Method for evaluating risk of road damage caused by earthquake landslide under different earthquake motions

By combining Bayesian probability method and machine learning model, a multi-factor impact model for the occurrence of earthquake landslides was established, which solved the problem of low accuracy and inability to quickly evaluate road damage after earthquake disasters, and achieved rapid development under different earthquake conditions Accurate assessment to support efficient disaster rescue.

CN119475981APending Publication Date: 2025-02-18NAT INST OF NATURAL HAZARDS MINISTRY OF EMERGENCY MANAGEMENT OF CHINA
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Patent Information

Application Number
CN202411510915.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-28
Publication Date
2025-02-18

AI Technical Summary

Technical Problem

The existing road damage situation and pass capacity assessment methods after earthquake disasters have problems such as the accuracy of the image resolution and the inability to be carried out quickly and accurately, and the risk of earthquake landslides on roads cannot be quickly and accurately evaluated.

Method used

The Bayesian probability method combined with machine learning model is used to establish a multi-factor impact model for the occurrence of seismic landslides. Through the analysis of historical co-seismic landslide data and the peak acceleration of different earthquakes, a distribution map of road damage risk under different earthquake scenarios is generated. .

Benefits of technology

It realizes rapid and accurate assessment under different earthquake conditions, improves the accuracy of earthquake landslide prediction and the efficiency of post-disaster road risk assessment, and supports efficient disaster rescue and recovery work.

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Abstract

The invention relates to a method for evaluating the risk of road damage caused by seismic landslide under different seismic motions, and the method comprises the steps: building a probability multi-factor influence model of seismic landslide occurrence through employing a Bayesian probability method and a machine learning model, and building a sample set according to the historical co-seismic landslide data in a region, taking the sample set as the input of a seismic landslide occurrence probability multi-factor influence model, expanding and applying the seismic landslide occurrence probability multi-factor influence model to a seismic landslide region, taking different seismic oscillation peak accelerations as seismic landslide trigger factors, and calculating the seismic landslide occurrence true probabilities under the different seismic oscillation peak accelerations; and obtaining seismic landslide area road data, and generating a risk level distribution diagram of road damage caused by landslide through spatial analysis by combining the seismic landslide area road data with the seismic landslide occurrence true probabilities under different seismic oscillation peak accelerations. According to the invention, rapid and accurate post-earthquake landslide road damage risk assessment is realized.
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Description

Technical Field

[0001] The invention relates to the field of earthquake research, and in particular to a method for assessing the hazard of earthquake landslide damage to a highway under different ground motions. Background Art

[0002] Earthquake landslides are the most serious secondary disasters caused by earthquakes. After an earthquake landslide occurs, it will cause road damage, affect transportation, increase the difficulty of post-earthquake rescue, and aggravate the impact of the disaster. In order to improve the efficiency of pre-earthquake defense and post-earthquake command and rescue work, it is necessary to determine the road disaster risk level in advance.

[0003] At present, the research on road damage and traffic capacity after earthquake disasters can be divided into two categories: the first category is to establish coefficients related to road damage, or parameters of its damage risk, and then establish a remote sensing assessment model for the degree of road damage in the disaster area based on mathematical statistical models. The second category is based on post-earthquake remote sensing images. With the development of remote sensing satellites, common remote sensing extraction and quantitative assessment methods for road earthquake damage information can be divided into three categories: visual interpretation, vector overlay and change detection.

[0004] The visual interpretation method is to extract road damage through manual visual interpretation, through interpretation signs and distribution characteristics of geological disasters, combined with the basic urban information data of the study area. The change detection method is to extract damaged road sections by combining remote sensing images before and after the disaster, combined with change detection methods such as ENVI (The Environment for Visualizing Images). Change detection methods generally include pixel-level, feature-level and target-level detection methods. The vector superposition method is also based on high-resolution optical images after the earthquake. It often uses object-oriented methods to extract road information, compares the intact road vector database before the earthquake, and then combines visual interpretation to extract the distribution of earthquake-damaged roads and evaluate the damage. The above methods for obtaining road damage in the disaster area are basically carried out after the earthquake. The data comes from the on-site survey of emergency rescue personnel in the disaster area, and the observation results are intuitive and reliable. However, it is usually limited by the damage of the road, cannot be carried out quickly, and there is a greater risk, low information integrity, and a long time. At the same time, due to the limitation of image resolution, medium and low-resolution images cannot accurately reflect the ground conditions. After the earthquake, although some landslides did not occur, they are extremely unstable and there is a possibility of landslides at any time. Visual interpretation does not provide a detailed picture of road damage, which creates obstacles for quickly obtaining disaster information.

[0005] Therefore, there is an urgent need for a rapid and high-precision method for assessing the hazard of road damage caused by earthquake landslides to meet emergency needs after disasters and provide strong support for efficient disaster relief. Summary of the invention

[0006] In order to solve the problems that the accuracy of existing methods for assessing road damage and traffic capacity after an earthquake disaster is affected by image resolution and cannot be carried out quickly, the present invention provides a method for assessing the hazard of highway damage caused by earthquake landslides under different seismic motions. Combined with the probability model of earthquake landslide occurrence, the method directly gives the distribution of road damage hazard under different seismic accelerations after the earthquake, thereby realizing rapid and accurate assessment of the hazard of road damage caused by landslides after the earthquake.

[0007] The present invention provides a method for assessing the risk of earthquake landslide damage to a highway under different ground motions, the method comprising: Step 1: Use the Bayesian probability method and machine learning model to establish a probability multi-factor influence model for earthquake landslides. Create a sample set based on historical co-seismic landslide data in the region and use the sample set as the input of the probability multi-factor influence model for earthquake landslides. Step 2: Extend the probability multi-factor influencing model of earthquake landslides to earthquake landslide areas, take different peak seismic accelerations as earthquake landslide triggering factors, and calculate the true probability of earthquake landslides under different peak seismic accelerations; Step 3: Obtain highway data in earthquake-landslide areas; Step 4: Using the highway data in the earthquake-landslide area and the actual probability of earthquake landslides under different peak seismic accelerations, a distribution map of the hazard level of road damage caused by landslides is generated through spatial analysis.

[0008] Furthermore, the step 1 specifically includes: Step 1.1: Obtain historical coseismic landslide data in the earthquake landslide area. The landslide is represented by surface elements, and the elevation, slope, slope aspect, terrain moisture index, peak ground acceleration, distance from the fault, lithology and annual precipitation are used as landslide influencing factors; Step 1.2: Based on the logistic regression model, a multi-factor influencing model of the probability of earthquake landslide occurrence was constructed; Step 1.3: Select the area with peak seismic acceleration ≥ 0.09g in the earthquake landslide area, collect points at ≥ 1000 points per square kilometer, obtain training sample points, and use the GIS spatial data extraction function to extract the landslide type and factor values ​​corresponding to the sample points as the input of the multi-factor influencing model of the probability of earthquake landslide occurrence.

[0009] Furthermore, the probability multi-factor influencing model of earthquake landslide occurrence described in step 1.2 is shown in formula (1): Z = β 0 +β 1 χ 1 +β 2 χ 2 +β 3 χ 3 …βi χ i (1); Furthermore, Z = β 0 +β 1* Elevation + β 2* Slope + β 3* Slope Aspect+β 4* Topographic wetness index + β 5* Peak ground acceleration + β 6* Distance from fault + β 7* Lithology and annual precipitation + lithology; Among them, Z represents the linear weight value after variable superposition; χ i Represents each impact factor, β i are the logistic regression coefficients.

[0010] Furthermore, the actual probability of earthquake landslide in step 2 is as shown in formula (2): P = 1 / (1 + e -z )(2); Among them, P represents the probability of earthquake landslide occurrence, which ranges from [0, 1].

[0011] Furthermore, the step 2 specifically includes: According to formulas (1) and (2), the peak acceleration of earthquake motion in formula (1) is replaced by the earthquake motion of different scenarios, that is, the probability of earthquake landslide occurrence at 10 different peak accelerations of earthquake motion, namely 0.1g, 0.2g, 0.3g, 0.4g, 0.5g, 0.6g, 7g, 0.8g, 0.9g and 1.0g, is calculated respectively; The probability of earthquake landslide occurrence refers to the percentage of landslide area within a unit window.

[0012] Furthermore, steps 3 to 4 specifically include: The actual probability of earthquake landslide under different peak seismic accelerations is used to generate an earthquake landslide probability prediction map; According to the probability of earthquake landslides, the earthquake landslide area is divided into multiple levels of dangerous probability intervals; The lithology data in the earthquake landslide area are classified according to the stratigraphic age, and the collected data are preprocessed, including data cleaning, format conversion and coordinate unification, to ensure the accuracy and consistency of the data. All data are unified in the coordinate system of WGS84, the range and size of the data are consistent, and all data layers are converted into raster layers; Using buffer zone analysis, assuming that the road width is 30m, it is superimposed and clipped with the earthquake landslide probability prediction map to generate a road damage prediction map caused by earthquake landslides.

[0013] Furthermore, the parameters of the raster layer include: a) The file format is tif, and the grid resolution is not less than 30*30m; a) For landslide data, the landslide area should be assigned a value of 1 and the non-landslide area should be assigned a value of 0; b) For vector point data, such as rainfall data at a meteorological station, spatial interpolation is used to obtain raster data; c) Prepare distance data from the epicenter, distance data from the earthquake fault and distance data from the water system, using Euclidean distance; d) The seismic motion data are spatially interpolated to obtain the grid data of continuous intensity distribution in the study area.

[0014] Through the above technical solution, the beneficial effects of the present invention are: 1 The present invention provides an earthquake landslide assessment method based on the combination of Bayesian probability method and machine learning model, which can comprehensively consider the influence of probability multi-factors and improve the accuracy of earthquake landslide prediction. Combined with the modeling of regional historical co-seismic landslide data, the accurate calculation of the probability of earthquake landslide occurrence is improved, especially in complex earthquake environments. By introducing different seismic peak accelerations as trigger factors, the landslide hazard distribution around the road under different seismic scenarios is given. Using spatial analysis technology, a risk distribution map of landslide damage to the highway is generated, and a rapid assessment of landslide hazard and highway damage is achieved. This method can be widely used in post-earthquake road risk assessment, improve emergency response efficiency, and assist post-disaster rescue and recovery work.

[0015] 2 The present invention combines the Bayesian probability method with the machine learning model, which can effectively integrate historical earthquake landslide data and probabilistic multi-factor influencing factors, and constructs a probabilistic multi-factor influencing model of earthquake landslide occurrence through logistic regression, ensuring that the model has good flexibility under different seismic conditions. This method is not only applicable to a variety of seismic peak acceleration conditions, but also can be adaptively adjusted according to the historical landslide data of specific areas, thereby improving the universality of the model and the reliability of prediction. Through the integrated analysis of seismic peak acceleration and other multidimensional data such as terrain, lithology, slope, etc., a landslide probability prediction map is generated, and further refined into multi-level hazard probability intervals to achieve accurate division of landslide area risks. At the same time, using high-resolution raster data (such as 30-meter resolution) combined with buffer analysis technology, a prediction map of road damage caused by landslides can be quickly generated, providing more timely and accurate decision support for post-earthquake emergency response. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a step diagram of a method for assessing the hazard of earthquake landslide damage to a highway under different ground motions of the present invention; Figure 2It is a schematic diagram of selecting landslide points and non-landslide points based on landslide surface elements in a method for assessing the hazard of a highway damaged by earthquake landslide under different earthquake motions of the present invention; Figure 3 This is a method for assessing the risk of earthquake landslide damage to roads under different ground motions. It is a probability distribution diagram of landslide occurrence under different ground motion peak accelerations. Figure 4 It is a road landslide hazard classification diagram in the earthquake landslide damage highway hazard assessment method under different ground motions; Figure 5 It is a probability classification diagram of the hazard of roads and their surrounding environment in the method of evaluating the hazard of highways damaged by earthquake landslides under different ground motions. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution in the embodiment of the present invention will be clearly described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] Example 1 like Figures 1 to 5 As shown, an embodiment of the present invention provides a method for assessing the hazard of earthquake landslide damage to a highway under different earthquake motions, the method comprising the following steps: Step 1: using a Bayesian probability method and a machine learning model to establish a probability multi-factor influence model for earthquake landslide occurrence, establishing a sample set based on historical co-seismic landslide data in the region, and using the sample set as an input to the probability multi-factor influence model for earthquake landslide occurrence; Step 2: Extend the probability multi-factor influencing model of earthquake landslides to earthquake landslide areas, take different peak seismic accelerations as earthquake landslide triggering factors, and calculate the true probability of earthquake landslides under different peak seismic accelerations; Step 3: Obtain highway data in earthquake-landslide areas; Step 4: Using the highway data in the earthquake-landslide area and the actual probability of earthquake landslides under different peak seismic accelerations, a distribution map of the hazard level of road damage caused by landslides is generated through spatial analysis.

[0019] The step 1 specifically includes: Step 1.1: Obtain historical coseismic landslide data in the earthquake landslide area. The landslide is represented by surface elements, and the elevation, slope, slope aspect, terrain moisture index, peak ground acceleration, distance from the fault, lithology and annual precipitation are used as landslide influencing factors; Step 1.2: Based on the logistic regression model, a multi-factor influencing model of the probability of earthquake landslide occurrence was constructed; Step 1.3: Select the area with peak seismic acceleration ≥ 0.09g in the earthquake landslide area, collect points at ≥ 1000 points per square kilometer, obtain training sample points, and use the GIS spatial data extraction function to extract the landslide type and factor values ​​corresponding to the sample points as the input of the multi-factor influencing model of the probability of earthquake landslide occurrence.

[0020] The probability multi-factor influencing model of earthquake landslide occurrence described in step 1.2 is shown in formula (1): Z = β 0 +β 1 χ 1 +β 2 χ 2 +β 3 χ 3 …β i χ i (1); Specifically, Z = β 0 +β 1* Elevation + β 2* Slope + β 3* Slope Aspect+β 4* Topographic wetness index + β 5* Peak ground acceleration + β 6* Distance from fault + β 7* Lithology and annual precipitation + lithology; Among them, Z represents the linear weight value after variable superposition; χ i Represents each impact factor, β i are the logistic regression coefficients.

[0021] The actual probability of earthquake landslide in step 2 is shown in formula (2): P = 1 / (1 + e -z )(2); Among them, P represents the probability of earthquake landslide occurrence, which ranges from [0, 1].

[0022] The step 2 specifically includes: According to formulas (1) and (2), the peak acceleration of earthquake motion in formula (1) is replaced with the earthquake motion of different scenarios, and the probability of earthquake landslide occurrence at 10 different peak accelerations of earthquake motion are calculated respectively: 0.1g, 0.2g, 0.3g, 0.4g, 0.5g, 0.6g, 7g, 0.8g, 0.9g and 1.0g; The probability of earthquake landslide occurrence refers to the percentage of landslide area within a unit window.

[0023] The steps 3-4 specifically include: The actual probability of earthquake landslide under different peak seismic accelerations is used to generate an earthquake landslide probability prediction map; According to the probability of earthquake landslides, the earthquake landslide area is divided into multiple levels of dangerous probability intervals; The lithology data in the earthquake landslide area are classified according to the stratigraphic age, and the collected data are preprocessed, including data cleaning, format conversion and coordinate unification, to ensure the accuracy and consistency of the data. All data are unified in the coordinate system of WGS84, the range and size of the data are consistent, and all data layers are converted into raster layers; Using buffer zone analysis, assuming that the road width is 30m, it is superimposed and clipped with the earthquake landslide probability prediction map to generate a road damage prediction map caused by earthquake landslides.

[0024] The parameters of the raster layer include: a) The file format is tif, and the grid resolution is not less than 30*30m; a) For landslide data, the landslide area should be assigned a value of 1 and the non-landslide area should be assigned a value of 0; b) For vector point data, such as rainfall data at a meteorological station, spatial interpolation is used to obtain raster data; c) Prepare distance data from the epicenter, distance data from the earthquake fault and distance data from the water system, using Euclidean distance; d) Earthquake intensity data, perform spatial interpolation to obtain raster data of continuous intensity distribution in the study area.

[0025] In order to prove the advantages of the method of the present invention, the following is described in conjunction with the figure: In this embodiment, the lithological data contained in the study area are divided into the following according to the stratigraphic age: Quaternary (Q), Neogene (N), Paleogene (P), Cretaceous (K), Jurassic (J), Triassic (T), Permian (P), Carboniferous (C), Devonian (D), Silurian (S), Ordovician (O), Cambrian (Є), Precambrian (Pre-Є) and other intrusive rocks, and can also be combined in age according to regional lithological characteristics.

[0026] The Bayesian probability idea is used to select samples, such as Figure 2 As shown in the figure, the sample points are randomly selected (uniformly) in the entire study area. The sample points that fall within the landslide surface element are landslide sample points, and the sample points that fall outside the landslide surface are non-landslide sample points. 0 and 1 are usually used to represent negative samples and positive samples. This ensures that the proportion of samples is basically consistent with the proportion of landslide and non-landslide areas in the study area.

[0027] Areas with peak seismic acceleration ≥ 0.09g in earthquake landslide areas were selected, and sampling was carried out at a rate of ≥ 1000 points per square kilometer (to ensure the stability of the calculation results of probabilistic hazard assessment). In the study area, 13,656,000 training sample points were finally obtained.

[0028] According to the spatial distribution of sample points, the values ​​of landslide impact factor data corresponding to the sample points are extracted. The environmental impact factors are selected for the extracted data, including: factor collinearity check and significance test. If there are strong collinearity or serious collinearity environmental impact factors, delete or merge related variables. If the factor is significant, retain the factor.

[0029] Convert the processed samples into a format suitable for model input. The requirements are as follows: a) Matrix format, which organizes feature data into a matrix form, with each row representing a sample and each column representing a feature; b) Text format: organize the feature data into text txt format, where each row represents a sample and each column represents a feature.

[0030] The training sample data are input into the probability multi-factor influencing model of earthquake landslide occurrence to obtain the model evaluation results.

[0031] like Figure 3 As shown in the figure, according to the coefficients of each factor of the prediction model, by superimposing each influencing factor layer, the distribution of the landslide probability index of the prediction model can be obtained. That is, according to formulas (1) and (2), the peak acceleration of the earthquake motion in formula (1) is replaced by the earthquake motion of different scenarios, that is, the probability of earthquake landslide occurrence at 10 different peak accelerations of earthquake motion of 0.1g, 0.2g, 0.3g, 0.4g, 0.5g, 0.6g, 7g, 0.8g, 0.9g and 1.0g is calculated respectively; the probability of earthquake landslide occurrence refers to the percentage of landslide area in the unit window.

[0032] like Figure 4 and 5 As shown in the figure, the earthquake landslide probability hazard index defines the area with probability value < 0.01% as the extremely low earthquake landslide hazard area, the area with probability value 0.01% ≤ < 0.1% as the low hazard area, the area with probability value 0.1% ≤ < 1% as the medium hazard area, the area with probability value 1% ≤ < 10% as the high hazard area, and the area with probability value ≥ 10% as the extremely high hazard area.

[0033] Collect road vector data in the study area, apply buffer analysis, assume that the road width is 30m, and overlay and clip it with the landslide probability prediction map, such as Figure 5 As shown, they are classified according to five risk probability intervals.

[0034] a) Extremely low risk area: The possibility of landslides around the road is extremely low and the road is basically in a stable state; b) Low-risk area: The possibility of landslides around the road is low, but landslides may still occur under special circumstances; c) Medium-risk area: The possibility of landslides around the road is medium, and the impact of triggering factors such as earthquakes needs to be considered; d) High-risk area: The possibility of landslides around the road is high. Landslides are prone to occur under earthquakes or other triggering factors; e) Extremely high risk area: The area around the road where landslides are most likely to occur. Under the influence of earthquakes or other triggering factors, the probability of landslides is very high.

[0035] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, any equivalent changes or modifications made according to the structures, features and principles described in the patent scope of the present invention should be included in the scope of the patent application of the present invention.

Claims

1. A method for assessing the risk of earthquake landslide damage to a highway under different ground motions, characterized in that: The method comprises: Step 1: Use the Bayesian probability method and machine learning model to establish a probability multi-factor influence model for earthquake landslides. Create a sample set based on historical co-seismic landslide data in the region and use the sample set as the input of the probability multi-factor influence model for earthquake landslides. Step 2: Extend the probability multi-factor influencing model of earthquake landslides to earthquake landslide areas, take different peak seismic accelerations as earthquake landslide triggering factors, and calculate the true probability of earthquake landslides under different peak seismic accelerations; Step 3: Obtain highway data in earthquake-landslide areas; Step 4: Using the highway data in the earthquake-landslide area and the actual probability of earthquake landslides under different peak seismic accelerations, a distribution map of the hazard level of road damage caused by landslides is generated through spatial analysis.

2. The method for assessing the risk of earthquake landslide damage to a highway under different ground motions according to claim 1, characterized in that: The step 1 specifically includes: Step 1.1: Obtain historical coseismic landslide data in the earthquake landslide area. The landslide is represented by surface elements, and the elevation, slope, slope aspect, terrain moisture index, peak ground acceleration, distance from the fault, lithology and annual precipitation are used as landslide influencing factors; Step 1.2: Based on the logistic regression model, a multi-factor influencing model of the probability of earthquake landslide occurrence was constructed; Step 1.3: Select the area with peak seismic acceleration ≥ 0.09g in the earthquake landslide area, collect points at ≥ 1000 points per square kilometer, obtain training sample points, and use the GIS spatial data extraction function to extract the landslide type and factor values ​​corresponding to the sample points as the input of the multi-factor influencing model of the probability of earthquake landslide occurrence.

3. The method for assessing the risk of earthquake landslide damage to a highway under different ground motions according to claim 2, characterized in that: The probability multi-factor influencing model of earthquake landslide occurrence described in step 1.2 is shown in formula (1): Z=β0+β1χ1+β2χ2+β3χ3…β i x i (1); Among them, Z represents the linear weight value after variable superposition; χ i Represents each impact factor, β i is the logistic regression coefficient, χ i These include elevation, slope, aspect, terrain moisture index, peak ground acceleration, distance from the fault, lithology, and annual precipitation.

4. The method for assessing the risk of earthquake landslide damage to a highway under different ground motions according to claim 3, characterized in that: The actual probability of earthquake landslide in step 2 is shown in formula (2): P=1 / (1+e -z )(2); Among them, P represents the probability of earthquake landslide occurrence, which ranges from [0, 1].

5. The method for assessing the risk of earthquake landslide damage to highway under different ground motions according to claim 4, characterized in that: The step 2 specifically includes: According to formulas (1) and (2), the probability of landslide occurrence under 10 different peak accelerations of earthquake motion, namely 0.1g, 0.2g, 0.3g, 0.4g, 0.5g, 0.6g, 7g, 0.8g, 0.9g and 1.0g, is calculated respectively. The probability of earthquake landslide occurrence refers to the percentage of landslide area within a unit window.

6. The method for assessing the risk of earthquake landslide damage to a highway under different ground motions according to claim 1, characterized in that: The steps 3-4 specifically include: The actual probability of earthquake landslide under different peak seismic accelerations is used to generate an earthquake landslide probability prediction map; According to the probability of earthquake landslides, the earthquake landslide area is divided into multiple levels of dangerous probability intervals; The lithology data in the earthquake landslide area are classified according to the stratigraphic age, and the collected data are preprocessed, including data cleaning, format conversion and coordinate unification, to ensure the accuracy and consistency of the data. All data are unified in the coordinate system of WGS84, the range and size of the data are consistent, and all data layers are converted into raster layers; Using buffer zone analysis, assuming that the road width is 30m, it is superimposed and clipped with the earthquake landslide probability prediction map to generate a road damage prediction map caused by earthquake landslides.

7. The method for assessing the risk of earthquake landslide damage to a highway under different ground motions according to claim 6, characterized in that: The parameters of the raster layer include: a) The file format is tif, and the grid resolution is not less than 30*30m; a) For landslide data, the landslide area should be assigned a value of 1 and the non-landslide area should be assigned a value of 0; b) For vector point data, such as rainfall data at a meteorological station, spatial interpolation is used to obtain raster data; c) Prepare distance data from the epicenter, distance data from the earthquake fault and distance data from the water system, using Euclidean distance; d) The seismic motion data are spatially interpolated to obtain the grid data of continuous intensity distribution in the study area.

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