# Multi-Temporal InSAR Structural Damage Assessment: The London Crossrail Case Study
## 2 Dataset and Area of Interest  
Our dataset includes 72 CSK images acquired from April 2011 to December 2015, combined to produce time-series of cumulative deformation and ground based measurements of 14 buildings affected by tunneling induced subsidence. The ground data was obtained from the Underground Construction Information Management System (UCIMS), a web-based geotechnical data management system designed for the project [36].  
CSK is a constellation of 4 low Earth orbit satellites carrying an X-band SAR antenna (3.1 cm wavelength) enabling a better (3 m) resolution and sampling rate (up to 176.25 MHz) of ground displacements than longer wavelength systems (e.g., 6 cm for C-band, 24 cm for L-band). Each satellite has a repeat cycle of 16 days, but shorter repeats may be achieved using the constellation. Here, we used data acquired from the CSK background mission covering all the largest cities worldwide with a population bigger than one hundred thousand inhabitants with an average sampling rate of 16 days. The SAR image dataset is formed by a stack of CSK STRIPMAP-HIMAGE covering a 40 \(\times\) 40 km swath, at 3 m resolution in both azimuth (along track) and range (cross track) directions. Polarization of the electromagnetic waves is HH (horizontal transmit and receive). The incidence angle is \(\sim\)29 degrees across the swath.  
We analyzed a sub-area of the entire frame in single-look complex (SLC) format of 5 km \(\times\) 5 km in the azimuth and range directions, respectively (Figure 1). The analyzed area covers the central route section of the Crossrail project, which is currently the largest underground excavation project in Europe and involves the boring of 21 km of twin tunnel of 6.2 m diameter and up to 40 m deep, and the construction of 10 new stations under central London.  
The local geology of the region of London under consideration consists of layers (from top to bottom) of Terrace Deposits, London clay, the Lambeth Group (gravels, sands, silt, and clay), Thanet sands, and Chalk. Tunneling was primarily through the London clay and Lambeth Group layers, resulting in settlements with the typical characteristics of tunneling in soft ground. In the region two aquifers are present, with piezometric surface at approximately zero Ordnance Datum (OD) and between \(-\)40 m and \(-\)50 m OD, respectively [37].  
The tunneling was executed by soft-ground pressure-balance tunnel-boring machines between May 2012 and May 2015. Compensation grouting was adopted in several locations along the tunnel route and near the stations to minimize ground settlements. The 14 selected buildings are located directly above, or in close proximity to, the tunnel track (Figure 1), and therefore were potentially at risk of being damaged by the tunnel-induced settlement [37].  
To verify the accuracy of the MT-InSAR measurements, the satellite-based ground displacements of one transect transverse to the tunnel track were compared with the displacements measured by Precise Levelling Points (PLP). The PLPs were installed on the ground prior to the beginning of the excavation and could measures the difference in elevation between two or more points with high orders of accuracy (0.3-0.9 mm). In this work, we used precise levelling measurements acquired with daily frequency between May 2012 and August 2014, and therefore covering the passage of the tunnel boring machine in the area of interest. The analysis of the data confirmed the typical Gaussian shape of the settlement trough along the tunnel, combined with larger settlements near to the station excavations.  
Figure 1: Cumulative displacement map over London spanning April 2011–December 2015. Negative values indicate subsidence. Blue stars indicate the locations of the analysed buildings. (**a–d**) represent the locations of the non-linear time series analysis, which are shown beneath the satellite image (in mm).