S1008: Using the boundary point cloud data as a slope constraint, fuse the middle point cloud data to generate a landslide surface.

[0107] In this step, the point cloud data in the middle of the landslide is first reconstructed by interpolation to obtain dense point cloud data in the middle. Combined with the slope constraints corresponding to each region in the boundary point cloud data, dense point cloud data extending inward is generated.

[0108] The dense point cloud data in the central area is fused with the dense point cloud data at the boundary, and a landslide surface is generated through Poisson surface reconstruction, corresponding to... Figure 11 The landslide surface reconstruction process is constrained by the boundary and sparse points.

[0109] Step S1009: Generate a solid model with the terrain surface as the top boundary.

[0110] In this step, the terrain surface is used as the top boundary. After being stretched vertically and subjected to a Boolean clipping operation, a solid model with bottom and side boundaries is generated, corresponding to... Figure 11 The terrain surface stretching and trimming process in the middle.

[0111] Step S1010: Embed the ground surface and landslide surface into the solid model to obtain the landslide geological model.

[0112] In this step, Boolean operations are used to embed the ground plane and landslide surface into the solid model to obtain a topologically continuous landslide geological body model, with each geological interface forming a shared boundary with the landslide geological body model.

[0113] Step S1011: Discretize the geological body model to generate a discrete mesh model.

[0114] In this step, an unstructured mesh generation method is used to divide the landslide geological body model into tetrahedral meshes, which can be used to refine the mesh locally for target areas such as the landslide body.

[0115] Alternatively, the overall landslide geological model can be meshed first, generating multiple mesh units. Using the ground surface and landslide surface as cutting planes, the geological zone to which each mesh unit belongs in the geological model can be determined. Each mesh unit is then assigned to its corresponding geological zone, resulting in a discrete mesh model. Figure 11 The process of generating unstructured tetrahedral meshes.

[0116] Step S1012: Perform numerical calculation and analysis tasks based on the discrete grid model.

[0117] In this step, the discrete mesh model is imported into the numerical simulation platform, corresponding geotechnical parameters are matched for different geological zones, and numerical calculation and analysis tasks such as landslide stability evaluation and deformation evolution simulation are performed.

[0118] By constructing an integrated modeling process from data processing, surface reconstruction, geological body model generation to discrete mesh model generation, the construction and integration of geological interfaces such as topographic surfaces and ground planes are realized, achieving automated and rapid construction of three-dimensional geological bodies without relying on multi-software interaction and complex data conversion.

[0119] Figure 12 This is a schematic diagram illustrating the structure of an electronic device according to an exemplary embodiment of this application. The electronic device may be, for example, a mobile phone, computer, digital broadcasting terminal, messaging device, game console, tablet device, personal digital assistant, server, smart home appliance, in-vehicle system, etc. (Reference) Figure 12 At the hardware level, the electronic device includes a processor 1201, an internal bus 1202, a network interface 1203, memory 1204, and non-volatile memory 1205, and may also include other hardware required for business operations. The processor 1201 reads the corresponding computer program from the non-volatile memory 1205 into the memory 1204 and then runs it, forming a geological body modeling device at the logical level. Of course, in addition to the software implementation, this application does not exclude other implementation methods, such as logic devices or a combination of hardware and software, etc. That is to say, the execution subject of the following processing flow is not limited to individual logic units, but can also be hardware or logic devices.

[0120] Figure 13 This is a block diagram illustrating a geological body modeling apparatus according to an exemplary embodiment of this application. (Refer to...) Figure 13 The device may include: The acquisition module 1301 is used to acquire geological data of the geological body, including topographic point cloud data and stratigraphic borehole data; The generation module 1302 is used to generate a terrain surface based on the terrain point cloud data and to generate a ground surface based on the stratum borehole data; Module 1303 is used to construct a geological body model based on the topographic surface and the ground surface. Discretization module 1304 is used to discretize the geological body model to generate a discrete mesh model.

[0121] Optionally, the geological body model includes: a landslide geological body model; the geological data further includes: landslide point cloud data, which includes central point cloud data and boundary point cloud data; The device further includes: The fusion module is used to fuse the middle point cloud data with the boundary point cloud data as a slope constraint to generate a landslide surface; The construction module 1303 is used to: construct the landslide geological body model based on the topographic surface, the ground surface and the landslide surface.

[0122] Optionally, the fusion module, when used to fuse the central point cloud data with the boundary point cloud data as a slope constraint to generate a landslide surface, includes: The central point cloud data is interpolated to generate central dense point cloud data; Based on the spatial structure characteristics of multiple regions in the boundary point cloud data, the slope constraints corresponding to each region are determined. Based on the slope constraints corresponding to each region, dense point cloud data of the boundary extending towards the middle of the landslide is generated. The landslide surface is generated based on the central dense point cloud data and the boundary dense point cloud data.

[0123] Optionally, the multiple regions in the boundary point cloud data include the landslide back wall, the landslide side wall, and the landslide outlet; Wherein, the slope constraint of the landslide rear wall is greater than the slope constraint of the landslide outlet, and / or the slope constraint of the landslide side wall is greater than the slope constraint of the landslide outlet.

[0124] Optionally, the generation module 1302, when generating a terrain surface based on the terrain point cloud data, includes: The terrain point cloud data is subjected to sparsification processing to generate a regularly distributed terrain elevation point matrix; The terrain surface is generated based on the terrain elevation point matrix.

[0125] Optionally, the generation module 1302, when used to generate a formation surface based on the formation borehole data, includes: Using the formation borehole data as interpolation constraint points, an interpolation function is established; Within the spatial distribution range of the formation borehole data, a regularly distributed sampling grid is generated; Using the interpolation function, the elevation value of each grid node in the sampling grid is determined to obtain the stratigraphic elevation matrix; The ground plane is generated based on the aforementioned stratigraphic elevation lattice.

[0126] Optionally, the formation borehole data includes subsurface discrete point data; The generation module 1302, when used to generate the ground surface based on the ground elevation lattice, includes: The planar coordinates of the stratum elevation lattice are scaled to generate an extended sampling grid; Using the interpolation function, the elevation value of each grid node in the extended sampling grid is determined to obtain the extended elevation matrix; The ground plane is generated based on the stratigraphic elevation lattice and the extended elevation lattice.

[0127] Optionally, the construction module 1303, when used to construct a geological body model based on the topographic surface and the ground surface, includes: Using the terrain surface as the top boundary, a solid model with a bottom boundary and side boundaries is generated; The geological body model is obtained by embedding the ground stratum into the solid model, and the geological body model and the ground stratum form a shared boundary.

[0128] Optionally, the discretization module 1304, when used to discretize the geological body model to generate a discrete mesh model, includes: The geological body model is meshed to generate multiple mesh cells; Using the aforementioned stratum as a cutting plane, determine the geological zone to which each grid cell belongs in the geological body model; Each grid cell is assigned to a corresponding geological partition to obtain the discrete grid model.

[0129] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0130] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0131] In an exemplary embodiment, a non-transitory computer-readable storage medium including instructions, such as a memory including instructions, is also provided, which can be executed by a processor of a geological body modeling apparatus to implement the method as described in any of the above embodiments.

[0132] The non-transitory computer-readable storage medium may be ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk and optical data storage device, etc., and this application does not limit it.

[0133] In an exemplary embodiment, a computer program product including a computer program / instructions is also provided, which can be executed by a processor of a geological body modeling apparatus to implement the method described in any of the above embodiments.

[0134] The foregoing has described specific embodiments of this application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired results. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0135] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention filed herein. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and alterations can be made without departing from its scope. The scope of this application is limited only by the appended claims.

[0136] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for modeling geological bodies, characterized in that, The method includes: Obtain geological data of the geological body, including topographic point cloud data and stratigraphic borehole data; A terrain surface is generated based on the terrain point cloud data, and a ground surface is generated based on the stratum borehole data; Based on the topographic surface and the ground stratum, a geological body model is constructed; The geological body model is discretized to generate a discrete mesh model.

2. The method according to claim 1, characterized in that, The geological model includes a landslide geological model; the geological data also includes landslide point cloud data, which includes central point cloud data and boundary point cloud data. The method further includes: Using the boundary point cloud data as a slope constraint, the middle point cloud data is fused to generate a landslide surface; The construction of a geological body model based on the topographic surface and the ground stratum includes: Based on the topographic surface, the ground surface, and the landslide surface, a landslide geological model is constructed.

3. The method according to claim 2, characterized in that, The step of fusing the central point cloud data with the boundary point cloud data as a slope constraint to generate a landslide surface includes: The central point cloud data is interpolated to generate central dense point cloud data; Based on the spatial structure characteristics of multiple regions in the boundary point cloud data, the slope constraints corresponding to each region are determined. Based on the slope constraints corresponding to each region, dense point cloud data of the boundary extending towards the middle of the landslide is generated. The landslide surface is generated based on the central dense point cloud data and the boundary dense point cloud data.

4. The method according to claim 3, characterized in that, The boundary point cloud data includes multiple regions such as the landslide back wall, landslide side wall, and landslide exit; Wherein, the slope constraint of the landslide rear wall is greater than the slope constraint of the landslide outlet, and / or the slope constraint of the landslide side wall is greater than the slope constraint of the landslide outlet.

5. The method according to claim 1, characterized in that, The step of generating a terrain surface based on the terrain point cloud data includes: The terrain point cloud data is subjected to sparsification processing to generate a regularly distributed terrain elevation point matrix; The terrain surface is generated based on the terrain elevation point matrix.

6. The method according to claim 1, characterized in that, The step of generating the ground plane based on the formation borehole data includes: Using the formation borehole data as interpolation constraint points, an interpolation function is established; Within the spatial distribution range of the formation borehole data, a regularly distributed sampling grid is generated; Using the interpolation function, the elevation value of each grid node in the sampling grid is determined to obtain the stratigraphic elevation matrix; The ground plane is generated based on the aforementioned stratigraphic elevation lattice.

7. The method according to claim 6, characterized in that, The formation borehole data includes discrete point data from underground locations; The process of generating the ground surface based on the stratigraphic elevation lattice includes: The planar coordinates of the stratum elevation lattice are scaled to generate an extended sampling grid; Using the interpolation function, the elevation value of each grid node in the extended sampling grid is determined to obtain the extended elevation matrix; The ground plane is generated based on the stratigraphic elevation lattice and the extended elevation lattice.

8. The method according to claim 1, characterized in that, The construction of a geological body model based on the topographic surface and the ground stratum includes: Using the terrain surface as the top boundary, a solid model with a bottom boundary and side boundaries is generated; The geological body model is obtained by embedding the ground stratum into the solid model, and the geological body model and the ground stratum form a shared boundary.

9. The method according to claim 1, characterized in that, The discretization process of the geological body model to generate a discrete mesh model includes: The geological body model is meshed to generate multiple mesh cells; Using the aforementioned stratum as a cutting plane, determine the geological zone to which each grid cell belongs in the geological body model; Each grid cell is assigned to a corresponding geological partition to obtain the discrete grid model.

10. A geological body modeling device, characterized in that, The device includes: The acquisition module is used to acquire geological data of the geological body, including topographic point cloud data and stratigraphic borehole data; The generation module is used to generate a terrain surface based on the terrain point cloud data and to generate a ground surface based on the stratum borehole data. A construction module is used to construct a geological body model based on the topographic surface and the ground stratum; The discrete module is used to discretize the geological body model to generate a discrete mesh model.

11. An electronic device, characterized in that, include: processor; A memory for storing processor-executable instructions; wherein the processor implements the steps of the method as described in any one of claims 1-9 by executing the executable instructions.

12. A computer-readable storage medium, characterized in that, It stores computer instructions that, when executed by a processor, implement the steps of the method as described in any one of claims 1-9.

13. A computer program product, characterized in that, Includes a computer program / instructions that, when executed by a processor, implement the steps of the method as described in any one of claims 1-9.

Images