Tetrahedron gravity forward modeling method, device and system and storage medium

Abstract

The invention provides a tetrahedron gravity forward modeling method, device and system and a storage medium, and relates to the technical field of geophysical survey, and the method comprises the steps: obtaining a field source body model and format data of the field source body model; subdividing the field source body model according to a preset mode to obtain a plurality of tetrahedrons; the preset mode corresponds to the format data; obtaining coordinate data of the observation points, and performing parallel processing on each tetrahedron based on an improved Gauss cross section method according to the coordinate data to obtain a temporary gravity field generated by each tetrahedron at the observation points; and obtaining a gravity field generated by the field source body at the observation point according to all the temporary gravity fields. Through the advanced processing method, the gravitational field distribution of the complex geologic body can be simulated more accurately. Meanwhile, the parallel processing technology is utilized, the calculation time is remarkably shortened, the effect is particularly obvious when large-scale data are processed, and the gravity field forward modeling precision and the calculation efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the field of geophysical survey technology, and in particular to a tetrahedron gravity forward modeling method, device, system and storage medium. Background Art

[0002] Gravity forward modeling is a method that calculates the gravity field at an observation point by specifying the shape and density distribution of a source. This technology has important applications in exploring deep Earth structures, defining oil and gas basins, conducting environmental monitoring, and determining satellite orbits. However, existing traditional gravity forward modeling methods have some significant problems.

[0003] Many traditional methods use rectangular grids to segment the source volume. However, when the source volume has a complex shape, rectangular grids cannot effectively approximate its surface shape. In this case, the resulting gravity field calculation results will have large errors, affecting the accurate analysis of geological structures.

[0004] Although some methods have introduced tetrahedral meshes to divide the field source, improving their adaptability to complex geometries, the traditional horizontal section method uses the unequally spaced Simpson formula for vertical integration when calculating the gravity field caused by the tetrahedron. This means that each tetrahedron can only have an odd number of horizontal sections. This limitation not only complicates the calculations but also significantly increases the number of horizontal sections required to achieve high accuracy, further increasing the computational effort and reducing computational efficiency. Summary of the Invention

[0005] The problem solved by the present invention is one or more of the above-mentioned related technical problems.

[0006] To solve the above problems, the present invention provides a tetrahedron gravity forward modeling method, device, system and storage medium.

[0007] In a first aspect, the present invention provides a tetrahedron gravity forward modeling method, comprising: Acquire a field source body model corresponding to the field source body and format data of the field source body model; Dividing the field source body model according to a preset method to obtain a plurality of tetrahedrons; the preset method corresponds to the format data; Acquiring coordinate data of the observation point, and performing parallel processing on each of the tetrahedrons based on the improved Gauss cross-section method according to the coordinate data to obtain a temporary gravity field generated by each tetrahedron at the observation point; Based on all the temporary gravity fields, the gravity field generated by the field source body at the observation point is obtained.

[0008] Optionally, the step of performing parallel processing on each tetrahedron based on the improved Gauss cross-section method according to the coordinate data and the basic data of the field source body to obtain the corresponding temporary gravity field generated at the observation point includes: Performing horizontal segmentation on each of the tetrahedrons to obtain a plurality of horizontal cross-sectional data; Obtaining the gravity field of each horizontal cross section according to the coordinate data and the horizontal cross section data; Based on the Gaussian integral algorithm, a temporary gravity field of each tetrahedron is obtained according to the gravity fields of all the horizontal cross sections.

[0009] Optionally, the horizontal cross-sectional data includes vertex coordinate data; and the horizontal segmentation of each tetrahedron to obtain a plurality of horizontal cross-sectional data includes: Determine the Gaussian integration node values; Determine a plurality of splitting planes according to the Gaussian integral node values, and perform horizontal splitting on each of the tetrahedrons according to each of the splitting planes to obtain a plurality of horizontal cross sections; The corresponding vertex coordinate data is obtained according to the intersection of each side length of the horizontal cross section and the corresponding dividing surface.

[0010] Optionally, the Gaussian integral algorithm includes: Determining the coordinate range of each tetrahedron in the vertical direction; A linear transformation is performed on the coordinate range to determine a Gaussian quadrature node and a Gaussian quadrature coefficient of the Gaussian integral algorithm.

[0011] Optionally, performing a linear transformation on the coordinate range to determine a Gaussian quadrature node and a Gaussian quadrature coefficient of the Gaussian integral algorithm includes: Performing linear transformation on the coordinate range using Formula 1 and Formula 2 respectively to determine the Gaussian quadrature node and the Gaussian quadrature coefficient; The formula 1 is: ; The formula 2 is: ; Wherein, [z1,z2] is the coordinate range, is the reference quadrature node, is the reference quadrature coefficient, z k is the Gaussian quadrature node, is the Gaussian quadrature coefficient.

[0012] Optionally, the Gaussian integral algorithm further includes: The Gaussian integral formula is: ; in, is the temporary gravity field generated by the tetrahedron at the observation point, is the Gaussian quadrature coefficient, is the gravity field generated by the kth horizontal cross section at the observation point, n is the total number of Gaussian integration nodes, and V is the gravity field generated by each horizontal cross section at the observation point.

[0013] Optionally, the format data includes a VTK file, an STL file, and a three-dimensional coordinate point cloud; and the field source body model is segmented according to a preset method to obtain a plurality of tetrahedrons, including: When the format data is the STL file or the three-dimensional coordinate point cloud, the field source body model is segmented using a preset segmentation model to obtain a plurality of tetrahedrons; When the format data is the VTK file, the plurality of tetrahedrons are determined according to the VTK file.

[0014] In a second aspect, the present invention provides a tetrahedron gravity forward modeling device, comprising: an acquiring unit, configured to acquire a field source body model corresponding to the field source body and format data of the field source body model; a segmentation unit, configured to segment the field source body model according to a preset method to obtain a plurality of tetrahedrons; the preset method corresponds to the format data; A processing unit is used to obtain coordinate data of the observation point, and based on the coordinate data, perform parallel processing on each tetrahedron based on the improved Gauss cross-section method to obtain a temporary gravity field generated by each tetrahedron at the observation point; based on all the temporary gravity fields, obtain the gravity field generated by the field source body at the observation point.

[0015] In a third aspect, the present invention provides a tetrahedron gravity forward modeling system, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the tetrahedron gravity forward modeling method as described in the first aspect when executing the computer program. In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the tetrahedron gravity forward modeling method as described in the first aspect is implemented.

[0016] The tetrahedron gravity forward modeling method, device, system and storage medium of the present invention have the following beneficial effects: First, the acquired source model is divided into multiple tetrahedrons using a predefined method (e.g., meshing). This predefined method must correspond to the format data to ensure proper meshing and accurate calculations. Tetrahedroning breaks down complex 3D geometry into simple units, simplifying and streamlining the gravity field calculation process.

[0017] Next, we select and obtain the spatial coordinate data (such as longitude, latitude, and altitude) for multiple observation points where the gravity field influence needs to be calculated. Using a modified Gauss cross-section method, we parallelize the temporary gravity field generated by each tetrahedron at the observation point. This parallel processing improves computational efficiency, allowing the modified Gauss method to more precisely capture gravity field variations, resulting in more accurate results.

[0018] Finally, the temporary gravity fields generated by all tetrahedrons are integrated to calculate the total gravity field generated by the source body at the observation point.

[0019] Therefore, the present invention can simulate the gravity field distribution of complex geological bodies more accurately through advanced processing methods. At the same time, the use of parallel processing technology significantly reduces the calculation time, especially when processing large-scale data. The method is applicable to different types of field source bodies and their geometric shapes, providing flexible adaptability. Accurate gravity field data can be used for further geological analysis, resource exploration and scientific research, and help to make more scientific decisions. In short, this tetrahedral gravity forward modeling method not only has a solid foundation in theory, but also shows significant benefits in practical applications. It is suitable for many fields such as civil engineering, mining exploration and environmental monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Schematic diagram of a flow chart of a tetrahedron gravity forward modeling method according to an embodiment of the present invention; Figure 2 This is a schematic structural diagram of a field source model according to an embodiment of the present invention; Figure 3 is a schematic diagram of an arbitrary horizontal cross-section polygon according to an embodiment of the present invention; Figure 4 This is a schematic structural diagram of a rectangular field source model according to an embodiment of the present invention; Figure 5 A schematic diagram of the distribution of the gravity field generated by the prismatic forward modeling of a rectangular parallelepiped model according to an embodiment of the present invention; Figure 6 A schematic diagram of a rectangular parallelepiped field source model according to an embodiment of the present invention being divided into tetrahedral meshes; Figure 7A schematic diagram of the distribution of the gravity field generated by the conventional cross-section forward modeling of a rectangular parallelepiped according to an embodiment of the present invention; Figure 8 A schematic diagram of the distribution of the gravity field generated by the rectangular parallelepiped model obtained by the tetrahedral gravity forward modeling method according to an embodiment of the present invention; Figure 9 Schematic diagram of the root mean square error of the gravity field results of the rectangular parallelepiped model obtained by two methods according to an embodiment of the present invention. DETAILED DESCRIPTION

[0021] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. Although certain embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as being limited to the embodiments described herein. Instead, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0022] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0023] The term "including" and its variations used in this document are open inclusions, that is, "including but not limited to"; the term "based on" means "based at least in part on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one other embodiment"; the term "some embodiments" means "at least some embodiments"; the term "optionally" means "optional embodiments". The relevant definitions of other terms will be given in the following description. It should be noted that the concepts of "first", "second", etc. mentioned in the present invention are only used to distinguish different devices, modules or units, and are not used to limit the order or interdependence of the functions performed by these devices, modules or units.

[0024] It should be noted that the modifications of "one" and "multiple" mentioned in the present invention are illustrative rather than restrictive. Those skilled in the art should understand that unless otherwise clearly indicated in the context, it should be understood as "one or more".

[0025] The names of the messages or information exchanged between multiple devices in the embodiments of the present invention are only used for illustrative purposes and are not used to limit the scope of these messages or information.

[0026] In response to the problems existing in the above-mentioned related technologies, embodiments of the present invention provide a tetrahedron gravity forward modeling method device, system and storage medium.

[0027] like Figure 1 As shown, an embodiment of the present invention provides a tetrahedron gravity forward modeling method, including: Step S100: Acquire a field source body model corresponding to a field source body and format data of the field source body model.

[0028] Specifically, a field source body refers to an object that affects the gravity field, such as an ore body, groundwater reservoir, structure, etc. Each field source body has a unique shape, density and physical properties. Figure 2 , a schematic diagram of a field source body model. In the right-handed Cartesian coordinate system with the z-axis pointing downward, for a three-dimensional field source body of a rectangular parallelepiped in space, wherein. )and ) is the coordinate of the midpoint of the field source body.

[0029] Data source collection can be accomplished through: 1. Geological Surveys: Obtaining basic information about the source body through surface or underground exploration, geological sampling, and drilling. This includes its location, shape, volume, and internal structure. 2. Remote Sensing: Utilizing satellite imagery, aerial photography, or geophysical surveys (such as gravity and magnetometry) to collect geometric characteristics of the source body. 3. Historical Data: Consulting existing geological literature, electronic databases, and mining records to obtain previous research results and data relevant to the target area.

[0030] Convert the collected data into a computer-processable geometric model. This step typically involves creating a three-dimensional model of the source body using 3D modeling software (such as AutoCAD, Geosoft, etc.), ensuring that the model accurately reflects its physical properties. Metadata organization: Equip the model with the necessary format data, including the physical properties of each source body (such as density, elasticity, etc.) and the model's coordinate system information. This information is crucial for subsequent calculations. Verify the accuracy of the acquired source body model and format data to ensure that they meet the preset mathematical and physical requirements. Perform cross-validation when necessary to ensure data reliability.

[0031] Finally, the processed model data is input into the gravity field forward calculation system to prepare for the next step of calculation.

[0032] Through a rigorous data collection and formatting process, the accuracy of the source model is ensured, providing a reliable foundation for subsequent calculations and thus helping to improve the accuracy of gravity field predictions. In addition, accurate geometric modeling and detailed metadata provide more comprehensive and rich information for analysis, enabling the model to truly reflect complex geological bodies.

[0033] Formatting and standardizing the source body model reduces data inconsistencies that may be encountered during the calculation and analysis phases, simplifying the subsequent calculation process. This step is not only applicable to a single type of source body, but can also integrate multiple types of source body models to meet the needs of complex geological environments, enhancing the model's flexibility and breadth of application.

[0034] The prepared and formatted field source model can be conveniently used in subsequent analysis, visualization and decision support, providing effective data support for geological research and resource exploration.

[0035] Through the efficient step S100, a solid foundation will be laid for the entire tetrahedral gravity forward modeling method, providing necessary input and reliable data support for subsequent complex gravity calculations and analyses.

[0036] Step S200 , dividing the field source body model according to a preset method to obtain a plurality of tetrahedrons; the preset method corresponds to the format data.

[0037] Specifically, before performing tetrahedral meshing, an appropriate meshing method must be selected. Common meshing methods include: uniform meshing, which divides the source model into uniformly sized tetrahedrons and is suitable for models with regular shapes; and adaptive meshing, which dynamically adjusts the size and number of tetrahedrons based on the model's complexity and density to ensure detailed meshing of important areas within the model (such as boundaries and faults).

[0038] According to the format data obtained in step S100, the field source body model is segmented through a program or algorithm.

[0039] During the segmentation process, the vertices, edges, and faces of each tetrahedron must conform to the preset geometric constraints to ensure the correct position and relationship of the generated tetrahedrons in space. The segmentation process can use the three-dimensional modeling technology in computer graphics to automatically generate multiple tetrahedrons. During the segmentation process, the vertices, edges, and faces of each tetrahedron must conform to the preset geometric constraints to ensure the correct position and relationship of the generated tetrahedrons in space. The segmented tetrahedrons are assigned unique identifiers and their properties, including volume, surface area, density, and connectivity information, are recorded. This information will play an important role in subsequent gravity field calculations.

[0040] By finely meshing the source body model, we can better describe complex geological structures and their physical properties. This high-resolution representation helps improve the accuracy of subsequent gravity field calculations. Furthermore, the application of adaptive meshing technology can effectively handle source bodies with complex shapes or dramatic changes, providing more computational detail in key information areas, thereby enabling more accurate simulation of gravity field changes.

[0041] The tetrahedron model generated through the segmentation process can not only be used for gravity field calculations, but can also be widely used in other geological analyses, further enhancing the application breadth and flexibility of the model.

[0042] The tetrahedral division of the field source body model in step S200 not only provides an efficient and accurate data basis for the calculation of the gravity field, but also provides richer information support for geological research, engineering design and other fields.

[0043] Step S300 , obtaining coordinate data of the observation point, and performing parallel processing on each tetrahedron based on the improved Gauss cross-section method according to the coordinate data to obtain a temporary gravity field generated by each tetrahedron at the observation point.

[0044] Specifically, an observation point is defined as a point on the ground or at a specific location where the gravity field needs to be measured. Some common observation points can be exploration sites, geological survey points, or data collection locations.

[0045] The three-dimensional coordinate data (x, y, z) of each observation point is obtained through GPS, geographic information system (GIS) or specific geological exploration equipment. These coordinate data provide the necessary spatial reference for subsequent gravity field calculations.

[0046] Based on the generated tetrahedron model and its corresponding physical properties (such as density), the spatial information of the tetrahedron is mobilized to prepare the calculation of the gravitational influence of each tetrahedron on the observation point.

[0047] For each observation point, a parallel algorithm is used to calculate the gravity field generated by each tetrahedron at the observation point. The temporary gravity field of each tetrahedron can be calculated independently, which improves the computational efficiency.

[0048] The gravitational influence of each tetrahedron relative to the observation point is calculated using a modified Gauss cross-section method. This method, based on the principles of mass concentration and the inverse square of distance, allows for a rapid assessment of each tetrahedron's contribution to the observation point.

[0049] For each tetrahedron, the temporary gravity field generated by the tetrahedron at the observation point is calculated based on its density, volume and distance from the observation point, and these results are stored for subsequent summary.

[0050] Parallel processing technology enables the simultaneous calculation of the gravity fields of multiple tetrahedrons at the same observation point, significantly improving computational efficiency and shortening overall calculation time. Furthermore, the improved Gauss cross-section method more accurately describes the gravitational influence of the tetrahedrons on the observation point, reducing errors that may occur in traditional calculation methods and thus enhancing the reliability of the results.

[0051] This method is applicable to large-scale tetrahedron models and can effectively handle a large number of observation points in complex geological environments, improving the versatility and applicability of geological data analysis. Furthermore, the generated temporary gravity field information can provide more refined quantitative data for subsequent gravity inversion, exploration decision-making, and resource assessment, enhancing our understanding of the gravity field distribution. Furthermore, the implementation of this step can be adjusted to meet different needs, such as adding new observation points or changing calculation parameters, to ensure the flexibility and adaptability of the method.

[0052] Through the effective implementation of step S300, the efficiency and accuracy of gravity field calculation can be ensured, providing important support for subsequent data analysis and decision-making.

[0053] Step S400: Obtain the gravity field generated by the field source body at the observation point based on all the temporary gravity fields.

[0054] Specifically, the gravity field data of all tetrahedrons at the observation point are integrated to form a complete gravity field distribution model of the field source body in space (the gravity field generated by the field source body at the observation point). This model is a three-dimensional gravity field dataset that can be used for visualization or analysis.

[0055] In this embodiment, the tetrahedral gravity forward modeling method divides the acquired field source model into multiple tetrahedrons according to a preset method (e.g., meshing). This preset method must correspond to the format data to ensure the rationality of the meshing and the accuracy of the calculation. Tetrahedral meshing breaks down complex three-dimensional geometric objects into simple units, thereby simplifying and improving the efficiency of gravity field calculations.

[0056] Next, we select and obtain the spatial coordinate data (such as longitude, latitude, and altitude) for multiple observation points where the gravity field influence needs to be calculated. Using a modified Gauss cross-section method, we parallelize the temporary gravity field generated by each tetrahedron at the observation point. This parallel processing improves computational efficiency, allowing the modified Gauss method to more precisely capture gravity field variations, resulting in more accurate results.

[0057] Finally, the temporary gravity fields generated by all tetrahedrons are integrated to calculate the total gravity field generated by the source body at the observation point.

[0058] Therefore, the present invention can simulate the gravity field distribution of complex geological bodies more accurately through advanced processing methods. At the same time, the use of parallel processing technology can significantly reduce the calculation time, especially when processing large-scale data. The effect is particularly obvious, that is, the accuracy and computational efficiency of the gravity field forward modeling are improved. This method is applicable to different types of field source bodies and their geometric shapes, providing flexible adaptability. Accurate gravity field data can be used for further geological analysis, resource exploration and scientific research, and help to make more scientific decisions. In short, this tetrahedral gravity forward modeling method not only has a solid foundation in theory, but also shows significant benefits in practical applications. It is suitable for many fields such as civil engineering, mining exploration and environmental monitoring.

[0059] Optionally, the step of performing parallel processing on each tetrahedron based on the coordinate data and an improved Gauss cross-section method to obtain a corresponding temporary gravity field generated at the observation point includes: Performing horizontal segmentation on each of the tetrahedrons to obtain a plurality of horizontal cross-sectional data; Obtaining the gravity field of each horizontal cross section according to the coordinate data and the horizontal cross section data; Based on the Gaussian integral algorithm, a temporary gravity field of each tetrahedron is obtained according to the gravity fields of all the horizontal cross sections.

[0060] Optionally, the horizontal cross-sectional data includes vertex coordinate data; and the horizontal segmentation of each tetrahedron to obtain a plurality of horizontal cross-sectional data includes: Determine the Gaussian integration node values; Determine a plurality of splitting planes according to the Gaussian integral node values, and perform horizontal splitting on each of the tetrahedrons according to each of the splitting planes to obtain a plurality of horizontal cross sections; The corresponding vertex coordinate data is obtained according to the intersection of each side length of the horizontal cross section and the corresponding dividing surface.

[0061] Optionally, the Gaussian integral algorithm includes: Determining the coordinate range of each tetrahedron in the vertical direction; A linear transformation is performed on the coordinate range to determine a Gaussian quadrature node and a Gaussian quadrature coefficient of the Gaussian integral algorithm.

[0062] Optionally, performing a linear transformation on the coordinate range to determine a Gaussian quadrature node and a Gaussian quadrature coefficient of the Gaussian integral algorithm includes: Performing linear transformation on the coordinate range using Formula 1 and Formula 2 respectively to determine the Gaussian quadrature node and the Gaussian quadrature coefficient; The formula 1 is: ; The formula 2 is: ; in,[ z 1, z 2] is the coordinate range, is the reference quadrature node, is the reference quadrature coefficient, z k is the Gaussian quadrature node, is the Gaussian quadrature coefficient.

[0063] Optionally, the Gaussian integral algorithm further includes: The Gaussian integral formula is: ; in, is the temporary gravity field generated by the tetrahedron at the observation point, is the Gaussian quadrature coefficient, is the gravity field generated by the kth horizontal cross section at the observation point, n is the total number of Gaussian integration nodes, and V is the gravity field generated by each horizontal cross section at the observation point.

[0064] Specifically, if Figure 2 As shown, when calculating the gravity field (temporary gravity field) of each tetrahedron at the observation point, Represents the three-dimensional coordinates of any point in the field source body. The density of any point in the field source body is , then the source body is at the observation point Gravity field at for: (1); Where G is the gravitational constant, is the distance between any point in the source body and the observation point, that is: ; Since the tetrahedron has an irregular shape, it is difficult to directly calculate the above integral. Therefore, the commonly used method to calculate the gravity field generated by a single tetrahedron is the cross-section method. If the coordinate range of the tetrahedron in the vertical direction is [ z 1, z 2], within this range, multiple horizontal planes perpendicular to the Z axis are cut into the tetrahedron. For the selected horizontal plane, the intersection points of each line segment of the tetrahedron and the horizontal plane are calculated. The intersection set is the vertex coordinates of the cross-section polygon, thereby obtaining multiple horizontal cross sections. If the gravity field generated by a single horizontal cross section polygon is , then the temporary gravity field generated by the tetrahedron at the observation point can be expressed as: (2); As for Figure 3 For an arbitrary horizontal cross section shown, the plane is at a height of , the polygon density is , the vertex coordinates of the polygon are , the projection of the measuring point in the plane of the horizontal cross section is , for The distance from the polygon vertex, if the polygon has edges, then the gravity field generated by the polygon at the observation point can be converted into a line integral along the edge length, which has an analytical expression after simplification: (3); in, , , , , , , , .

[0065] in The value of The sign of reflects whether the order of traversing the edges of the polygon is clockwise or counterclockwise. The distance from the origin to the first The distance between the edges, is the origin and the polygon vertex The connection of The cosine of the angle between the sides, is the origin and the polygon vertex The connection of The cosine of the complementary angle of the included angle of the two sides, The origin and the The cross product of the line vectors connecting the two vertices of an edge, The horizontal cross section The length of the side.

[0066] For the traditional cross-section method, when calculating the integral of formula (2), the traditional cross-section method uses the unequal-interval Simpson formula (also known as the quadratic Lagrange interpolation integral formula), assuming that The gravity fields generated by the cross-sectional polygons obtained at the height at the observation point are , then The gravitational field generated by the field source body between is: (4); If the vertical coordinate range of the tetrahedron is arrive ,along Take multiple horizontal cross sections of the tetrahedron and combine equations (2) and (4) to get the integral interval Divided into multiple subintervals, the temporary gravity field generated by the entire tetrahedron at the observation point for: (5); The traditional cross-section method introduces the unequally spaced Simpson formula to calculate the vertical integral. As can be seen from Equation (5), the number of horizontal cross-section layers can only be an odd number, and its convergence speed is slow. More horizontal cross-section layers are required to achieve higher accuracy. However, the more horizontal cross-section layers there are, the greater the amount of calculation, resulting in a slow calculation speed.

[0067] The improved Gauss cross section method in this embodiment is to improve the defects of the traditional cross section method, and the Gauss integral algorithm is used instead of the unequally spaced Simpson formula to calculate the vertical integral.

[0068] For any integrand , the n-point Gaussian integral formula on the interval [-1, 1] is: (6); in is the reference quadrature node, is the benchmark quadrature coefficient, n can be determined according to the Gaussian integral node value. When the number of Gaussian nodes n is determined, the root of the corresponding orthogonal polynomial can be uniquely determined. and , and it is applicable to any integrand. From formula (2), we can see that when calculating the tetrahedral gravity field, the integration interval is , then the Gaussian quadrature node needs to be obtained through the following linear transformation and Gaussian quadrature coefficient : The formula 1 is: (7); The formula 2 is: (8); in,[ z 1, z 2] is the coordinate range, is the reference quadrature node, is the reference quadrature coefficient, z k is the Gaussian quadrature node, is the Gaussian quadrature coefficient.

[0069] Through the horizontal plane where the above-mentioned quadrature node is located, that is, along Take the horizontal cross section of the tetrahedron. If we use formula (3) to calculate the gravity field generated by each horizontal cross section at the observation point, it is , then the temporary gravity field generated by the tetrahedron at the observation point can be expressed as: (9); Compared with the unequally spaced Simpson formula, the Gaussian integral formula has no restrictions on the number of Gaussian integral nodes, so any number of horizontal cross-section layers can be taken. The Gaussian integral formula has high calculation accuracy and fast convergence speed. A smaller number of Gaussian integral nodes can achieve higher accuracy. A smaller number of Gaussian integral nodes also means that fewer horizontal cross-section layers are required, which means less calculation and faster calculation speed.

[0070] The gravity field generated by the field source body at the measurement point is accumulated. After the field source body is divided into a tetrahedral grid, the gravity field generated by the field source body at the observation point is the sum of the temporary gravity fields generated by all tetrahedrons in the tetrahedral grid at the observation point. If the number of tetrahedrons is n, then: (10); in, The source body is at the measuring point The gravitational field generated at For the The temporary gravity field generated by each tetrahedron at the observation point. Since the temporary gravity field generated by each tetrahedron in the grid at the observation point is calculated independently, multi-process parallel computing technology is used to accelerate the calculation process. The gravity field forward modeling task is divided into multiple subtasks. Each subtask independently calculates the gravity field generated by a tetrahedron unit at the observation point. Taking advantage of the multi-core CPU, multiple processes are created simultaneously. Each process executes a subtask. Multiple processes execute multiple subtasks in parallel. After all processes are executed, the calculation results are accumulated to obtain the gravity field generated by the field source body at the observation point, which improves the calculation speed.

[0071] Optionally, the format data includes a VTK file, an STL file, and a three-dimensional coordinate point cloud; and the field source body model is segmented according to a preset method to obtain a plurality of tetrahedrons, including: When the format data is the STL file or the three-dimensional coordinate point cloud, the field source body model is segmented using a preset segmentation model to obtain a plurality of tetrahedrons; When the format data is the VTK file, the plurality of tetrahedrons are determined according to the VTK file.

[0072] Specifically, when the format data is an STL file (a triangular mesh representing the surface geometry of a model) or a 3D point cloud (a set of spatial points that reflects the surface or internal structure of a model), a predefined or user-defined meshing template or parameters (such as mesh density, regional detail level, etc.) is used.

[0073] The subdivision process includes: establishing the model geometry, building a continuous 3D model geometry from an STL file or point cloud, and applying a subdivision strategy: applying a preset subdivision model to the model geometry, ensuring that the model is subdivided into multiple tetrahedrons through minimization.

[0074] Specific methods include meshing techniques (such as Delaunay meshing and Marching Tetrahedron). Refining the mesh based on complex areas of the model increases model detail. Through algorithmic processing, the model is divided into multiple tetrahedral elements that meet geometric and topological requirements.

[0075] When the format data is a VTK (Visualization Toolkit) file, it itself consists of a tetrahedral mesh and does not require further subdivision.

[0076] The above process supports multiple geometric data formats, enhancing model compatibility and flexibility. By utilizing pre-set meshing models and standard algorithms (such as Delaunay meshing), strict meshing rules and high-quality elements are ensured, contributing to the stability of subsequent calculations. For VTK data, direct use of existing mesh information avoids repeated calculations and manual intervention, improving operational efficiency.

[0077] Whether describing complex geometries in STL files, point clouds, or VTK files, high-quality tetrahedral meshes can be finely meshed to reveal richer details. High-quality tetrahedral meshes ensure more accurate and robust gravity field simulations and analyses, enhancing the scientific nature and reliability of the models.

[0078] In summary, this process effectively achieves high-quality segmentation of the model by combining data structures in different formats, adopting preset segmentation schemes, or directly utilizing mesh information in VTK. This provides a solid foundation for subsequent geological analysis and numerical simulation, and significantly improves work efficiency and the accuracy of results.

[0079] Optionally, the tetrahedron gravity forward modeling method further includes: A plurality of field source body models are obtained, where the field source body models may include models corresponding to ore bodies, groundwater, structures, and the like.

[0080] Merging the field source body models to obtain a comprehensive model; Execute steps S200-S400 to obtain the gravity field at the observation point according to the comprehensive model.

[0081] Specifically, multiple gravity-related source models are collected. These models may include: Ore body models: These represent the geometry and density distribution of underground mineral deposits. Groundwater models: These describe the shape and flow characteristics of groundwater bodies, which influence groundwater levels and gravity field fluctuations. Tectonic models: These include the geometric features of geological structures (such as folds and faults), which significantly influence gravity fields.

[0082] These models can be derived from a variety of data acquisition methods, including geological exploration and surveying, remote sensing technology, geophysical surveying, etc. Ensuring the accuracy and reliability of the models is crucial.

[0083] The individual source models are combined to form a comprehensive model. In this process, the relative positions, physical properties (such as density) and mutual influences between different source bodies need to be considered.

[0084] For example, unification of geometry and physical properties: When merging, the geometry and properties of different models are unified to ensure physical consistency in the combined model. For example, the density of multiple field sources at the same location needs to be properly superimposed.

[0085] Executing steps S200-S400 to calculate the gravity field according to the comprehensive model specifically includes: The comprehensive model is tetrahedronized to obtain the detailed geometric structure of each field source body. Based on the tetrahedronization results, the gravity field of each tetrahedron is calculated using the improved Gauss cross-section method.

[0086] The gravity fields generated by each source are combined to calculate the total gravity field at each observation point. This calculation comprehensively considers the gravitational influence of each source on the observation point to ensure the accuracy of the calculated results. The final gravity field result is output and visualized to help users intuitively understand the spatial distribution characteristics of the gravity field.

[0087] By combining models of multiple source bodies, this process can fully capture the combined impact of different geological factors on the gravity field, significantly improving the accuracy of gravity field predictions. Furthermore, the integrated model is adaptable to complex geological conditions and effectively integrates the characteristics of various source bodies, ensuring that the calculated results better reflect the actual situation.

[0088] This process helps geologists analyze gravity variations at multiple levels (such as rock layers and groundwater layers), providing a deeper understanding of the spatial distribution of geological bodies and their underlying structures. Accurate calculation and analysis of gravity fields can support the exploration and management of mineral deposits, groundwater, and other resources, optimize resource development strategies, and reduce resource waste.

[0089] In addition, visualization has enhanced users' understanding of data and decision-making capabilities, providing strong data support for geological research, engineering design, environmental management and other fields, helping researchers and decision makers to intuitively understand complex geological conditions.

[0090] In summary, the introduction of the multi-source body joint model significantly improves the effect and application value of the tetrahedral gravity forward modeling method, providing strong support for geological exploration and resource management.

[0091] In some embodiments, in order to verify the advantages of the tetrahedron gravity forward modeling method over the traditional method, the experimental results are demonstrated in combination with specific field source bodies, such as Figure 4 As shown in the figure, the second schematic diagram of a rectangular field source model (rectangular model) has a density of Since the gravity field generated by a single cuboid can be forward-modeled by the prism method, which has an analytical expression, the result of the prism method forward modeling is considered the exact solution, and the difference between the forward modeling results of other methods and the exact solution is considered the forward modeling error. The observation plane is located at the Z = 0 plane. Starting from the origin, 20 observation points are set along the positive X and Y directions, and the grid spacing is 500 meters. The exact solution of the gravity field of the cuboid model on the observation plane calculated by the prism method is as follows: Figure 5 shown.

[0092] Because the rectangular parallelepiped model is relatively simple, the Delaunay tetrahedron partitioning algorithm is directly used to obtain the tetrahedron mesh (tetrahedron) as shown below: Figure 6 As shown, the grid is composed of 6 tetrahedrons, which can accurately represent the shape of a cuboid. First, the traditional tetrahedron partitioning method is used. Taking the 7-layer cross-section method as an example, the gravity field generated by the cuboid model (field source model) on the observation surface is calculated as follows: Figure 7 As shown in Figure 2, in order to evaluate the calculation accuracy of the method, the root mean square error between the forward modeling result and the exact solution is calculated. The calculation formula is: (11); in is the exact solution (generated gravity field) of the source body obtained by the prism method at the t-th observation point, is the forward modeling result (generated gravity field) of the source body at the t-th observation point by other methods, and n is the total number of observation points; the larger the root mean square error, the lower the accuracy of the method. At the same time, in order to evaluate the calculation speed of the method, the running time of the forward modeling program was counted. In order to reduce the error caused by different calculation states, the average time spent on running the forward modeling program five times on the same computer was taken as the calculation time of the method, and the program was run using multi-process parallel technology. Since the traditional cross-section method can only have an odd number of horizontal cross-section layers, the root mean square error and calculation time of the cross-section layers from 3 to 27 are counted as shown in Table 1: Table 1 Forward modeling results of traditional cross sections with different numbers of layers

[0093] It can be seen from the table that when the number of cross-section layers increases, the program running time increases, the root mean square error decreases, and the calculation results are closer to the exact value.

[0094] The improved Gauss cross section method of the present invention is used for the same tetrahedral mesh. Taking the 5-layer Gauss cross section method as an example, the gravity field generated by the model on the observation surface is calculated as follows: Figure 8 As shown in Table 2, since the improved Gauss cross-section method can take any number of cross-section layers, the calculation accuracy and calculation time of the cross-section layers from 3 to 15 layers are statistically analyzed on the same computer. Table 2 Forward modeling results of Gauss cross sections with different numbers of layers

[0095] As can be seen from the table, when the number of cross-section layers increases, the program running time continues to increase. When the number of cross-section layers is between 3 and 7, the root mean square error decreases as the number of cross-section layers increases. When the number of cross-section layers continues to increase, the root mean square error stabilizes at This order of magnitude fluctuates.

[0096] Comparing the calculation results of the Gauss cross-section method of the present invention with those of the traditional cross-section method, it can be found that when the number of cross-section layers is the same, the root mean square error between the forward gravity field modeled by the Gauss cross-section method and the exact solution is much smaller than that of the traditional cross-section method, and when the number of cross-section layers is 8, the root mean square error has gradually stabilized within an extremely small order of magnitude, while the traditional cross-section method obviously requires more cross-section layers to gradually stabilize the error, indicating that the Gauss cross-section method has higher calculation accuracy. Considering the calculation speed, assuming that the forward error is required to reach At this order of magnitude, the traditional cross-section method requires 19 layers of cross-sections and the program runs in 7.0 seconds. However, the Gauss cross-section method, due to its higher accuracy, only requires 5 layers of cross-sections and the program runs in 2.6 seconds. This reduces the running time by 4.4 seconds compared to the cross-section method, and the calculation speed is increased by 2.7 times. Moreover, for more complex models, the number of tetrahedrons in the tetrahedral mesh is greater, and the amount of calculation is greater. The Gauss cross-section method will help reduce more calculation time and save computing resources. In order to more intuitively demonstrate the difference in calculation accuracy and convergence speed between the present invention and the traditional cross-section method, the root mean square error of the two methods obtained from the above experiment is plotted as a function of the number of horizontal cross-section layers, as shown in Figure 2. Figure 9As can be seen from the figure, the root mean square error of the Gauss cross-section method is smaller than that of the traditional cross-section method, which shows that the forward modeling result of the method of the present invention is closer to the exact solution, has higher calculation accuracy, and converges faster. When the required accuracy of the forward modeling task is given, the method of the present invention requires fewer cross-section layers and has a faster calculation speed.

[0097] Comparing the calculation results of the Gauss cross-section method of the present invention with those of the traditional cross-section method reveals that, when the number of cross-section layers is the same, the root mean square error between the forward modeled gravity field and the exact solution using the Gauss cross-section method is much smaller than that of the traditional cross-section method. Furthermore, when the number of cross-section layers reaches eight, the error of the Gauss cross-section method gradually stabilizes to a very small order of magnitude, while the traditional cross-section method requires significantly more cross-section layers for the error to stabilize, demonstrating that the Gauss cross-section method offers higher computational accuracy.

[0098] In terms of calculation speed, assuming that the forward error required reaches At this level, the traditional cross-section method requires 19 layers of cross-sections and a program run time of 7.0 seconds. However, the Gauss cross-section method, under the same error requirements, requires only 5 layers of cross-sections and a program run time of 2.6 seconds, saving 4.4 seconds and increasing the calculation speed by approximately 2.7 times. This is especially true for complex models, which require more tetrahedrons and are more computationally intensive. The Gauss cross-section method can effectively reduce calculation time and conserve significant computing resources.

[0099] In order to more intuitively demonstrate the advantages of the method of the present invention in terms of calculation accuracy and convergence speed, we plotted the root mean square error of the two methods as a function of the number of horizontal cross-section layers (see Appendix Figure 9 As can be seen from the figure, the Gauss cross-section method consistently produces smaller errors than the traditional cross-section method, indicating that its forward modeling results are closer to the exact solution, with higher computational accuracy and faster convergence. When meeting the accuracy requirements of a specific forward modeling task, the method of the present invention requires significantly fewer cross-section layers and achieves faster overall computational speed.

[0100] An embodiment of the present invention provides a tetrahedron gravity forward modeling device, comprising: an acquiring unit, configured to acquire a field source body model corresponding to the field source body and format data of the field source body model; a segmentation unit, configured to segment the field source body model according to a preset method to obtain a plurality of tetrahedrons; the preset method corresponds to the format data; A processing unit is used to obtain coordinate data of the observation point, and based on the coordinate data, perform parallel processing on each tetrahedron based on the improved Gauss cross-section method to obtain a temporary gravity field generated by each tetrahedron at the observation point; based on all the temporary gravity fields, obtain the gravity field generated by the field source body at the observation point.

[0101] An embodiment of the present invention provides a tetrahedron gravity forward modeling system, comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the tetrahedron gravity forward modeling method described above when executing the computer program.

[0102] In other words, a tetrahedron gravity forward modeling system includes a memory and a processor coupled to the memory; the memory is configured to store a computer program; and the processor is configured to perform the following operations when executing the computer program: Acquire a field source body model corresponding to the field source body and format data of the field source body model; Dividing the field source body model according to a preset method to obtain a plurality of tetrahedrons; the preset method corresponds to the format data; Acquiring coordinate data of the observation point, and performing parallel processing on each of the tetrahedrons based on the improved Gauss cross-section method according to the coordinate data to obtain a temporary gravity field generated by each tetrahedron at the observation point; Based on all the temporary gravity fields, the gravity field generated by the field source body at the observation point is obtained.

[0103] An embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the tetrahedron gravity forward modeling method described above is implemented.

[0104] In other words, a non-volatile computer-readable storage medium stores a computer program, which, when executed by a processor, causes the processor to perform the following operations: Acquire a field source body model corresponding to the field source body and format data of the field source body model; Dividing the field source body model according to a preset method to obtain a plurality of tetrahedrons; the preset method corresponds to the format data; Acquiring coordinate data of the observation point, and performing parallel processing on each of the tetrahedrons based on the improved Gauss cross-section method according to the coordinate data to obtain a temporary gravity field generated by each tetrahedron at the observation point; Based on all the temporary gravity fields, the gravity field generated by the field source body at the observation point is obtained.

[0105] A tetrahedron gravity forward modeling system that can serve as a server or client of the present invention will now be described, which is an example of a hardware device that can be applied to various aspects of the present invention. The tetrahedron gravity forward modeling system is intended to represent various forms of digital electronic computer equipment, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The tetrahedron gravity forward modeling system can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or claimed herein.

[0106] The tetrahedral gravity forward modeling system includes a computing unit that can perform various appropriate actions and processes based on a computer program stored in a read-only memory (ROM) or loaded from the storage unit into a random access memory (RAM). The RAM can also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. An input / output (I / O) interface is also connected to the bus.

[0107] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM). In this application, the units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network elements. Some or all of these units can be selected based on actual needs to achieve the objectives of the embodiments of the present invention. Furthermore, the functional units in the various embodiments of the present invention can be integrated into a single processing unit, each unit can exist physically separately, or two or more units can be integrated into a single unit. These integrated units can be implemented in either hardware or software functional units.

[0108] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A tetrahedron gravity forward modeling method, characterized in that: include: Acquire a field source body model corresponding to the field source body and format data of the field source body model; Dividing the field source body model according to a preset method to obtain a plurality of tetrahedrons; The preset mode corresponds to the format data; Acquiring coordinate data of the observation point, and performing parallel processing on each of the tetrahedrons based on the improved Gauss cross-section method according to the coordinate data to obtain a temporary gravity field generated by each tetrahedron at the observation point; Based on all the temporary gravity fields, the gravity field generated by the field source body at the observation point is obtained.

2. The tetrahedron gravity forward modeling method according to claim 1, characterized in that: The method of performing parallel processing on each tetrahedron based on the improved Gauss cross-section method according to the coordinate data and the basic data of the field source body to obtain the corresponding temporary gravity field generated at the observation point includes: Performing horizontal segmentation on each of the tetrahedrons to obtain a plurality of horizontal cross-sectional data; Obtaining the gravity field of each horizontal cross section according to the coordinate data and the horizontal cross section data; Based on the Gaussian integral algorithm, a temporary gravity field of each tetrahedron is obtained according to the gravity fields of all the horizontal cross sections.

3. The tetrahedron gravity forward modeling method according to claim 2, characterized in that: The horizontal cross-sectional data includes vertex coordinate data; the horizontal segmentation of each tetrahedron is performed to obtain a plurality of horizontal cross-sectional data, including: Determine the Gaussian integration node values; Determine a plurality of splitting planes according to the Gaussian integral node values, and perform horizontal splitting on each of the tetrahedrons according to each of the splitting planes to obtain a plurality of horizontal cross sections; The corresponding vertex coordinate data is obtained according to the intersection of each side length of the horizontal cross section and the corresponding dividing surface.

4. The tetrahedron gravity forward modeling method according to claim 3, characterized in that: The Gaussian integral algorithm includes: Determining the coordinate range of each tetrahedron in the vertical direction; A linear transformation is performed on the coordinate range to determine a Gaussian quadrature node and a Gaussian quadrature coefficient of the Gaussian integral algorithm.

5. The tetrahedron gravity forward modeling method according to claim 4, characterized in that: The linear transformation of the coordinate range to determine the Gaussian quadrature nodes and Gaussian quadrature coefficients of the Gaussian integral algorithm includes: Performing linear transformation on the coordinate range using Formula 1 and Formula 2 respectively to determine the Gaussian quadrature node and the Gaussian quadrature coefficient; The formula 1 is: ； The formula 2 is: ； in,[ z 1, z 2] is the coordinate range, is the reference quadrature node, is the base quadrature coefficient, z k is the Gaussian quadrature node, is the Gaussian quadrature coefficient.

6. The tetrahedron gravity forward modeling method according to claim 4, characterized in that: The Gaussian integral algorithm also includes: The Gaussian integral formula is: ； in, is the temporary gravity field generated by the tetrahedron at the observation point, is the Gaussian quadrature coefficient, is the gravity field generated by the k-th horizontal cross section at the observation point, n is the total number of Gaussian integration nodes, V is the gravity field generated by each of the horizontal cross sections at the observation point.

7. The tetrahedron gravity forward modeling method according to claim 5, characterized in that: The format data includes a VTK file, an STL file, and a three-dimensional coordinate point cloud; the field source body model is segmented according to a preset method to obtain a plurality of tetrahedrons, including: When the format data is the STL file or the three-dimensional coordinate point cloud, the field source body model is segmented using a preset segmentation model to obtain a plurality of tetrahedrons; When the format data is the VTK file, the plurality of tetrahedrons are determined according to the VTK file.

8. A tetrahedron gravity forward modeling device, characterized in that: include: an acquiring unit, configured to acquire a field source body model corresponding to the field source body and format data of the field source body model; A segmentation unit, configured to segment the field source body model according to a preset method to obtain a plurality of tetrahedrons; The preset mode corresponds to the format data; A processing unit is used to obtain coordinate data of the observation point, and based on the coordinate data, perform parallel processing on each tetrahedron based on the improved Gauss cross-section method to obtain a temporary gravity field generated by each tetrahedron at the observation point; based on all the temporary gravity fields, obtain the gravity field generated by the field source body at the observation point.

9. A tetrahedron gravity forward modeling system, characterized in that: The invention comprises a memory and a processor; the memory is used to store a computer program; the processor is used to implement the tetrahedron gravity forward modeling method according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by the processor, the tetrahedron gravity forward modeling method according to any one of claims 1 to 7 is implemented.

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