Beijing, as the capital of China, suffers severe subsidence caused by groundwater withdrawal. In this paper, the SBAS-InSAR technique was used to detect surface deformations in the Beijing plain. 47 scenes Envisat ASAR images obtained during June 2003 to August 2010, and 24 Radarsat-2 images obtained during November 2010 to December 2013 were employed to retrieve vertical deformation characteristic over this area. The deformation magnitude, evolution process and spatial distribution of representative targets that occurred during 11 years were retrieved. The vertical surface displacement rates during two periods were validated via leveling observations, which have an RMSE =1.15mm/a, which indicates that the two types of subsidence matched very well. The interferometric results revealed that the subsidence during the two periods show similar special distributions and have an uneven spatial-temporal trend. The scope and deformation rates of funnels continuously increased with from 2003 to 2013. Meanwhile, multiple expressways and urban ring roads spanned the subsidence funnel with sharp deformation rate, and showed different subsidence properties along their paths. Additionally, the spatial and temporal correlation analyses between the deformation measurements and the dynamic variation of groundwater pumping was also performed to explore the response relationship.

High-rise buildings in the modern urban setting may have a considerable impact on land subsidence. The process of urbanization in Beijing has been found to be in direct relationship with the land subsidence. The permanent scatterers interferometric aperture radar (PSInSAR) technology is becoming a conventional tool for land subsidence monitoring. Synthetic aperture radar (SAR) tomography, as an extension of PSInSAR technology, allows a full 3D imaging, and is useful to reconstruct 3D urban building maps. In this study, a SAR tomography method “scale-down by L1 norm minimization, model selection, and estimation reconstruction” (SL1MMER) was applied to 33 TerraSAR-X images to retrieve building height. The object-oriented classification method based on the support vector machine was applied on the World View 2 image to extract geometry of building footprints and to aggregate SL1MMER derived building heights for each building. The building footprints and building heights were used to calculate the volume of buildings. The Stanford method for persistent scatterers, a PSInSAR methodology, was used to obtain land subsidence rates. The correlation coefficient between the building volumes and land subsidence showed no positive relationship for buildings that were below a certain volume. However, at local scale, with the increase of the building volumes, the correlation increased. The larger the volume of buildings, the stronger the relationship became. Once the volume of buildings became larger than 3.00 × 10⁵ m³, the impact of building volume on land subsidence remained stable.

Land subsidence is a major issue in the Beijing Plain in China, caused by the construction of new buildings and infrastructure combined with groundwater extraction. This study employs a multi-level two-dimensional wavelet decomposition to decompose land subsidence into high- and low-frequency components, and Moran’s I index to analyze the spatial distribution of land subsidence and its main influencing factors. By comparing the spatial distributions of the high- and low-frequency components, we estimate the correlation between land subsidence and influencing factors at different scales. Utilizing a combination of wavelet decomposition and Moran’s I analysis, our study establishes a clear spatial correlation between continuously varying factors such as groundwater and clay layer thickness, and the low-frequency components of land subsidence, allowing for a focused analysis of the relationship between surface building density and the high-frequency components of land subsidence. Quantitatively, the study identifies a significant correlation at specific granularities, particularly at 480 m and 960 m, underscoring the nuanced interaction between urban development and land subsidence patterns. These insights into the spatial distribution of land subsidence and its contributing factors can inform the development of effective strategies to address this issue.

Identifying Persistent Scatterers (PSs) is one of the key processing steps of the Persistent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) technique. The number, density, and reliability of identified PSs directly affect the monitoring accuracy of land subsidence, especially in higher density urban environments. As a result of the side-looking viewing geometry of SAR, the layover effect poses a major challenge to the PS identification. This research proposes joint modeling of the PS-InSAR technique and RELAX algorithm for SAR tomography (PS-InSAR+RELAX) to detect single and double scatterers and to improve the identification and reliability of PSs. It has been demonstrated that RELAX improves separation of the scatterers when compared to two other spectral analysis methods for SAR tomography, Beam-Forming (BF) and Singular Value Decomposition (SVD). RELAX exhibits the least noise when the number of baseline changes from 15 to 30, and it can separate the scatterers at a lower Normal-Slant-Range (NSR) height than the two other methods. As RELAX can better identify, separate, and then filter out layover scatterers, the number and density of PSs identified by PS-InSAR+RELAX is reduced and visually simplified, suggesting that the method can effectively reduce the influence of the layover effect on the PS identification. Also, the PSs identified by PS-InSAR+RELAX are more coherent than those identified by the traditional PS-InSAR technique. The proposed technique has been applied to Sentinel-1A data acquired from 2014 to 2016, to monitor land subsidence in the city of Beijing, China. When evaluated against the leveling measurements, PS-InSAR+RELAX performs better than the traditional PS-InSAR technique, with the correlation coefficients (r) of r = 0.98 and r = 0.95, respectively.

Land subsidence is one of the main geological disasters in the Beijing Plain. Accurate and quantitative monitoring of the evolution of land subsidence will help scientifically guide the prevention and control of land subsidence. We use PS-InSAR technology and TerraSAR 3m resolution images as our data source to study the temporal and spatial evolution characteristics of Beijing’s land subsidence from 2012 to 2015. The research indicates that, from a spatial perspective, the land subsidence presents a funnel shape, the central area of the settlement funnel is maintained at 112.5km², and the total land subsidence area remains basically unchanged. From the temporal point of view, the central area of the ground subsidence funnel subsides at a rate of 110mm/y, the ground subsidence rate in other areas decreases as it far away from the settlement center.

This paper considers option pricing under a regime-switching model. The switching process takes two different modes, and the underlying stock price evolves in accordance with the two modes dictated by a continuous-time, 2-state Markov chain. At a given instance, the price follows either a model of geometric Brownian motion or mean-reversion model on its market mode. We build stochastic approximation algorithms for model calibration. Convergence and rate of convergence are provided. Option market data are used to predict future market mode.