基于震前-震后高精度地形点云数据提取三维地表同震位移场信息

doi:10.3969/j.issn.0253-4967.2025.01.011

摘要/Abstract

摘要：

地震破裂带附近同震位移和变形模式对于深入理解地震破裂过程、断层行为及活动断层与地形地貌关系等至关重要。文中提出一种迭代最近点(ICP)算法, 利用地震前后地形点云进行差分确定断层近场三维同震地表位移。在川西大凉山断裂带交际河断层上选取2期SfM地形点云叠加同震位移场模拟震前-震后点云, 测试ICP方法获取同震位移场的精度。该方法在网格边长>50m的条件下可准确恢复同震位移场的方向和幅度, 水平和垂直精度分别为20~10cm, 这与地形点云定位精度相当。随着点云密度和网格窗口尺寸减小, 该方法恢复同震位移场等的精度将降低。通过分析树木生长、房屋建设、河流侵蚀等地形变化对恢复位移场的潜在影响, 研究结果表明扩大网格尺寸可使震前-震后点云具有足够地形结构进行匹配, 以减小局部地形变化对恢复位移场的影响, 网格窗口尺寸是在具有足够地形结构的大尺度和具有更精细分辨率的小尺度之间的权衡。文中所述的ICP方法利用震前-震后高精度点云可获取地震破裂带附近精细的三维地表位移场, 为浅层断层滑动和破裂带变形提供了新的约束, 有助于研究地震破裂过程和断层生长过程。

关键词: 三维同震位移场, ICP算法, 地形点云, 地震破裂, 活动断层

Abstract:

After a major earthquake, in addition to determining the location and magnitude of the earthquake, the analysis of the coseismic displacement and deformation patterns near the seismic rupture zone is equally critical, which is crucial for an in-depth understanding of the seismic rupture process, fault behavior, and the relationship between active faults and topography. Although the geodetic techniques for observing the coseismic displacement field of the earth's surface at various spatial and temporal scales are developing rapidly, obtaining a detailed seismic rupture zone and displacement field remains challenging. Current techniques for obtaining these measurements, including Global Navigation Satellite Systems(GNSS), radar or optical remote sensing, and field observations, have their respective limitations regarding observation density, coverage area, measurement dimensions, and operational efficiency. Recently, the widespread adoption and application of high-precision and high-density topographic observation technologies(such as SfM and LiDAR)have enabled geomorphologists and geologists to capture various Earth surface features with unprecedented spatiotemporal resolution and detail. This has made it possible to map detailed three-dimensional displacement fields.

This paper introduces an Iterative Closest Point(ICP)algorithm that uses pre- and post-earthquake topographic point clouds to determine near-field three-dimensional coseismic surface displacements. The main purpose of developing this algorithm is to quickly provide data on the coseismic displacement field near the seismic rupture zone after a major earthquake, compensating for the deficiencies of existing geodetic measurements or field observations. To test the applicability and workflow of the ICP algorithm for obtaining topographic data through aerial photogrammetry in the Sichuan-Yunnan region, we selected two sets of SfM topographic point cloud data from the Jiaoji River fault on the Daliangshan fault zone. By superimposing the coseismic deformation field to simulate the pre-earthquake and post-earthquake topographic point cloud sets, we explored the accuracy of this method under different grid sizes and point cloud densities. This method can accurately recover the direction and magnitude of the coseismic displacement field under a grid size exceeding 50 meters, with horizontal and vertical accuracies of approximately 20cm and 10cm, respectively, comparable to the positioning accuracy of the topographic point clouds. As the point cloud density and grid window size decrease, the accuracy of this method in recovering co-seismic displacement fields declines.

By analyzing the potential impact of terrain changes such as tree growth, house construction, and river erosion on displacement field recovery, the results show that increasing the grid size allows pre- and post-earthquake point clouds to have sufficient terrain structure for matching, reducing the impact of local terrain changes on displacement field recovery. The grid window size is a trade-off between 1)a large scale with sufficient terrain structure and 2)a smaller scale with finer resolution. The ICP method, utilizing high-precision point clouds from before and after the earthquake, can obtain detailed three-dimensional surface displacement fields near earthquake rupture zones, providing new constraints for shallow fault slip and rupture zone deformation and aiding the study of seismic rupture processes and fault growth.

Key words: Three-Dimentional coseismic displacement, ICP algorithm, Terrain point cloud, seismic rupture, active fault

魏占玉, 何宏林, 邓亚婷, 席茜. 基于震前-震后高精度地形点云数据提取三维地表同震位移场信息[J]. 地震地质, 2025, 47(1): 167-188.

WEI Zhan-yu, HE Hong-lin, DENG Ya-ting, XI Xi. THREE-DIMENSIONAL SURFACE COSEISMIC DISPLACEMENTS FROM DIFFERENCING PRE- AND POST-EARTHQUAKE TERRAIN POINT CLOUDS[J]. SEISMOLOGY AND GEOLOGY, 2025, 47(1): 167-188.

图/表 16

表1 地面控制点信息表

Table1 Ground control point information

控制点ID	X/m	Y/m	Z/m	X_err/m	Y_err/m	Z_err/m
GCP1	281937.2	3043654.3	2417.41	0.11	0.05	0.14
GCP2	281511.2	3043984.3	2447.69	0.07	0.12	0.18
GCP3	281599.8	3043479.6	2463.05	0.10	0.11	0.22
GCP4	281074.5	3044292.1	2463.67	0.08	0.10	0.11
GCP5	281145.7	3044564.7	2442.65	0.04	0.12	0.14
GCP6	280745.4	3044789.5	2491.84	0.11	0.07	0.16
GCP7	280864.7	3044540.2	2492.15	0.12	0.04	0.10
GCP8	281154.8	3043974.3	2491.36	0.09	0.05	0.13
GCP9	281479.9	3043723.6	2469.53	0.07	0.15	0.20

图1 实验地形点云数据采集 a 交际河断裂及数据采集位置, 黑块标识数据采集位置; b 数据采集区及附近断层位置, 底图为Google Earth影像; c SfM点云生成的DEM地势图, 白框为实验数据范围, 黑点及编号指示地面控制点位置及编号

Fig. 1 Experimental terrain point cloud data collection.

图2 2期SfM点云的高程渲染图和比较差异分布图 a、b SfM点云的高程渲染图; c 2期SfM点云比较差异的分布图

Fig. 2 Elevation rendering diagram and comparative difference distribution diagram of SfM point clouds in two periods.

图3 同震水平位移场模拟 a 不同走向断层的同震水平位移场模拟; b 阶区断层的同震水平位移场模拟

Fig. 3 Simulation of coseismic horizontal displacement field.

图4 模拟同震位移场和震后点云 a 模拟的同震水平位移矢量图, 断层两盘左旋滑动各3m; b 模拟的同震垂直位移矢量图, 断层南西盘垂直抬升2m, 北东盘无垂直位移; c SfM地形点云叠加三维模拟同震位移场后的点云高程渲染图

Fig. 4 Simulated coseismic displacement field and post-seismic point cloud.

图5 迭代最近点(ICP)算法示意图

Fig. 5 Schematic diagram of the Closest Point of iteration(ICP)algorithm.

图6 三维刚体平移(T)和旋转(R)变换矩阵构成及坐标旋转示意图

Fig. 6 The transformation matrices for three-dimensional rigid body translation(T) and rotation(R), and the schematic diagram illustrating the coordinate rotation.

图7 基于震前-震后点云ICP算法提取同震位移矢量示意图

Fig. 7 Schematic diagram of co-seismic displacement vector extraction based on pre-earthquake-post-earthquake point cloud ICP algorithm.

图8 ICP算法提取同震位移矢量技术流程图

Fig. 8 Technical flow chart of ICP algorithm to extract coseismic displacements.

图9 网格中心模拟位移矢量 d - ⇀与恢复位移矢量 d ' ⇀比较示意图红色线代表模拟位移矢量, 浅红色为垂直和水平位移量; 蓝色线代表恢复位移矢量, 浅蓝色为垂直和水平位移量

Fig. 9 Comparison between simulated displacement d - ⇀ and recovered displacement d ' ⇀ in the center of grid.

图10 100m×100m网格条件下ICP提取同震位移场 a 同震垂直位移场; b 同震水平位移场

Fig. 10 ICP extraction of coseismic displacement field under 100m×100m grid.

图11 100m×100m网格恢复位移场的误差直方图

Fig. 11 Error histogram of the displacement field of 100m×100m grid restoration.

图12 原点云数据在50m、20m和10m网格窗口下恢复同震位移场图e和f中的黑框代表图14的范围

Fig. 12 The origin cloud data recovers the coseismic displacement field under the 50m, 20m and 10m grids.

图13 原点云数据在50m、20m和10m尺寸的网格窗口下恢复同震位移场的误差直方图

Fig. 13 Error histogram of coseismic displacement field of origin cloud data under 50m, 20m and 10m grids.

图14 在10m尺寸的网格窗口下恢复同震位移场的局部放大图图中空白区为新建民房区域, 恢复的位移矢量混乱

Fig. 14 Local magnification of the recovered coseismic displacement field under a 10m grid.

图15 基于密度约为2个/m2的点云在20m和10m尺寸的网格下恢复的水平位移场

Fig. 15 Horizontal displacement field recovered by point cloud density of ~2/m2 under a 20m and 10m grid.

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