A landslide susceptibility evaluation method based on deformation and posterior probability

Abstract

The application provides a landslide susceptibility evaluation method based on deformation and posterior probability, and relates to the technical field of geological disaster evaluation and remote sensing spatial information processing, and the method comprises the following steps: performing slope surface segmentation processing on digital elevation model data to obtain slope units; performing probability estimation processing on the slope units based on traditional static control factor data to obtain prior susceptibility probability; extracting surface deformation features of the slope units based on synthetic aperture radar interferometry data; performing updating processing on the surface deformation features and the prior susceptibility probability by using dynamic evidence and combining with a updating method of logistic transformation to obtain posterior susceptibility probability of the slope units; and performing result output processing on the posterior susceptibility probability by using a statistical evaluation method to obtain landslide susceptibility evaluation results. The application solves the problems that the existing landslide susceptibility evaluation method is difficult to effectively fuse dynamic deformation information, lacks data reliability consideration, and leads to insufficient identification ability of slope units with significant deformation activities.

Description

Technical Field

[0001] This invention relates to the field of geological hazard assessment and remote sensing spatial information processing technology, and in particular to a landslide susceptibility assessment method based on deformation and posterior probability. Background Technology

[0002] Landslides, due to their suddenness and destructive nature, pose a serious threat to public safety and critical lifeline infrastructure in mountainous areas. As human activities continue to expand into mountainous regions, landslide susceptibility assessments, which accurately predict the spatial distribution of landslides, are of paramount practical importance for geological disaster prevention and control.

[0003] Generally, traditional landslide susceptibility assessment methods are mainly based on static control factors such as topography, geology, and hydrology, and employ statistical or machine learning models for analysis. However, these conventional methods face two main limitations: First, static models struggle to capture the progressive failure mechanisms of slopes and their time-dependent characteristics, failing to reflect the dynamic changes during landslide evolution; second, they fail to fully utilize time-series InSAR surface deformation monitoring data provided by technologies such as Synthetic Aperture Radar Interferometry (InSAR), resulting in a significant discrepancy between the predicted static high-susceptibility areas and the actual active dangerous slope areas.

[0004] To incorporate dynamic deformation into the evaluation, existing techniques typically employ a feature-layer fusion strategy. This involves forcibly converting sparse and spatially unevenly distributed InSAR point observation velocities into continuous raster predictors using interpolation methods such as Kriging, and then feeding them along with static control factors as additional input variables into the classification model. However, this interpolation-based input-layer fusion method has significant drawbacks: First, mountainous terrain is complex, and InSAR observations are strongly affected by coherence; forcibly performing spatial interpolation on sparse and uneven point data easily introduces spatial artifacts and anomalous noise. Second, this approach implicitly assumes that deformation and static factors are of equal importance, failing to reflect the differences in the reliability of deformation signals in different regions, thus weakening the robustness of deformation signal representation. Finally, existing techniques lack a clear and interpretable probabilistic framework, failing to effectively reveal the interaction between static susceptibility backgrounds and dynamic slope activity. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a landslide susceptibility assessment method based on deformation and posterior probability. This method solves the problems of existing landslide susceptibility assessment methods, which struggle to effectively integrate dynamic deformation information, and directly interpolate sparse radar interferometric data as static feature inputs, which can easily introduce spatial artifacts and lack data reliability considerations, thus resulting in insufficient ability to identify slope units with significant deformation activity.

[0006] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a landslide susceptibility assessment method based on deformation and posterior probability, comprising: S1: The digital elevation model data is segmented into multiple slope units by using the method of extracting the boundaries of concave and convex terrain. S2: Based on traditional static control factor data, the slope unit is probabilistically estimated using a basic classification algorithm to obtain the prior susceptibility probability of the slope unit. S3: Based on synthetic aperture radar interferometry data, the surface deformation characteristics of slope units are extracted using a method that includes information on deformation rate and number of monitoring points along the radar line of sight, resulting in deformation intensity index, activity index and data density index. S4: Based on deformation intensity index, activity index, data density index and prior susceptibility probability, the posterior susceptibility probability of the slope unit is obtained by using dynamic evidence of constructing activity index and coverage weight and combining logistic transformation update method. S5: Use statistical evaluation methods to process the posterior susceptibility probability output to obtain the landslide susceptibility evaluation results and complete the landslide susceptibility evaluation.

[0007] The beneficial effects of this invention are as follows: This invention provides a landslide susceptibility assessment method based on deformation and posterior probability. At the slope unit scale, it uses a spatial aggregation method to extract deformation intensity, activity, and data density indices from synthetic aperture radar interferometry data to characterize surface deformation features. Compared to existing technologies that directly perform continuous interpolation on sparse points, this invention reduces the dependence on continuous spatial interpolation by aggregating InSAR deformation observation data at the slope unit scale. This helps reduce interpolation noise, spatial artifacts, and anomalous deformation diffusion caused by sparse and unevenly distributed observation points. Furthermore, it can distinguish between missing data and low-deformation states, improving the stability of posterior probability updates and the reliability of susceptibility assessment results.

[0008] This invention does not use deformation as a static feature of the input layer. Instead, it first uses a basic classification algorithm to calculate the prior susceptibility probability determined by static factors. Then, in the logit space (log-dominance space), it constructs dynamic evidence using deformation indices for posterior update processing. This mechanism clearly distinguishes between the "long-term static background" and "deformation activity during the observation period" of slope instability, and achieves their fusion through a probability domain update method based on the dominance ratio. This improves the interpretability of the landslide susceptibility assessment process and the reliability of the assessment results. This invention extracts data density indices and incorporates them into the construction of dynamic evidence, using data density as a reliability weight. This allows deformation information to effectively enhance susceptibility estimation in densely observed areas, while avoiding over-amplification of error signals in areas with insufficient observational constraints. This process results in a statistically higher area under the receiver operating characteristic (AUD) of the final landslide susceptibility assessment, and a larger proportion of known historical landslides are precisely concentrated in the extremely high and high susceptibility zones in the final output, greatly improving the ability to identify slopes in an active, hazardous state.

[0009] Further, S1 includes: Based on digital elevation model data, smoothing and curvature calculation algorithms are used to extract the boundaries of concave and convex terrains, and boundary merging and slope segmentation are performed to obtain closed polygons as multiple slope units.

[0010] By employing slope segmentation methods that include smoothing, curvature calculation, extraction of concave and convex terrain boundaries, and boundary merging, the resulting slope unit boundaries are coordinated with ridge lines, valley lines, and natural slope break lines. This approach can more completely preserve the geomorphic structure of a single slope than regular grids, reduce the bias caused by the fragmentation of the same slope or the mixing of different slopes in statistics, and provide a spatial basis for the aggregation of static control factors and deformation indices within a unified evaluation unit.

[0011] Further, S2 includes: Based on traditional static control factor data that includes topographic factors, geological factors, hydrological and human activity-related factors, and multi-year average rainfall factors, the random forest algorithm, which serves as the basic classification algorithm, is used for probability estimation to obtain the prior susceptibility probability of slope units.

[0012] By aggregating long-term stable control factors such as topography, geology, hydrology, human activities, and rainfall into slope units and using the random forest algorithm for prior probability estimation, it is possible to characterize the nonlinear relationships and interactions between multiple factors, reduce the limitations of a single statistical distribution assumption on the evaluation results, form a prior probability that reflects the long-term environmental susceptibility background of the slope, and provide a stable benchmark for subsequent updates of dynamic deformation evidence.

[0013] Further, S3 includes: Based on the line-of-sight deformation rate information in the synthetic aperture radar interferometry data, a specified percentile is obtained using the percentile statistical method and used as an index of deformation intensity. Based on the radar line-of-sight deformation rate and the number of monitoring points in the synthetic aperture radar interferometry data, a threshold determination algorithm is used to calculate the ratio of the number of monitoring points exceeding the velocity threshold to the total number of monitoring points in the slope unit, which serves as an activity indicator. Based on the number of monitoring points and slope unit area in the synthetic aperture radar interferometry data, the ratio of the number of effective monitoring points to the corresponding slope unit area is calculated using a method that includes spatial overlay statistics and ratio calculation, and is used as a data density index; among them, the deformation intensity index, activity index and data density index constitute the surface deformation characteristics of the slope unit.

[0014] By constructing deformation intensity, activity, and data density indices respectively, the magnitude of significant deformation within a slope unit, the spatial coverage of active deformation, and the sufficiency of observational data can be simultaneously characterized. Among these, using percentile statistics to characterize deformation intensity can reduce the impact of a small number of extreme outliers on the results, avoiding the problem that a single mean or maximum value cannot adequately address both robustness and the ability to identify high-value deformations.

[0015] Furthermore, the expression for the activity index is: ; in, Indicators of activity This represents the radar line-of-sight deformation rate obtained from inversion of synthetic aperture radar interferometry data. This indicates the speed threshold set based on whether the monitoring point is in an active state. This indicates that the absolute value of the velocity at the monitoring point is greater than or equal to the velocity threshold. This indicates the number of monitoring points that exceed the speed threshold. This indicates the total number of monitoring points within the slope unit.

[0016] By characterizing activity by the proportion of monitoring points exceeding the speed threshold to the total number of valid monitoring points, the index is normalized to a unified dimension of zero to one. This reduces the impact of differences in the absolute number of monitoring points in different slope units on the comparison results and distinguishes between local high deformation and large-scale active deformation, providing comparable spatial activity parameters for the construction of the activity index.

[0017] Furthermore, the expression for the data density index is: ; in, Indicates data density index, Indicates the number of valid monitoring points within the slope unit. This represents the area of ​​the slope unit calculated based on digital elevation model data.

[0018] By characterizing data density by the number of effective monitoring points per unit area, the InSAR observation coverage of different slope units can be quantitatively reflected, and a reliable basis for subsequent coverage weight calculation can be provided. This suppresses the dynamic update of sparsely observed slope units, thereby reducing the risk of over-amplifying local deformation signals due to insufficient data.

[0019] Further, S4 includes: Based on the deformation intensity index and the activity index, the activity index is obtained by using a normalization and weighted summation algorithm. Based on the data density index, the saturation function algorithm is used to perform constraint calculations to obtain the coverage weight; Based on the activity index and coverage weight, dynamic evidence is constructed using the index parameterization method to obtain the multiplicative advantage factor. Based on the prior susceptibility probability, the prior logarithmic advantage is obtained using the logistic transformation algorithm. The advantage space is updated based on the multiplicative advantage factor and the prior logarithmic advantage. Finally, the posterior susceptibility probability of the slope cell is obtained by processing it using the inverse logistic transformation function, which restricts it to a specific interval.

[0020] Deformation intensity and activity indices are normalized and weighted and fused, and dynamic evidence is constrained by saturation coverage weights based on data density. This allows the update magnitude of deformation evidence to be controlled by both activity level and observation reliability. By constructing a positive multiplicative dominance factor through exponential parameterization and updating it in the logarithmic dominance space, slope units with reliable active deformation evidence can be selectively enhanced while preserving the prior susceptibility background. Furthermore, the inverse logistic transformation is used to ensure that the output results are within the legal probability range of zero to one.

[0021] Furthermore, the expression for the posterior susceptibility probability of the slope unit is: ; ; ; in, This represents the posterior susceptibility probability of the slope element. This represents the prior susceptibility probability. This represents the overall update intensity coefficient set based on the background noise level of the study area. Indicates the activity index, Indicates the coverage weight. This represents the weighting coefficients set based on the relative contributions of the deformation components. Indicates the deformation strength index. This represents the normalization upper limit parameter set based on the specified percentile extracted from the distribution of effective deformation intensity index. Indicators of activity This represents the saturation coefficient set based on the density of observations. This represents a data density index. Attached Figure Description

[0022] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein: Figure 1 This is an exemplary flowchart illustrating a landslide susceptibility assessment method based on deformation and posterior probability, according to some embodiments of this specification. Figure 2 This is an exemplary schematic diagram illustrating the aggregation of InSAR monitoring points within a slope unit and the generation process of deformation intensity indicators, activity indicators, and data density indicators, according to some embodiments of this specification. Figure 3 This is an exemplary schematic diagram illustrating the calculation relationship between the prior landslide susceptibility probability, activity index, coverage weight, and posterior landslide susceptibility probability, according to some embodiments of this specification. Detailed Implementation

[0023] 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.

[0024] Example Figure 1 This is an exemplary flowchart illustrating a landslide susceptibility assessment method based on deformation and posterior probability, according to some embodiments of this specification. Figure 1 As shown, the process includes the following steps. In some embodiments, the process may be executed by a processor.

[0025] S1: The digital elevation model data is segmented by extracting the boundaries of concave and convex terrain to obtain multiple slope units.

[0026] Concave-convex terrain boundaries refer to spatial boundary data that reflects changes in landform undulation and abrupt topographic changes. For example, concave-convex terrain boundaries can include geographic coordinates and geometric contour information related to ridgelines, valley lines, and natural slope break lines. This data is used to spatially delineate relatively uniform surface areas.

[0027] In some embodiments, the processor can receive digital elevation model data as input, first smooth the digital elevation model data to eliminate local noise, then calculate the curvature characteristics of the land surface, identify the locations where the land surface morphology changes significantly based on the positive and negative changes in curvature and extract the corresponding feature lines, and finally merge and close these feature lines to obtain the concave and convex terrain boundary data.

[0028] Digital elevation model (DEM) data refers to a spatial set of elevation points used to digitally represent the undulating shape of a physical terrain. For example, DEM data may include the longitude, latitude, and corresponding surface elevation values ​​of regular grid points within a specific geographic area. This data provides fundamental three-dimensional spatial information support for geomorphological structure analysis and slope morphology extraction, and is stored in a specific format in a computer system for spatial analysis.

[0029] In some embodiments, the processor acquires digital elevation model (DEM) data covering the study area, performs cropping, coordinate system unification, resampling, and data quality checks on the DEM data to obtain DEM data that meets preset spatial resolution and spatial reference requirements, and performs slope cell division and terrain factor extraction based on the DEM data. The DEM data can be SRTM, ALOS, ASTER, or other publicly available or self-acquired DEM products.

[0030] A slope unit refers to a basic evaluation unit with relatively consistent morphology, spatially divided based on topographic and geomorphic features. For example, a slope unit may include a spatial region composed of closed polygons, whose boundaries closely match natural ridgelines and valley lines. This region can serve as an independent and complete geological or geomorphic entity, used to extract and statistically analyze various control factor data related to slope instability.

[0031] In some embodiments, the processor can acquire pre-extracted contour lines of the terrain boundary, perform topological checks and geometric editing on these lines using geographic information system spatial analysis tools, extend and intersect discontinuous boundaries, construct multiple spatially continuous and non-overlapping closed polygonal contours, and map these contours onto the geographic coordinate system of the study area to obtain multiple slope unit data. For example... Figure 2 The diagram shown is an exemplary schematic diagram illustrating the aggregation of InSAR monitoring points within a slope unit and the generation process of deformation intensity indicators, activity indicators, and data density indicators, according to some embodiments of this specification.

[0032] In some embodiments, the processor can extract the boundaries of concave and convex terrain based on digital elevation model data using smoothing and curvature calculation algorithms, perform boundary merging processing, and perform slope segmentation processing to obtain closed polygons as multiple slope units.

[0033] S2: Based on traditional static control factor data, the slope unit is probabilistically estimated using a basic classification algorithm to obtain the prior susceptibility probability of the slope unit.

[0034] Traditional static control factor data refers to a set of multi-source spatial features that are relatively stable over a long time scale and can reflect the long-term environmental susceptibility to landslides. For example, traditional static control factor data may include topographic factors, geological factors, hydrological and human activity-related factors, and regional rainfall factors.

[0035] In some embodiments, the processor can acquire basic geographic and geological data from multiple sources, and for each independent slope unit, use spatial overlay and regional statistical operations to extract the numerical or categorical attributes of each factor within the slope unit. For example, it can calculate the average slope of the pixels within the slope unit as the slope factor, or measure the spatial Euclidean distance from the centroid of the slope unit to the nearest fault zone as the distance factor from the fault, thereby summarizing the traditional static control factor data covering the entire study area.

[0036] Prior susceptibility probability refers to the numerical value of the likelihood of a slope becoming unstable, assessed solely based on long-term stable environmental conditions without considering real-time or near-real-time surface dynamics. For example, prior susceptibility probability may include a predicted value between 0 and 1 for each slope unit, which mainly characterizes the long-term tendency of surface landscape and geological background to landslide occurrence, reflecting the static susceptibility background.

[0037] In some embodiments, the processor can train a basic classification model containing multiple decision trees by acquiring historical sample data with landslide and non-landslide labels and corresponding traditional static control factor data as a training set. After the model training is completed, the traditional static control factor data of the target slope unit is input into each decision tree to obtain the single probability prediction value output by each decision tree. Finally, the prediction values ​​output by all decision trees are arithmetically averaged to obtain the prior susceptibility probability of the slope unit.

[0038] In some embodiments, the processor can perform probability estimation processing using the random forest algorithm as the basic classification algorithm based on traditional static control factor data that includes topographic factors, geological factors, hydrological and human activity-related factors, and multi-year average rainfall factors, to obtain the prior susceptibility probability of slope units.

[0039] In some embodiments, the expression for the prior susceptibility probability is: ; in, This represents the prior susceptibility probability of the slope element. This represents the traditional static control factor data of the slope unit as an input feature. This represents the total number of trees in the base classification model, which contains multiple decision trees. This total number is set based on the model training parameters. Indicates the first The decision tree calculates and outputs a single probability prediction value based on the traditional static control factor data.

[0040] S3: Based on synthetic aperture radar interferometry data, the surface deformation characteristics of slope units are extracted using a method that includes information on the deformation rate and the number of monitoring points along the radar line of sight, resulting in deformation intensity index, activity index, and data density index.

[0041] Synthetic Aperture Radar Interferometry (SAR) data refers to a dynamic monitoring dataset that reflects minute surface displacement characteristics, obtained by interferometric processing of multi-temporal radar satellite imagery. SAR interferometry data specifically refers to surface deformation monitoring data obtained by interferometric processing of multi-temporal radar satellite imagery. In some embodiments, the SAR interferometry data includes at least the spatial coordinates of effective InSAR observation points, the deformation rate along the radar line of sight, and corresponding data quality information. The number of effective InSAR observation points within a slope unit is obtained by spatially overlaying the effective InSAR observation points with the slope unit, while the slope unit area is obtained through spatial calculation using a geographic information system based on the slope unit's geometric boundaries.

[0042] In some embodiments, the processor acquires multiple radar satellite images covering the study area, combines them with digital elevation model data to remove terrain phase effects and perform atmospheric error correction; an interferometric network is constructed based on temporal and spatial baseline conditions, and after interferometric processing, phase unwrapping, and time-series inversion, the spatial coordinates, radar line-of-sight deformation rate, and corresponding data quality information of the effective InSAR observation points within the study area are obtained. Subsequently, the effective InSAR observation points are spatially overlaid with slope units, the number of effective InSAR observation points in each slope unit is counted, and the area of ​​the slope unit is calculated based on the geometric boundaries of the slope unit. The multiple radar satellite images can be Sentinel-1A images.

[0043] In some embodiments, the expression for the interferometric phase involved in acquiring the synthetic aperture radar interferometric measurement data is as follows: ; The expression for the radar line-of-sight displacement after removing the non-deformation term is: ; in, This indicates the interferometric phase obtained through radar satellite image interferometry. This indicates the radar wavelength obtained based on satellite sensor parameters. Indicates the displacement of the radar line of sight. This represents the terrain phase components calculated based on digital elevation model data. Indicates atmospheric phase components, Represents the phase component of the orbital error. Represents the residual noise term. This represents the deformable phase component after removing the non-deformation phase component.

[0044] In some embodiments, when acquiring the radar line-of-sight deformation rate information from the synthetic aperture radar interferometry data, the relevant observation equations and least-squares inversion expressions are as follows: ; ; in, Indicates the first The and the first Interference phase between time phases Indicates incremental displacement. Indicates the error term. This represents the incremental deformation vector obtained by inversion estimation using the least squares method, used to derive the radar line-of-sight deformation rate. Represents the design matrix. Represents the weight matrix. This represents the observation vector.

[0045] Surface deformation characteristics refer to a set of quantitative characteristic indicators that comprehensively characterize the surface deformation status and the distribution of observation data within a specific spatial region. For example, surface deformation characteristics may include deformation intensity indicators to characterize the dominant high-value deformation signals in the region, activity indicators to characterize the proportion of monitoring points in an active state in the region, and data density indicators to describe the spatial coverage density of radar observation data.

[0046] In some embodiments, the processor spatially overlays effective InSAR observation points with slope units, determines the slope unit to which each effective InSAR observation point belongs based on its spatial coordinates, and for each slope unit, statistically analyzes the radar line-of-sight deformation rate distribution of effective InSAR observation points within it, the number of observation points exceeding a preset deformation rate threshold, and the total number of effective InSAR observation points, and calculates the slope unit area based on its geometric boundaries. Based on this, deformation intensity, activity, and data density indices are calculated to form surface deformation characteristic data at the slope unit scale.

[0047] Deformation intensity indexes are statistical values ​​used to reflect a representative level of high deformation rate within a specific area. For example, a deformation intensity index may include a specific percentile of the radar line-of-sight velocity distribution across all valid radar monitoring points within a slope unit. This index aims to reduce the sensitivity of the overall average to a few extreme outliers while significantly highlighting significant deformation characteristics within the area.

[0048] In some embodiments, the processor can obtain the line-of-sight deformation rate values ​​corresponding to all synthetic aperture radar interferometry monitoring points inside the target slope unit, sort the absolute values ​​of these rate values ​​in ascending order, and then perform an index search in the sorted value sequence according to a preset percentile threshold ratio to extract the rate value at that specific percentile position, thereby obtaining the deformation intensity index data.

[0049] Activity indicators are numerical values ​​used to characterize the spatial activity of surface deformation within a specific area. For example, an activity indicator may include the ratio between the number of radar monitoring points within a slope unit whose deformation rate exceeds a preset threshold and the total number of all valid monitoring points within that slope unit. The value of this indicator is limited to between 0 and 1, and is used to distinguish whether the deformation is localized or widespread.

[0050] In some embodiments, the processor can acquire the deformation rate values ​​of each radar monitoring point within the slope unit, compare the absolute values ​​of these deformation rates with a pre-set determination velocity threshold, and count the number of active monitoring points whose absolute values ​​are greater than or equal to the velocity threshold. Then, using this number of active monitoring points as the numerator and the total number of all valid monitoring points acquired within the slope unit as the denominator, a division operation is performed to obtain the activity index data.

[0051] Data density metrics are parameters used to measure the sufficiency of spatially distributed dynamic surface observation data. For example, a data density metric may include the specific number of effective radar interferometry monitoring points per square kilometer within a slope unit. This data objectively reflects the spatial coverage and sufficiency of InSAR observations and serves as a proxy indicator for observation reliability, providing support for avoiding excessive amplification of errors due to insufficient observation constraints in subsequent processing.

[0052] In some embodiments, the processor can obtain the total number of valid radar interferometry monitoring points statistically derived for a specific slope unit, and simultaneously obtain the actual physical area value of the geometric polygon enclosed by the boundary of the slope unit in a spatial coordinate system. Then, by dividing the total number by the physical area value, a unit area conversion operation is performed to obtain the data density index data.

[0053] In some embodiments, the processor can use a percentile statistical method to obtain a specified percentile based on the line-of-sight deformation rate information in the synthetic aperture radar interferometry data, as a deformation intensity index; based on the line-of-sight deformation rate and the number of monitoring points in the synthetic aperture radar interferometry data, it can use a threshold determination algorithm to calculate the ratio of the number of monitoring points exceeding the velocity threshold to the total number of monitoring points in the slope unit, as an activity index; based on the number of monitoring points and the slope unit area in the synthetic aperture radar interferometry data, it can use a method including spatial superposition statistics and ratio calculation to calculate the ratio of the number of effective monitoring points in the synthetic aperture radar interferometry to the corresponding slope unit area, as a data density index.

[0054] In some embodiments, the expression for the activity index is: ; in, Indicators of activity This represents the radar line-of-sight deformation rate obtained from inversion of synthetic aperture radar interferometry data. This indicates the speed threshold set based on whether the monitoring point is in an active state. This indicates that the absolute value of the velocity at the monitoring point is greater than or equal to the velocity threshold. This indicates the number of monitoring points that exceed the speed threshold. This indicates the total number of monitoring points within the slope unit.

[0055] In some embodiments, the expression for the data density metric is: ; in, Indicates data density index, Indicates the number of valid monitoring points within the slope unit. This represents the area of ​​the slope unit calculated based on digital elevation model data.

[0056] S4: Based on deformation intensity index, activity index, data density index, and prior susceptibility probability, the posterior susceptibility probability of the slope unit is obtained by using dynamic evidence of constructing activity index and coverage weight and combining it with the logistic transformation update method.

[0057] The activity index is a comprehensive dynamic characteristic quantity obtained by standardizing and fusing multiple independent parameters that characterize the deformation amplitude and the range of deformation activity. For example, the activity index may include a deformation intensity parameter after upper limit scaling and normalization and an activity parameter after range truncation, combined with each other according to a specific weight ratio to form a dimensionless value, which is used to comprehensively assess the deformation state of a region.

[0058] In some embodiments, the processor can obtain the deformation intensity index and activity index of the slope unit. First, it performs upper limit division on the deformation intensity index using a preset regional upper limit extreme value, and then normalizes the result by truncating it within a specific interval using an extreme value function. Subsequently, the same extreme value function truncation process is performed on the activity index. Finally, the two normalized indices are multiplied by their corresponding weight allocation coefficients and added together to obtain the activity index data.

[0059] Dynamic evidence refers to a combination of multiplicative factors introduced as supplementary evidence during the updating of probabilistic models. These factors reflect the latest state of surface activity and are subject to reliability constraints. For example, dynamic evidence may include an exponential function result with a natural constant base, which is composed of an activity index characterizing the overall deformation intensity of the region, a data density constraint function characterizing the sufficiency of data observations, and a preset coefficient used to adjust the overall update intensity.

[0060] In some embodiments, the processor can obtain a calculated activity index and a coverage weight value generated based on a data density index, while introducing a system-preset overall update intensity adjustment constant. The processor multiplies the activity index, the coverage weight value, and the overall update intensity adjustment constant to obtain a composite index term. Then, it uses this composite index term as the independent variable of the natural exponential function to perform an exponentialization operation, thereby obtaining dynamic evidence data.

[0061] The posterior susceptibility probability refers to the final predicted value of slope instability obtained by overlaying the latest dynamic surface monitoring evidence on the basis of the static background assessment results. For example, the posterior susceptibility probability may include an updated value limited to the range of 0 to 1, which retains the long-term susceptibility tendency characterized by environmental control factors, while selectively enhancing the susceptibility probability of areas with detectable deformation activity characteristics.

[0062] In some embodiments, the processor can obtain the posterior logarithmic advantage value by adding the prior logarithmic advantage to the logarithmically transformed multiplicative advantage factor, and then use the negative of the posterior logarithmic advantage value as an exponent to perform nonlinear mapping processing in an inverse transformation function containing a natural constant. This mapping process re-compresses the value to a specific probability interval, thereby obtaining the posterior susceptibility probability data. For example... Figure 3 The diagram shown is an exemplary schematic diagram illustrating the calculation relationship between the prior landslide susceptibility probability, activity index, coverage weight, and posterior landslide susceptibility probability according to some embodiments of this specification.

[0063] In some embodiments, the processor can calculate the activity index based on the deformation intensity index and the activity index using a normalization and weighted summation algorithm; calculate the coverage weight based on the data density index using a saturation function algorithm; construct dynamic evidence based on the activity index and the coverage weight using an index parameterization method to obtain the multiplicative dominance factor; obtain the prior logarithmic dominance based on the prior susceptibility probability using a logistic transformation algorithm; perform an update process for dominance space calculation based on the multiplicative dominance factor and the prior logarithmic dominance; and process the data using an inverse logistic transformation function to obtain the posterior susceptibility probability of the slope cell restricted to a specific interval.

[0064] Multiplicative advantage factor refers to an adjustment parameter used in the logarithmic advantage space calculation system to amplify or reduce the initial advantage probability by a factor of several. For example, the multiplicative advantage factor may include a positive value determined by both surface activity characteristics and data observation density. This positive value, as dynamic evidence, is directly multiplied with the prior advantage in the probabilistic advantage expression form to amplify the advantage in areas with significant deformation.

[0065] In some embodiments, the processor can obtain the calculated composite activity index value and the data density coverage weight combined with saturation constraints. The processor multiplies the activity index value, the data density coverage weight, and a scaling parameter that controls the overall effect to obtain a composite variable. This composite variable is then input into the index calculation module for exponentiation to obtain the multiplicative dominance factor data.

[0066] Prior logarithmic advantage refers to the mathematical transformation of traditional probability predictions between 0 and 1 into a linear metric distributed across the entire real number domain. For example, prior logarithmic advantage could be the natural logarithm of the ratio between the prior probability of a landslide occurring in a given slope unit and the probability of it not occurring. This value primarily serves to provide an unbounded value space to facilitate the incorporation of external updated evidence.

[0067] In some embodiments, the processor can obtain the prior susceptibility probability value output by the basic classification model, first subtract the prior susceptibility probability value from 1 to obtain the non-occurrence probability, then perform a division operation with the prior susceptibility probability value as the numerator and the non-occurrence probability as the denominator to calculate the prior advantage ratio, and finally take the natural logarithm of the prior advantage to obtain the prior log advantage.

[0068] In some embodiments, the expression for the posterior susceptibility probability of a slope element is: ; ; ; in, This represents the posterior susceptibility probability of the slope element. This represents the prior susceptibility probability. This represents the overall update intensity coefficient set based on the background noise level of the study area. Indicates the activity index, Indicates the coverage weight. This represents the weighting coefficients set based on the relative contributions of the deformation components. Indicates the deformation strength index. This represents the normalization upper limit parameter set based on the specified percentile extracted from the distribution of effective deformation intensity index. Indicators of activity This represents the saturation coefficient set based on the density of observations. This represents a data density index.

[0069] S5: Use statistical evaluation methods to process the posterior susceptibility probability output to obtain the landslide susceptibility evaluation results and complete the landslide susceptibility evaluation.

[0070] Landslide susceptibility assessment results refer to the final spatial distribution information of landslide susceptibility output for the target study area after integrating static geological and geomorphological trends and dynamic evidence of surface deformation. For example, landslide susceptibility assessment results may include posterior probability values ​​assigned to each slope unit in the study area, as well as distribution maps of multiple susceptibility levels such as extremely low, low, medium, high, and extremely high, based on these probability values.

[0071] In some embodiments, the processor can obtain the set of calculated posterior susceptibility probability values ​​for all slope units and set a series of probability interval thresholds based on statistical distribution patterns. The processor then determines the range of threshold intervals into which the posterior susceptibility probability value of each slope unit falls, assigns it a corresponding susceptibility level label, and finally merges and summarizes the information of these slope units with risk level labels to obtain the landslide susceptibility assessment result.

[0072] In some embodiments, this method involves setting multiple constant parameters, the specific values ​​of which are determined or set according to the following: (1) the velocity threshold The setting is based on determining whether the monitoring point is in a state of significant deformation activity. The deformation rate threshold (Thr) can be set to 5–20 mm / yr, preferably 8–15 mm / yr. In this embodiment, the velocity threshold... The weighting coefficient is set to 10 mm / yr. (2) The weighting coefficients are set based on the relative contributions of the normalized deformation intensity and the normalized activity ratio. It can be set to 0.5–0.9, preferably 0.6–0.8. In this embodiment, the weighting coefficient... The value is set to 0.7. (3) The saturation coefficient This is used to determine the coverage weight based on the data density of effective InSAR monitoring points within a slope unit, such that the coverage weight increases with the increase of effective monitoring point density, and in ( When the value is greater than or equal to 1, the coverage weight is limited to 1. The saturation coefficient (K) can be set to 0.04 to 0.125 km² / effective InSAR monitoring point, preferably 0.067 to 0.10 km² / effective InSAR monitoring point. In this embodiment, the saturation coefficient (K) is set to 0.08 km² / effective InSAR monitoring point, and the corresponding saturation data density is 12.5 effective InSAR monitoring points / km². (4) The overall update intensity coefficient Its setting is based on controlling the overall correction magnitude of dynamic evidence to the prior logarithmic advantage, the posterior probability update strength coefficient ( The value can be set to 0.3–1.2, preferably 0.5–1.0. In this embodiment, the overall update intensity coefficient... Set to 0.7. (5) The normalized upper limit of the deformation intensity ( The effective deformation intensity index within the study area can be used as a basis. The statistical distribution of ) is determined, and the effective deformation intensity index () is preferably selected. The 95th to 99.5th percentiles, more preferably the 97th to 99th percentiles, of the value. In this embodiment, The effective deformation strength index extracted from all slope units within the study area is set as follows: The above parameters are the 98th percentile of the numerical distribution. These parameters can be adjusted based on the deformation amplitude of the study area, background noise level, InSAR monitoring point coverage density, and model validation results.

Claims

1. A landslide susceptibility assessment method based on deformation and posterior probability, characterized in that, include: S1: The digital elevation model data is segmented by extracting the boundaries of concave and convex terrain to obtain multiple slope units; S2: Based on traditional static control factor data, the slope unit is probabilistically estimated using a basic classification algorithm to obtain the prior susceptibility probability of the slope unit. S3: Based on synthetic aperture radar interferometry data, the surface deformation characteristics of slope units are extracted using a method that includes information on deformation rate and number of monitoring points along the radar line of sight, resulting in deformation intensity index, activity index and data density index. S4: Based on deformation intensity index, activity index, data density index and prior susceptibility probability, the posterior susceptibility probability of the slope unit is obtained by using dynamic evidence of constructing activity index and coverage weight and combining logistic transformation update method. S5: Use statistical evaluation methods to process the posterior susceptibility probability output to obtain the landslide susceptibility evaluation results and complete the landslide susceptibility evaluation.

2. The landslide susceptibility assessment method based on deformation and posterior probability according to claim 1, characterized in that, S1 includes: Based on digital elevation model data, smoothing and curvature calculation algorithms are used to extract the boundaries of concave and convex terrains, and boundary merging and slope segmentation are performed to obtain closed polygons as multiple slope units.

3. The landslide susceptibility assessment method based on deformation and posterior probability according to claim 1, characterized in that, S2 includes: Based on traditional static control factor data that includes topographic factors, geological factors, hydrological and human activity-related factors, and multi-year average rainfall factors, the random forest algorithm, which serves as the basic classification algorithm, is used for probability estimation to obtain the prior susceptibility probability of slope units.

4. The landslide susceptibility assessment method based on deformation and posterior probability according to claim 1, characterized in that, S3 includes: Based on the line-of-sight deformation rate information in the synthetic aperture radar interferometry data, a specified percentile is obtained using the percentile statistical method and used as an index of deformation intensity. Based on the radar line-of-sight deformation rate and the number of monitoring points in the synthetic aperture radar interferometry data, a threshold determination algorithm is used to calculate the ratio of the number of monitoring points exceeding the velocity threshold to the total number of monitoring points in the slope unit, which serves as an activity indicator. Based on the number of monitoring points and slope unit area in the synthetic aperture radar interferometry data, the ratio of the number of effective monitoring points to the corresponding slope unit area is calculated using a method that includes spatial overlay statistics and ratio calculation, and is used as a data density index; among them, the deformation intensity index, activity index and data density index constitute the surface deformation characteristics of the slope unit.

5. The landslide susceptibility assessment method based on deformation and posterior probability according to claim 4, characterized in that, The expression for the activity index is: ； in, Indicators of activity This represents the radar line-of-sight deformation rate obtained from inversion of synthetic aperture radar interferometry data. This indicates the speed threshold set based on whether the monitoring point is in an active state. This indicates that the absolute value of the velocity at the monitoring point is greater than or equal to the velocity threshold. This indicates the number of monitoring points that exceed the speed threshold. This indicates the total number of monitoring points within the slope unit.

6. The landslide susceptibility assessment method based on deformation and posterior probability according to claim 4, characterized in that, The expression for the data density index is: ； in, Indicates data density index, Indicates the number of valid monitoring points within the slope unit. This represents the area of ​​the slope unit calculated based on digital elevation model data.

7. The landslide susceptibility assessment method based on deformation and posterior probability according to claim 1, characterized in that, S4 includes: Based on the deformation intensity index and the activity index, the activity index is obtained by using a normalization and weighted summation algorithm. Based on the data density index, the saturation function algorithm is used to perform constraint calculations to obtain the coverage weight; Based on the activity index and coverage weight, dynamic evidence is constructed using the index parameterization method to obtain the multiplicative advantage factor. Based on the prior susceptibility probability, the prior logarithmic advantage is obtained using the logistic transformation algorithm. The advantage space is updated based on the multiplicative advantage factor and the prior logarithmic advantage. Finally, the posterior susceptibility probability of the slope cell is obtained by processing it using the inverse logistic transformation function, which restricts it to a specific interval.

8. The landslide susceptibility assessment method based on deformation and posterior probability according to claim 7, characterized in that, The expression for the posterior susceptibility probability of the slope element is: ； ； ； in, This represents the posterior susceptibility probability of the slope element. This represents the prior susceptibility probability. This represents the overall update intensity coefficient set based on the background noise level of the study area. Indicates the activity index, Indicates the coverage weight. This represents the weighting coefficients set based on the relative contributions of the deformation components. Indicates the deformation strength index. This represents the normalization upper limit parameter set based on the specified percentile extracted from the distribution of effective deformation intensity index. Indicators of activity This represents the saturation coefficient set based on the density of observations. This represents a data density index.

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