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Shanghai is a modern metropolis characterized by high urban density and anthropogenic ground motions. Although traditional deformation monitoring methods, such as GPS and spirit leveling, are reliable to millimeter accuracy, the sparse point subsidence information makes understanding large areas difficult. Multiple temporal space-borne synthetic aperture radar interferometry is a powerful high-accuracy (sub-millimeter) remote sensing tool for monitoring slow ground deformation for a large area with a high point density. In this paper, the Interferometric Point Target Time Series Analysis method is used to extract ground subsidence rates in Shanghai based on 31 C-Band and 35 X-Band synthetic aperture radar (SAR) images obtained by Envisat and COSMO SkyMed (CSK) satellites from 2007 to 2010. A significant subsidence funnel that was detected is located in the junction place between the Yangpu and the Hongkou Districts. A t-test is formulated to judge the agreements between the subsidence results obtained by SAR and by spirit leveling. In addition, four profile lines crossing the subsidence funnel area are chosen for a comparison of ground subsidence rates, which were obtained by the two different band SAR images, and show a good agreement.

Shanghai is one of the largest cities in China, with a population of more than 23,000,000. It is located to the northeast of the Yangtze River Delta in eastern China, which is fairly flat, at an average elevation of less than 4 m. Ground subsidence monitoring in Shanghai began in the 1920s. In the period from the 1920s to the 1960s, a large average accumulated subsidence of up to 1.69 m was detected in the central area of Shanghai, which was mainly caused by excessive groundwater withdrawal [

The main approach used to overcome the above-mentioned limitations is the Interferometric synthetic aperture radar (InSAR) time series analysis,

Here, MT-InSAR is performed by IPTA, which is a PSI and/or SBAS technique that has been demonstrated to be able to analyze the differential interferometric phase both spatially and temporally,

The so-called HCP indicates that the resolution cell is dominated by only one scatterer that is smaller than the resolution pixel and discriminates with the distributed target associated with the speckle behavior [

Given

With the assumption that the Line of Sight (LOS) deformation is linear, the two-dimensional linear phase regression model in terms of the ^{m}_{⊥} and _{noise}

To accurately obtain the relative height correction and the relative linear deformation, the individual phase component included in the phase noise should be separated. The baseline correction is conducted only with the point targets where the deformation rate is stable (smaller than 2 mm/yr), then, a least square method is used to fit with all the point targets. Then, the atmospheric path delay component and the non-linear deformation phase should be separated with the precondition that the phase additive noise is relatively small and without any unwrapping problems. However, as the atmospheric distortion and the non-linear deformation are correlated in space to a certain extent, it is impossible to separate the two components completely. As our experiment area is located in the center of Shanghai, we consider a scale of non-linear deformation larger than 500 m to not be in our interest; that is, when the non-linear deformation’s scale is larger than 500 m, we assign it to the atmospheric phase. The atmospheric distortion is removed by spatial filtering. Then, the two-dimensional phase regression analysis is conducted again for calculating further height corrections and linear deformation rate differences. The above procedures are taken in an iterative way until the improvement on the height corrections and linear deformation rate differences are small enough. More detailed data processing procedures are given in the user guide of the GAMMA software [

In this paper, 31 scenes of C-band ascending Envisat ASAR images from February 2007 to May 2010 and 35 scenes of X-band ascending CSK SAR images from December 2008 to November 2010 were used. The baseline distribution of interferograms is displayed in

As this paper is aimed to detect the deformation trend within the downtown area of Shanghai and test the agreements, two similar subset images of approximately 11 km × 10 km are selected within both ASAR and CSK SAR acquisitions, the location of which is displayed based on the averaged ASAR intensity image, see

According to the methodology in Section 2, GAMMA software is used to make the IPTA data processing in our experiments. The same IPTA procedures are implemented for both the ASAR and the CSK SAR acquisitions, except for some parameters, which differ in different bands of SAR images. For example, the range and azimuth multiple look values are different (ASAR: 1 × 5; CSK: 1 × 1). As the estimated deformation rate is relative to the reference point, the reference point is selected within the same stable area both in the ASAR and the CSK SAR images, which is displayed in

With the data processing of the MT-InSAR, there are 56,934 ASAR coherent point targets reserved from 74,464 candidates, while 502,150 CSK coherent point targets are reserved from 699,461 candidates. With the maintained point targets, the LOS mean deformation velocity is obtained and transformed to the vertical direction (divided by cos

To assess the accuracy of the ground subsidence rates obtained, standard deviations (DSD) of the ground subsidence rates of the point targets are displayed in

To determine whether the ground subsidence rate estimates are unbiased, a comparison of PSI deformation estimates, from ASAR and CSK, with spirit leveling measurements is implemented. In our chosen experimental area (rectangular box in

To further compare the subsidence rates obtained by MT-InSAR and leveling statistically, a t-test is formulated, which is defined as follows:

The null hypothesis is

The alternative hypothesis is

The statistic is
_{i}_{i}_{i}

Assuming _{i}_{i}_{di} denotes the mean of _{i}_{di} according to _{0}, while
_{i}

According to _{i}

For ASAR,

For CSK,

In our experiment, the total numbers of the sampling data are 152 and 148, respectively. Given the significance level _{α/2}(152) = _{α/2}(148) = 2.33; thus both t statistics are located within the acceptance interval. Therefore, we accept the null hypothesis, which means there is no significant difference between the MT-InSAR deformation estimates and the leveling measurements. Thus, the subsidence estimates obtained by MT-InSAR are unbiased and reliable.

In the above section, the validation comparison of the mean subsidence rates with the spirit leveling measurements shows that both the ASAR and the CSK results are acceptable statistically. From

The root mean square error (RMSE) of the differences of the subsidence rates between the two sensors along the four chosen profiles is listed in

As the spatial resolutions of the two sensors are different, ASAR is approximately 20 m × 5 m and CSK is approximately 2.5 m × 1.3 m, the spatial density of point targets is calculated in our MT-InSAR for comparison. For ASAR, this value is 500 point/km^{2}, while for CSK it is 4,500 point/km^{2}. This means that the high-resolution X-band CSK images offer a much higher density of point targets in the urban area. In addition to its short revisiting time period (8 days for CSK), CSK SAR can provide more details about the spatial and temporal distribution of the ground subsidence phenomena.

In this paper, the mean ground subsidence rates have been extracted using two different bands of SAR acquisitions, C-band ASAR and X-band CSK SAR. Both of them show a significant subsidence funnel located in the junction place of the Yangpu and the Hongkou Districts.

To ensure that the deformation rates by MT-InSAR are valid, a comparison of the ground subsidence rates of coherent point targets with the leveling measurements is implemented. Most of the differences between them are less than 3 mm/yr. A double tail t-test statistic is formulated, which demonstrates, with the significance level

However, the MT-InSAR of X-band CSK has a much higher point target density at the urban area. In addition to its shorter revisit period, X-band CSK SAR has a stronger ability to detect non-uniform ground subsidence both in space and time at the urban area.

This research is supported by the China National Science Foundation (No. 41074019). The Envisat ASAR data are supported by the European Space Agency Cat-1 project (CIP. 7351). Thanks goes to the Eastdown Company for providing the COSMO SAR data.

Flowchart of Interferometric Point Target Analysis (IPTA) main procedures.

Temporal and perpendicular baseline distribution of interferograms. The red circle denotes the master image while the blue ones denote the slave images.

Location of Shanghai. The study area is specified by the red square, the background is the averaged ASAR intensity image.

Linear deformation rates of point targets overlaid on the average amplitude SAR image.

Histogram of standard deviation of mean subsidence rates estimated.

Comparison of subsidence rates between Interferometric synthetic aperture radar (InSAR) and spirit leveling on bench marks.

Comparison of subsidence rates along the four chosen profiles. (

Root mean square error (RMSE) of the subsidence differences based on the four chosen profile lines.

RMSE (mm/yr) | 3.15 | 2.49 | 2.79 | 2.74 |