The Temporal and Spatial Analysis of Land Subsidence in Beijing Plain based on TPCA
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摘要: 时间主成分分析（Temporal Principal Component Analysis，TPCA）可用于地学领域中提取时空数据的时序特征和空间分布特征，北京平原区的地面沉降具有典型的时序和空间特征。本文在利用PS-InSAR技术获取的北京平原区2003年—2010年地面沉降数据的基础上，采用TPCA方法，分析了北京平原区地面沉降时空演化特征。经分析发现：（1） TPCA分析得到的第一主成分反应了地面沉降在该长时序阶段的空间分布特征。（2）第二主成分得分为正的空间点与可压缩层厚度在130m以上的区域在空间分布上有一致性和相关性。（3）在空间上，第一主成分为负值与第二主成分为正值的PS点，分布在年均沉降速率30mm/a以上的严重沉降区域。严重沉降区具有明显的南北沉降分类现象和季节性差异，具体表现为：北部沉降区在春夏季节的沉降量大于秋冬季节的；南部沉降区则与之相反。总之，基于时间主成分分析方法，可分析得到研究区的地面沉降时空演化规律，为城市安全监测提供数据支撑。Abstract: Objectives: Most of the characteristics of land subsidence are analyzed separately from the perspective of temporal or spatial, and the hidden information and possible laws in the data cannot be discovered simultaneously. Temporal Principal Component Analysis (TPCA) can be used to extract temporal and spatial characteristics of temporal-spatial data in the field of geosciences. The land subsidence in the Beijing Plain has typical temporal and spatial characteristics. Therefore, TPCA makes full use of the advantages of long-term coverage of land subsidence obtained by InSAR measurement. Methods: 1. Permanent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) technique provide a convenient method to measure land subsidence in sub-centimeter precision. 51 Envisat ASAR data acquired from 2003 to 2010 in the Beijing Plain were used to produce 50 interferograms and obtain time-series deformation with nonlinear model. The critical steps include preprocessing like master and auxiliary images registration and registration of control points; differential interference; extraction of PS(Permanent Scatterers); removal of atmospheric phase; unwrapping to obtain the final deformation. 2. Based on the land subsidence of about 100,000 points and 51-time series, construct the original data matrix X100000*51, calculate the correlation coefficient matrix, and use the TPCA method to analyze the temporal and spatial evolution characteristics of land subsidence in the Beijing Plain. The Eigenvector from TPCA is a time series, which represents the correlation between the PC spatial pattern and the subsidence. The principal component score is the spatial pattern obtained by TPCA decomposition, which represents different spatial characteristics, and further analyzes the characteristics of the new variable-principal component score. Results: It is found that:(1) The Eigenvalues determine the amount of information explained by each component. The information explained by the first three principal components (variance contribution rate) is 86.18%, 8.66%, and 2.37% respectively. (2) The eigenvector represents the degree of correlation between the principal component scores after linear combination and the original variables, and also represents the time trend of the principal component features. The eigenvector of PC1 remained stable around 0.15, indicating that the development trend of land subsidence remained consistent during this period. The overall variation range of the feature vectors of PC2 and PC3 is larger than that of PC1. The PC2 and PC3 can reveal some seasonal variation characteristics of land subsidence through further calculation. (3) The first principal component obtained by TPCA analysis represents the long-term development trend of the spatial distribution of land subsidence. (4) The area that the second principal component that is positive has a correlation in spatial distribution with the area of compressible layer thickness above 130m. (5) The PS points where the first principal component scores are negative and the second principal component scores are positive are distributed in the severe subsidence area above 30mm/a. There is an obvious classification of land subsidence and seasonal variation between north and south area in the severe subsidence area. Specifically, in the northern subsidence area, the amount of subsidence in spring and summer is larger than in autumn and winter, it is an opposite variation in the southern subsidence area. Conclusions: In general, the temporal and spatial variation of land subsidence could be studied for urban safety monitoring by TPCA. It also can identify the main characteristics of the space and the law of temporal and spatial evolution. Since TPCA is a linear combination, by finding the direction with the largest variance for projection, the variables obtained are just uncorrelated and not independent of each other. PCA only uses the second-order statistical information of the original data and ignores its high-order statistical information. Therefore, it is necessary to optimize by rotating principal components to find more physical meanings of principal components.
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