A method for reconstructing the bottom surface and estimating the volume of debris flow landslide source

Abstract

This invention provides a method for reconstructing the bottom surface and estimating the volume of debris flow landslide sources, relating to the field of geological disaster monitoring and prevention technology. The method includes acquiring vector boundary and elevation data of the debris flow landslide source and constructing a basic dataset using unified coordinates; fitting a principal trend constraint function along the sliding direction using elevation data points within the debris flow landslide source buffer zone to generate a trend-fitted elevation vector; performing interpolation propagation and extension based on the structural tensor and the trend-fitted elevation vector to obtain the initial bottom sliding surface elevation; constructing a sparse matrix system and using a generalized minimum residual method to globally optimize and fit the bottom sliding surface elevation; extending the bottom sliding surface to the ground surface, naturally intersecting with the top surface of the digital elevation model to form the volume of a closed landslide body. This invention solves the problems of insufficient interpolation direction control, imprecise boundary constraints, and inability to naturally intersect to form a closed volume in existing debris flow landslide source bottom sliding surface interpolation reconstruction methods.

Description

Technical Field

[0001] This invention relates to the field of geological disaster monitoring and prevention technology, and in particular to a method for reconstructing the bottom surface and estimating the volume of debris flow landslide material sources. Background Technology

[0002] Debris flows are a common and severe geological hazard in mountainous areas. Their activity is often accompanied by dramatic topographic changes, making accurate determination of the debris flow source volume crucial for disaster assessment, prevention engineering design, and evaluation of control effectiveness. Digital Elevation Models (DEMs), as important geographic information data characterizing debris flow landforms, are the fundamental data source for source volume estimation, risk assessment, and disaster control. Constructing an accurate base slip surface model is a key factor determining the accuracy of debris flow volume estimation. Currently, debris flow volume estimation methods are generally divided into two categories: traditional field measurement methods and remote sensing data-assisted methods. Traditional field measurement methods typically determine the location of the slip surface through on-site reconnaissance, drilling, or geological profile mapping. However, in practical mountainous work, this method is limited by complex on-site conditions, large workload, high cost, and discrete data, making it difficult to meet the needs of large-scale, rapid disaster investigation and monitoring. In recent years, with the rapid development of remote sensing technology, high-precision digital elevation models (DEMs) based on airborne lidar (LiDAR) have gradually become an important tool for debris flow investigation. Laser data with multiple echoes can effectively penetrate vegetation cover, quickly and accurately acquiring high-precision terrain data in debris flow areas, providing higher-quality input information for the three-dimensional reconstruction of the bottom sliding surface of landslide bodies.

[0003] However, existing remote sensing data-assisted methods for debris flow volume estimation still have significant limitations, particularly in the insufficient accuracy of reconstructing the three-dimensional spatial structure of the slip surface. Conventional geological surface modeling methods, such as inverse distance weighted (IDW), radial basis function (RBF) interpolation, or Kriging interpolation, typically only consider the distance relationships between spatial data points, neglecting the significant directionality caused by topographic aspect, slope, and geological structure during the formation of the geological slip body. This leads to unreasonable local depressions or bulges in the fitted slip surface model, severely affecting the accuracy of subsequent source volume calculations.

[0004] In recent years, some studies have also attempted to use the Discrete Smooth Interpolation (DSI) method with directional tensor constraints to construct geological surfaces in order to improve the spatial continuity and rationality of the bottom slip surface. Although these methods have improved the quality of bottom slip surface fitting to some extent, they still have the following prominent problems: (1) Uniqueness of interpolation propagation direction: Existing discrete smooth interpolation (DSI) methods mostly use fixed direction tensors for interpolation, which makes it difficult to fully consider the complex terrain conditions and geological structure direction changes in the slip area, resulting in poor local fitting effect of the interpolation results; (2) Lack of trend information of digital elevation model (DEM): Existing methods do not make full use of the terrain trend information outside the slip area, and do not consider the effective constraint of the trend of the digital elevation model (DEM) surface on the bottom slip surface interpolation, resulting in the interpolation surface being difficult to naturally connect and close with the surface digital elevation model (DEM); (3) Lack of effective global optimization strategy: Existing interpolation results are mostly local optimal solutions, lacking a global optimization strategy, which makes the overall consistency and uniformity of the interpolation results poor, and cannot directly form a closed body for volume calculation; (4) Unclear uncertainty range of interpolation results: Due to the complex terrain conditions in mountainous areas, the slope and terrain elevation difference are obvious, and traditional methods do not provide interpolation uncertainty quantification, making it difficult to use for risk assessment in engineering practice.

[0005] In reality, most current studies primarily employ traditional interpolation methods to construct the base surface of debris flows, failing to effectively utilize geological structural features and digital elevation model (DEM) trend information to guide base surface interpolation. There is a lack of suitable structural tensor guidance strategies to significantly improve interpolation accuracy and rationality. Accurately constructing a base surface model of a debris flow requires consideration of complex and diverse factors: First, the debris flow process is significantly influenced by slope and aspect, resulting in significant spatial differences in the direction and morphology of the base surface; second, DEM trend information plays a crucial role in fitting the boundary region of the slip surface, and existing methods generally lack full utilization of DEM trend information to guide interpolation; furthermore, the terrain within the debris flow area undergoes dramatic changes, and local propagation of base surface interpolation can easily lead to structural discontinuities, making it difficult for traditional methods to effectively control interpolation errors. Therefore, calculating the accurate closed slip volume from an ideal base surface model of a debris flow requires consideration of numerous factors. Summary of the Invention

[0006] To address the aforementioned shortcomings in existing technologies, this invention provides a method for reconstructing the bottom surface and estimating the volume of debris flow landslide source material. This method solves the problems of insufficient control over the interpolation direction, imprecise boundary constraints, and inability to naturally intersect and form a closed volume in existing debris flow landslide source material bottom surface interpolation reconstruction methods.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a method for reconstructing the bottom surface and estimating the volume of debris flow landslide source, comprising the following steps: S1. Obtain the vector boundary and elevation data of the debris flow landslide source, and construct a basic dataset by unifying coordinates; S2. Based on the constructed basic dataset, using the elevation data points within the debris flow landslide source buffer zone, fit the main trend constraint function in the sliding direction to generate a trend-fitted elevation vector, where the elevation data points include boundary points. S3. Based on the structural tensor and the trend-fitted elevation vector, perform direction-guided interpolation propagation to obtain the initial bottom slip surface elevation. S4. Construct a sparse optimization system that integrates structural tensor direction constraints and trend function control terms. Use the generalized minimum residual method to globally optimize the initial bottom slip surface elevation to obtain the optimal bottom slip surface elevation vector and complete the reconstruction of the bottom surface of the debris flow landslide source. S5. Based on the optimal bottom slip surface elevation vector and the surface of the digital elevation model, construct vertical volume units, estimate the closed volume between them, and obtain the volume of the landslide body.

[0008] The beneficial effects of this invention are as follows: This invention proposes an interpolation method guided by structural tensors. Considering various geological structural factors such as slope, aspect, and elevation data trends, the interpolation direction and propagation process are guided by both boundary trends and structural tensors. This reconstructs a more accurate and reasonable sliding bottom surface, directly forming a closed volume that naturally intersects with the top surface of the digital elevation model (DEM) for volume estimation. This supports the risk analysis and decision-making needs of actual disaster investigation and mitigation projects. Further, S1 includes the following steps: S101. Extract the effective elevation point set from the high-resolution elevation data of the study area, remove null values ​​and outliers, and form a point set. , This represents the set of valid points for elevation data. S102. Obtain the vector boundary of the debris flow landslide source and ensure that the boundary polygon... Closed, where the boundary polygon All vertices satisfy closure and coordinate consistency, and the boundary polygon The set of vertices is: ; in, Represents the set of boundary control points. Indicates the first The x-coordinates of the boundary points Indicates the first The ordinates of the boundary points Indicates the original topographic elevation at the boundary. Indicates the number of the boundary point, with a value range of 1. , M b Indicates the number of boundary points; S103. Constructing a point set for control and interpolation: in the boundary polygon Expand outward distance d The set of buffer control points extracted within the buffer and merged boundary control point set and buffer control point set The resulting set of control points for interpolation constraints : ; ; in, Indicates the boundary polygon Expand outward distance d The three-dimensional coordinates of the external constraint elevation data points extracted within the buffer. Indicates the number of the point within the buffer. Represents the control point set Numbering of all control points in the middle, Indicates the number of points in the buffer. Represents the control point set The number of all control points in the system Represents the boundary polygon and distance d The buffer zone formed by outward expansion Represents the three-dimensional coordinates of the control points; S104. Construct the bottom sliding surface interpolation mesh. And will interpolate the mesh from the bottom surface. The unknown elevation data points selected in the middle are set as the interpolation target point set. Interpolation target point set Interpolation mesh from the bottom surface The interpolation target point set after removing known control points: ; ; in, This represents the two-dimensional planar coordinates of a point in the bottom sliding interpolation grid, belonging to the real number field. , Represents the set of real numbers. Represents the boundary polygon The internal area, Indicates the first m The x and y coordinates of each interpolation target point correspond to the location of the unknown elevation in the bottom sliding surface interpolation grid. Indicates the first m The undetermined elevation of the interpolation target point K Represents the interpolation target point set Total points m Indicates the number in the set of interpolation target points. m ∈{1,2,…,K}.

[0009] The beneficial effects of the above-mentioned further solutions are: by constructing a set of boundary and buffer control points and extracting interpolation target points, the present invention achieves closed control of the interpolation region and structured organization of elevation data, providing high-quality data support for subsequent accurate fitting of the bottom slip surface and trend constraints.

[0010] Furthermore, S2 includes the following steps: S201, Set the boundary control points The sample set used as the main trend constraint function; S202. Based on the sample set of the main trend constraint function, a second-order polynomial function is used to perform regression fitting on the elevation data points to form the main trend constraint function. : ; in, Represents any two-dimensional point in the bottom sliding surface region. The trend of elevation, This represents the two-dimensional coordinates of any position to be predicted within the bottom sliding surface interpolation grid. Represents the coefficients of the polynomial to be regressed; S203. Solve for the fitting coefficients using the least squares method. Make the main trend constraint function Capable of fitting continuous terrain morphology outside the boundary: ; in, j Indicates the number of the point within the buffer. Indicates the number of points in the buffer. Indicates the boundary polygon Expand outward distance d The three-dimensional coordinates of the external constraint elevation data points extracted within the buffer. Indicates at point Predicted elevation values ​​at the location; S204, Apply the main trend constraint function Applied to interpolation target point set The trend-fitted elevation vector is obtained. : ; in, Indicates the first m The x and y coordinates of each interpolation target point correspond to the location of the unknown elevation in the bottom sliding surface interpolation grid. m Represents the interpolation target point set The number in m ∈{1,2,…,K}, K Represents the interpolation target point set Total points.

[0011] The beneficial effect of the above-mentioned further solution is that the present invention effectively avoids unreasonable fluctuations or depressions at the boundary of the bottom slip surface interpolation by introducing the main trend function constraint.

[0012] Furthermore, step S3 includes the following steps: S301, Based on interpolation target point set At each target point to be interpolated, extract its spatial neighborhood. k neighborhood points And calculate the structure tensor It is used to characterize the main extension direction of the neighborhood point set. This represents the three-dimensional spatial coordinates of the neighborhood points of the m-th interpolation target point. i This represents the first interpolation target point. i Neighboring points, This represents the set of control points used for interpolation constraints. S302. The structure tensor constructed at each interpolation target point Perform eigenvalue decomposition to extract the structure tensor. Maximum eigenvalue corresponding feature vector , to feature vector The main propagation direction for the current interpolation target point: ; in, Represents the structure tensor matrix. Represents the principal eigenvector of unit length; S303, in the main direction vector Under propagation control, a direction-guided interpolation weighting function is constructed by combining Gaussian distance weights for each neighboring point. Assign weights : ; ; in, Indicates the first m The nth interpolation target point is related to its nth i The structure tensor guides the weights assigned to each neighboring point. Indicates the distance from the current interpolation target point to the th i A vector of neighborhood points, This represents the Gaussian kernel width control parameter. express With the principal direction vector The included angle, Indicates the first i Two-dimensional coordinates of a neighboring point Indicates the first m Two-dimensional coordinates of the interpolation target point K Represents the interpolation target point set Total points m ∈{1,2,…,K}; S304. Combining the weighted elevations of each neighboring point, calculate the elevation value of the interpolated target point to obtain the initial bottom slip surface elevation. .

[0013] The beneficial effects of the above-mentioned further solutions are: the present invention realizes automatic guided interpolation propagation based on the principal direction of the structural tensor, which effectively improves the directional continuity and terrain adaptability of the bottom slip surface fitting.

[0014] Furthermore, the structural tensor matrix The expression is as follows: ; in, k Indicates the number of neighboring points. i Indicates the first i 1 neighboring point; The expression for the initial bottom surface is as follows: ; in, This represents the initial interpolated elevation value of the bottom slip surface. This represents the predicted elevation value using the trend function. This indicates the trend fusion weight.

[0015] Furthermore, step S4 includes the following steps: S401. Construct a sparse Laplacian matrix weighted by the structure tensor. , used to describe the propagation constraints of elevation; S402. Construct the trend constraint term matrix C and the trend elevation vector. Apply the fitted value of the trend function as a soft constraint to each interpolation target point; S403, Based on Sparse Laplacian Matrix and trend elevation vector A joint optimization system is constructed that integrates structural tensor direction constraints and trend function control terms, and the final solution form is defined. The trend constraint term matrix C is used to construct the weight coefficient matrix of the constraint terms in the joint optimization system equation. S404, Based on Sparse Laplacian Matrix The joint optimization system is transformed into a sparse linear system of equations. Based on the initial bottom slip surface elevation, a generalized minimum residual method is used to perform global optimization fitting of the bottom slip surface, and the optimal bottom slip surface elevation vector is iteratively solved. .

[0016] Furthermore, the expression for the joint optimization system is as follows: ; ; in, This represents the column vector of initial elevation predictions after interpolation propagation. This represents the column vector of the bottom slip surface elevation solution obtained by joint optimization. Indicates the initial bottom slip surface elevation. This represents the trend elevation of any two-dimensional point in the bottom slip surface region, and T represents the transpose operation; For each target point to be interpolated sparse Laplace matrix Each line in The row is constructed as follows: diagonal elements off-diagonal elements ,in, Indicates the first m The nth interpolation target point is related to its nth i The structure tensor guides the weights assigned to each neighboring point. k Indicates the number of neighboring points. Indicates the first i The global index of each neighboring point, except for diagonal elements and off-diagonal elements, is 0; The expression for the trend constraint term matrix C is as follows: ; in, This represents the penalty factor for the trend term, and I represents the identity matrix. K Represents the interpolation target point set Total points.

[0017] The beneficial effects of the above-mentioned further solutions are: the present invention proposes an interpolation strategy jointly guided by structural tensor and DEM trend, which improves the local continuity and global accuracy of bottom slip surface interpolation.

[0018] Furthermore, step S5 includes the following steps: S501, Calculate the optimal bottom sliding surface elevation vector Grid interpolation is performed within the boundary to construct a continuous bottom surface; S502. Within the fitted bottom slip surface and the top surface of the collapse material source, construct vertical unit columns and use the column volume method to estimate the closed volume between the two surfaces. S503. Based on the estimation results, the top surface of the landslide source and the fitted bottom sliding surface are plotted together in a three-dimensional coordinate system, and the landslide boundary line is marked to show the three-dimensional closed structure of the entire landslide body, forming the landslide volume of the closed landslide body, and completing the volume estimation of the landslide volume.

[0019] The beneficial effects of the above-mentioned further solutions are: the present invention provides a solution for the bottom slip surface to naturally intersect with the top surface of the digital elevation model (DEM) and form a closed volume, which improves the reliability and practicality of the volume estimation of landslide material sources.

[0020] Furthermore, the volume of the landslide body in S5 is calculated as follows: ; in, Indicates the volume of the landslide. Indicates the first Area of ​​each grid cell This represents the elevation data of the earth's surface. This indicates the fitted bottom sliding surface elevation. K Represents the interpolation target point set Total points m Indicates the number in the set of interpolation target points. m ∈{1,2,…,K}. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0022] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0023] Example like Figure 1 As shown, this invention provides a method for reconstructing the bottom surface and estimating the volume of debris flow landslide source, the implementation method of which is as follows: S1. Obtain the vector boundary and elevation data of the debris flow landslide source, and construct a basic dataset using unified coordinates. The implementation method is as follows: S101. Extract the effective elevation point set from the high-resolution elevation data of the study area, remove null values ​​and outliers, and form a point set. , This represents the set of valid points for elevation data. S102. Obtain the vector boundary of the debris flow landslide source and ensure that the boundary polygon... Closed, where the boundary polygon All vertices satisfy closure and coordinate consistency, and the boundary polygon The set of vertices is: ; in, Represents the set of boundary control points. Indicates the first The x-coordinates of the boundary points Indicates the first The ordinates of the boundary points Indicates the original topographic elevation at the boundary. Indicates the number of the boundary point, with a value range of 1. , M b Indicates the number of boundary points; S103. Constructing a point set for control and interpolation: in the boundary polygon Expand outward distance d The set of buffer control points extracted within the buffer and merged boundary control point set and buffer control point set The resulting set of control points for interpolation constraints : ; ; in, Indicates the boundary polygon Expand outward distance d The three-dimensional coordinates of the external constraint elevation data points extracted within the buffer. Indicates the number of the point within the buffer. Represents the control point set Numbering of all control points in the middle, Indicates the number of points in the buffer. Represents the control point set The number of all control points in the system Represents the boundary polygon and distance d The buffer zone formed by outward expansion Represents the three-dimensional coordinates of the control points; S104. Construct the bottom sliding surface interpolation mesh. And will interpolate the mesh from the bottom surface. The unknown elevation data points selected in the middle are set as the interpolation target point set. Interpolation target point set Interpolation mesh from the bottom surface The interpolation target point set after removing known control points: ; ; in, This represents the two-dimensional planar coordinates of a point in the bottom sliding interpolation grid, belonging to the real number field. , Represents the set of real numbers. Represents the boundary polygon The internal area, Indicates the first m The x and y coordinates of each interpolation target point correspond to the location of the unknown elevation in the bottom sliding surface interpolation grid. Indicates the first m The undetermined elevation of the interpolation target point K Represents the interpolation target point set Total points m Indicates the number in the set of interpolation target points. m ∈{1,2,…,K}.

[0024] In this embodiment, a digital elevation model (DEM) of the debris flow basin is constructed based on airborne lidar data, the vector boundaries of the debris flow landslide source are extracted, and coordinate unification processing is performed to obtain the basic dataset.

[0025] S2. Based on the constructed basic dataset, using elevation data points within the debris flow landslide source buffer zone, a principal trend constraint function is fitted along the sliding direction to generate a trend-fitted elevation vector. The elevation data points include boundary points. The implementation method is as follows: S201, Set the boundary control points The sample set used as the master trend constraint function is used to fit the elevation change trend outside the boundary and participate in the construction of the constraint term. This sample set is applied in subsequent S202 and S203 applications, using sample points as regression input data to fit the master trend constraint function using the least squares method. This master trend constraint function is used to: guide the propagation of the sliding surface interpolation (improving terrain continuity); construct the trend term in the generalized minimum residual method; and control the interpolation surface to avoid excessive concavity or bulging. S202. Based on the sample set of the principal trend constraint function, a second-order polynomial function is used to perform regression fitting on the elevation data points to form the principal trend constraint function. : ; in, Represents any two-dimensional point in the bottom sliding surface region. The trend of elevation, This represents the two-dimensional coordinates of any position to be predicted within the bottom sliding surface interpolation grid. Represents the coefficients of the polynomial to be regressed; S203. Solve for the fitting coefficients using the least squares method. Make the main trend constraint function Capable of fitting continuous terrain morphology outside the boundary: ; in, j Indicates the number of the point within the buffer. Indicates the number of points in the buffer. Indicates the boundary polygon Expand outward distance d The three-dimensional coordinates of the external constraint elevation data points extracted within the buffer. Indicates at point Predicted elevation values ​​at the location; S204, Apply the main trend constraint function Applied to interpolation target point set The trend-fitted elevation vector is obtained. : ; in, Indicates the first m The x and y coordinates of each interpolation target point correspond to the location of the unknown elevation in the bottom sliding surface interpolation grid. m Represents the interpolation target point set The number in m ∈{1,2,…,K}, K Represents the interpolation target point set Total points.

[0026] In this embodiment, a trend-fitted elevation vector is constructed by utilizing the boundary of the landslide source vector and the elevation data trend information.

[0027] S3. Based on the structural tensor and the trend-fitted elevation vector, direction-guided interpolation propagation is performed to obtain the initial bottom slip surface elevation. The implementation method is as follows: S301, Based on interpolation target point set At each target point to be interpolated, extract its spatial neighborhood. k neighborhood points And calculate the structure tensor It is used to characterize the main extension direction of the neighborhood point set. Indicates the firstm The three-dimensional spatial coordinates of the neighborhood points of the interpolation target point i This represents the first interpolation target point. i Neighboring points, This represents the set of control points used for interpolation constraints. S302. The structure tensor constructed at each interpolation target point Perform eigenvalue decomposition to extract the structure tensor. Maximum eigenvalue corresponding feature vector , to feature vector The main propagation direction for the current interpolation target point: ; in, Represents the structure tensor matrix. Represents the principal eigenvector of unit length; S303, in the main direction vector Under propagation control, a direction-guided interpolation weighting function is constructed by combining Gaussian distance weights for each neighboring point. Assign weights : ; ; in, Indicates the first m The nth interpolation target point is related to its nth i The structure tensor guides the weights assigned to each neighboring point. Indicates the distance from the current interpolation target point to the th i A vector of neighborhood points, This represents the Gaussian kernel width control parameter. express With the principal direction vector The included angle, Indicates the first i Two-dimensional coordinates of a neighboring point Indicates the first m Two-dimensional coordinates of the interpolation target point K Represents the interpolation target point set Total points m ∈{1,2,…,K}; S304. Combining the weighted elevations of each neighboring point, calculate the elevation value of the interpolated target point to obtain the initial bottom slip surface elevation. .

[0028] In this embodiment, the KD-Tree spatial indexing method is used in S301 at each target point to be interpolated. At that point, using a KD-Tree index structure built from a known set of points, the query function query() is called to quickly search for its nearest neighbor in the space. k neighborhood points , as its interpolation support point set.

[0029] In this embodiment, the structure tensor matrix The expression is as follows: ; in, k Indicates the number of neighboring points. i Indicates the first i 1 neighboring point.

[0030] In this embodiment, a round-by-round propagation interpolation strategy is adopted, using the interpolation target point calculated in the previous round as the neighborhood control point in the new round to participate in the subsequent interpolation process, gradually expanding the interpolation range, effectively solving the interpolation interruption problem caused by the sparse control points in the middle; the elevation expression of the target point to be interpolated is: ; in, This represents the initial interpolated elevation value of the bottom slip surface. This represents the predicted elevation value using the trend function. This indicates the trend fusion weight.

[0031] S4. Construct a sparse optimization system that integrates structural tensor direction constraints and trend function control terms. Use the generalized minimum residual method to globally optimize the initial bottom slip surface elevation to obtain the optimal bottom slip surface elevation vector, thus completing the reconstruction of the bottom surface of the debris flow landslide source. The implementation method is as follows: S401. Construct a sparse Laplacian matrix weighted by the structure tensor. , used to describe the propagation constraints of elevation; S402. Construct the trend constraint term matrix C and the trend elevation vector. Apply the fitted value of the trend function as a soft constraint to each interpolation target point; S403, Based on Sparse Laplacian Matrix and trend elevation vector A joint optimization system is constructed that integrates structural tensor direction constraints and trend function control terms, and the final solution form is defined. The trend constraint term matrix C is used to construct the weight coefficient matrix of the constraint terms in the joint optimization system equation. S404, Based on Sparse Laplacian Matrix The joint optimization system is transformed into a sparse linear system of equations. Based on the initial bottom slip surface elevation, a generalized minimum residual method is used to perform global optimization fitting of the bottom slip surface, and the optimal bottom slip surface elevation vector is iteratively solved. .

[0032] In this embodiment, the expression for the joint optimization system is as follows: ; ; in, This represents the column vector of initial elevation predictions after interpolation propagation. This represents the column vector of the bottom slip surface elevation solution obtained by joint optimization. Indicates the initial bottom slip surface elevation. This represents the trend elevation of any two-dimensional point in the bottom slip surface region, and T represents the transpose operation; For each target point to be interpolated sparse Laplace matrix Each line in The row is constructed as follows: diagonal elements off-diagonal elements ,in, Indicates the first m The nth interpolation target point is related to its nth i The structure tensor guides the weights assigned to each neighboring point. k Indicates the number of neighboring points. Indicates the first i The global index of each neighboring point, except for diagonal elements and off-diagonal elements, is 0; The expression for the trend constraint term matrix C is as follows: ; in, This represents the penalty factor for the trend term, and I represents the identity matrix. K Represents the interpolation target point set Total points; S5. Based on the optimal bottom slip surface elevation vector and the surface of the digital elevation model, vertical volume units are constructed, and the closed volumes between them are estimated to obtain the volume of the landslide body. The implementation method is as follows: S501, Calculate the optimal bottom sliding surface elevation vector Grid interpolation is performed within the boundary to construct a continuous bottom surface; S502. Within the fitted bottom slip surface and the top surface of the collapse material source, construct vertical unit columns and use the column volume method to estimate the closed volume between the two surfaces. S503. Based on the estimation results, the top surface of the landslide source and the fitted bottom sliding surface are plotted together in a three-dimensional coordinate system, and the landslide boundary line is marked to show the three-dimensional closed structure of the entire landslide body, forming the landslide volume of the closed landslide body, and completing the volume estimation of the landslide volume.

[0033] In this embodiment, the volume of the landslide body is calculated as follows: ;; in, Indicates the volume of the landslide. Indicates the first Area of ​​each grid cell This represents the elevation data of the earth's surface. This indicates the fitted bottom sliding surface elevation. K Represents the interpolation target point set Total points m Indicates the number in the set of interpolation target points. m ∈{1,2,…,K}.

[0034] In summary, the present invention, through the above design, solves the problems of insufficient control of interpolation direction, imprecise boundary constraints, and inability to naturally intersect and form a closed volume in existing debris flow landslide source bottom sliding surface interpolation reconstruction methods.

Claims

1. A method for reconstructing the bottom surface and estimating the volume of debris flow landslide source, characterized in that, Includes the following steps: S1. Obtain the vector boundary and elevation data of the debris flow landslide source, and construct a basic dataset by unifying coordinates; S2. Based on the constructed basic dataset, the main trend constraint function in the sliding direction is fitted using the elevation data points in the debris flow landslide source buffer, and a trend fitting elevation vector is generated, where the elevation data points include boundary points. S3. Based on the structural tensor and the trend-fitted elevation vector, perform direction-guided interpolation propagation to obtain the initial bottom slip surface elevation; S3 includes the following steps: S301, Based on interpolation target point set At each target point to be interpolated, extract its spatial neighborhood. k neighborhood points And calculate the structure tensor It is used to characterize the main extension direction of the neighborhood point set. This represents the three-dimensional spatial coordinates of the neighborhood points of the m-th interpolation target point. i This represents the first interpolation target point. i Neighboring points, This represents the set of control points used for interpolation constraints. k Indicates the number of neighboring points; S302. The structure tensor constructed at each interpolation target point Perform eigenvalue decomposition to extract the structure tensor. Maximum eigenvalue corresponding feature vector , to feature vector The main propagation direction for the current interpolation target point: ； in, Represents the structure tensor matrix. Represents the principal eigenvector of unit length; S303, in the main direction vector Under propagation control, a direction-guided interpolation weighting function is constructed by combining Gaussian distance weights for each neighboring point. Assign weights : ； ； in, Indicates the first m The nth interpolation target point is related to its nth i The structure tensor guides the weights assigned to each neighboring point. Indicates the distance from the current interpolation target point to the th i A vector of neighboring points This represents the Gaussian kernel width control parameter. express With the principal direction vector The included angle, Indicates the first i Two-dimensional coordinates of a neighboring point Indicates the first m Two-dimensional coordinates of the interpolation target point K Represents the interpolation target point set Total points m ∈{1,2,…,K}; S304. Combining the weighted elevations of each neighboring point, calculate the elevation value of the interpolated target point to obtain the initial bottom slip surface elevation. ; S4. Construct a sparse optimization system that integrates structural tensor direction constraints and trend function control terms. Use the generalized minimum residual method to globally optimize the initial bottom slip surface elevation to obtain the optimal bottom slip surface elevation vector and complete the reconstruction of the bottom surface of the debris flow landslide source. S5. Based on the optimal bottom slip surface elevation vector and the surface of the digital elevation model, construct vertical volume units, estimate the closed volume between them, and obtain the volume of the landslide body.

2. The method for reconstructing the bottom surface and estimating the volume of debris flow landslide source according to claim 1, characterized in that, S1 includes the following steps: S101. Extract the effective elevation point set from the high-resolution elevation data of the study area, remove null values ​​and outliers, and form a point set. , This represents the set of valid points for elevation data. S102. Obtain the vector boundary of the debris flow landslide source and ensure that the boundary polygon... Closed, where the boundary polygon All vertices satisfy closure and coordinate consistency, and the boundary polygon The set of vertices is: ； in, Represents the set of boundary control points. Indicates the first The x-coordinates of the boundary points Indicates the first The ordinates of the boundary points Indicates the original topographic elevation at the boundary. Indicates the number of the boundary point, with a value range of 1. , M b Indicates the number of boundary points; S103. Constructing a point set for control and interpolation: in the boundary polygon Expand outward distance d The set of buffer control points extracted within the buffer and merged boundary control point set and buffer control point set The resulting set of control points for interpolation constraints : ； ； in, Indicates the boundary polygon Expand outward distance d The three-dimensional coordinates of the external constraint elevation data points extracted within the buffer. Indicates the number of the point within the buffer. Represents the control point set Numbering of all control points in the middle, Indicates the number of points in the buffer. Represents the control point set The number of all control points in the system Represents the boundary polygon and distance d The buffer zone formed by outward expansion Represents the three-dimensional coordinates of the control points; S104. Construct the bottom sliding surface interpolation mesh. And will interpolate the mesh from the bottom surface. The unknown elevation data points selected in the middle are set as the interpolation target point set. Interpolation target point set Interpolation mesh from the bottom surface The interpolation target point set after removing known control points: ； ； in, This represents the two-dimensional planar coordinates of a point in the bottom sliding interpolation grid, belonging to the real number field. , Represents the set of real numbers. Represents the boundary polygon The internal area, Indicates the first m The x and y coordinates of each interpolation target point correspond to the location of the unknown elevation in the bottom sliding surface interpolation grid. Indicates the first m The undetermined elevation of the interpolation target point K Represents the interpolation target point set Total points m Indicates the number in the set of interpolation target points. m ∈{1,2,…,K}.

3. The method for reconstructing the bottom surface and estimating the volume of debris flow landslide source according to claim 2, characterized in that, S2 includes the following steps: S201, Set the boundary control points The sample set used as the main trend constraint function; S202. Based on the sample set of the main trend constraint function, a second-order polynomial function is used to perform regression fitting on the elevation data points to form the main trend constraint function. : ； in, Represents any two-dimensional point in the bottom sliding surface region. The trend of elevation, This represents the two-dimensional coordinates of any position to be predicted within the bottom sliding surface interpolation grid. Represents the coefficients of the polynomial to be regressed; S203. Solve for the fitting coefficients using the least squares method. Make the main trend constraint function Capable of fitting continuous terrain morphology outside the boundary: ； in, j Indicates the number of the point within the buffer. Indicates the number of points in the buffer. Indicates the boundary polygon Expand outward distance d The three-dimensional coordinates of the external constraint elevation data points extracted within the buffer. Indicates at point Predicted elevation values ​​at the location; S204, Apply the main trend constraint function Applied to interpolation target point set The trend-fitted elevation vector is obtained. : ； in, Indicates the first m The x and y coordinates of each interpolation target point correspond to the location of the unknown elevation in the bottom sliding surface interpolation grid. m Represents the interpolation target point set The number in m ∈{1,2,…,K}, K Represents the interpolation target point set Total points.

4. The method for reconstructing the bottom surface and estimating the volume of debris flow landslide source according to claim 1, characterized in that, The structural tensor matrix The expression is as follows: ； in, i Indicates the first i 1 neighboring point; The expression for the initial bottom surface is as follows: ； in, This represents the initial interpolated elevation value of the bottom slip surface. This represents the predicted elevation value using the trend function. This indicates the trend fusion weight.

5. The method for reconstructing the bottom surface and estimating the volume of debris flow landslide source according to claim 1, characterized in that, S4 includes the following steps: S401. Construct a sparse Laplacian matrix weighted by the structure tensor. , used to describe the propagation constraints of elevation; S402. Construct the trend constraint term matrix C and the trend elevation vector. Apply the fitted value of the trend function as a soft constraint to each interpolation target point; S403, Based on Sparse Laplacian Matrix and trend elevation vector A joint optimization system is constructed that integrates structural tensor direction constraints and trend function control terms, and the final solution form is defined. The trend constraint term matrix C is used to construct the weight coefficient matrix of the constraint terms in the joint optimization system equation. S404, Based on Sparse Laplacian Matrix The joint optimization system is transformed into a sparse linear system of equations. Based on the initial bottom slip surface elevation, a generalized minimum residual method is used to perform global optimization fitting of the bottom slip surface, and the optimal bottom slip surface elevation vector is iteratively solved. .

6. The method for reconstructing the bottom surface and estimating the volume of debris flow landslide source according to claim 5, characterized in that, The expression for the joint optimization system is as follows: ； ； in, This represents the column vector of initial elevation predictions after interpolation propagation. This represents the column vector of the bottom slip surface elevation solution obtained by joint optimization. Indicates the initial bottom slip surface elevation. This represents the trend elevation of any two-dimensional point in the bottom slip surface region, and T represents the transpose operation; For each target point to be interpolated sparse Laplace matrix Each line in The row is constructed as follows: diagonal elements off-diagonal elements ,in, Indicates the first m The nth interpolation target point is related to its nth i The structure tensor guides the weights assigned to each neighboring point. k Indicates the number of neighboring points. Indicates the first i The global index of each neighboring point, except for diagonal elements and off-diagonal elements, is 0; The expression for the trend constraint term matrix C is as follows: ； in, This represents the penalty factor for the trend term, and I represents the identity matrix. K Represents the interpolation target point set Total points.

7. The method for reconstructing the bottom surface and estimating the volume of debris flow landslide source according to claim 1, characterized in that, S5 includes the following steps: S501, Calculate the optimal bottom sliding surface elevation vector Grid interpolation is performed within the boundary to construct a continuous bottom surface; S502. Within the fitted bottom slip surface and the top surface of the collapse material source, construct vertical unit columns and use the column volume method to estimate the closed volume between the two surfaces. S503. Based on the estimation results, the top surface of the landslide source and the fitted bottom sliding surface are plotted together in a three-dimensional coordinate system, and the landslide boundary line is marked to show the three-dimensional closed structure of the entire landslide body, forming the volume of the landslide body of the closed landslide body, and completing the volume estimation of the landslide body.

8. The method for reconstructing the bottom surface and estimating the volume of debris flow landslide source according to claim 7, characterized in that, The volume of the landslide body in S5 is calculated as follows: ； in, Indicates the volume of the landslide. Indicates the first Area of ​​each grid cell This represents the elevation data of the earth's surface. This indicates the fitted bottom sliding surface elevation. K Represents the interpolation target point set Total points m Indicates the number in the set of interpolation target points. m ∈{1,2,…,K}.

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