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Existing studies have shown that satellite synthetic aperture radar (SAR) interferometry has two apparent drawbacks, i.e., temporal decorrelation and atmospheric contamination, in the application of deformation mapping. It is however possible to improve deformation analysis by tracking some natural or man-made objects with steady radar reflectivity, i.e., permanent scatterers (PS), in the frame of time series of SAR images acquired over the same area. For detecting land subsidence in Shanghai, China, this paper presents an attempt to explore an approach of PS-neighborhood networking SAR interferometry. With use of 26 ERS-1/2 SAR images acquired 1992 through 2002 over Shanghai, the analysis of subsiding process in time and space is performed on the basis of a strong network which is formed by connecting neighboring PSs according to a distance threshold. The linear and nonlinear subsidence, atmospheric effects as well as topographic errors can be separated effectively in this way. The subsidence velocity field in 10 years over Shanghai is also derived. It was found that the annual subsidence rates in the study area range from -2.1 to -0.6 cm/yr, and the averaged subsidence rate reaches -1.1 cm/yr.

As the largest metropolitan in China, Shanghai is directly close to the sea and Huangpu River. Built on coastal sand and clay that lie 70 meters below the ground surface, this city has been suffering from land subsidence for many years due to overuse of groundwater and rapid construction of skyscrapers [

Monitoring of land subsidence in Shanghai is apparently crucial for predicting potential geological hazards and designing compensation strategies. Over the past decades, the subsidence data has been collected on a regular basis by the conventional methods such as precise leveling and GPS [

To mitigate the aforementioned negative effects, Ferretti

This paper is organized as follows. This part is followed by a brief description of data preprocessing and PS-network formation. After this, we present the methodologies of data modeling and parameter estimating. The testing results are then shown and discussed. Conclusions are given in the final section.

Unlike the conventional DInSAR only dealing with a single interferogram, the PS-networking SAR interferometry utilizes the multiple interferograms to isolate deformation information from atmospheric and topographic effects.

Given

To guarantee the quality of all the interferograms, we select the optimal master image by maximizing the joint correlation (JC) of all the images with [^{m}^{k, m}

Since the accurate co-registration of SAR imagery is a key prerequisite for any change detection, all the SAR images have to be co-registered into the same space with sub-pixel accuracy [

In terms of PS detection, existing study shows that the statistical properties of phase data at any time-coherent pixel can be analyzed by the time series of SAR amplitude data [_{A}_{a}_{a}

After selection of all the PSs, we connect the neighboring PSs to form a network which is similar to a conventional geodetic network like leveling or GPS network. It will be seen that such network can provide a framework for modeling and improving parameter estimation and adjustment. Unlike a triangular irregular network (TIN) as applied by Kampes & Adam [_{r}_{a}_{0} is the distance threshold (e.g. 1 km) used to form a PS-PS connection which is thereafter called an arc.

It should be pointed out that 0

Prior to modeling and estimating on the FCN, several procedures must be followed for data reduction. These include computation of the initial interferograms and the differential interferograms. Each initial interferogram can be derived by a pixel-wise conjugate multiplication (equivalent to phase differencing) between the master SAR image and the co-registered slave SAR image.

Let us assume that the available DEM has errors and the land subsidence is of linear and nonlinear accumulation in time. The differential interferometric phase at an arbitrary pixel with coordinates (_{i}_{i}_{i})

In reality, any regionalized variable follows a fundamental geographic principal; that is the samples that are spatially closer together tend to be more alike than those that are farther apart. The idea of neighborhood differencing is therefore often employed to compensate some spatially correlated errors or offsets. For example, the differential global positioning system (DGPS) may reduce some systematic errors caused by atmospheric delay and orbital uncertainty so that the baseline components (coordinate increments) between two adjacent stations can be determined more accurately. Likewise, the differencing operation along each arc in PS network as shown in _{p}_{l}_{p}

It should be pointed out that the atmospheric effect and the nonlinear subsidence can most likely be cancelled out by neighborhood differencing embodied in

The theoretical investigation by Ferretti

Although the objective function is highly nonlinear and the phase datasets are measured in a wrapped version, the two unknowns Δε and Δ

With

Taking the adjustment of a linear-subsidence network as an example, we present some mathematical expressions as follows. A prototype observation equation for an arc is expressed as
_{l}_{p}_{pl}_{pl}. K

Furthermore, let the weighting matrix be

The above procedures can also be applied in a similar way onto the elevation-inconsistency network to estimate the elevation errors at all the true PSs. The Kriging interpolator can be used to generate grid data with the results available at sparse PSs [

The further analysis focuses on isolating the nonlinear subsidence from the atmospheric delay. For each interferometric pair, the residual phase increment (gradient) at each arc can be first calculated by

It is possible to separate the nonlinear subsidence from the undesired atmospheric delay because the two terms have different spectral structure in space and time domain [

The atmospheric phase

To detect subsidence evolution in Shanghai metropolitan (China) by the procedures presented above, we utilize 26 single look complex (SLC) SAR images which are available at hand. They were acquired from 1992 to 2002 by two C-band (wavelength λ = 5.6 cm) radar sensors onboard the satellites ERS-1 and ERS-2, respectively (both operated by European Space Agency). All the images were collected by a nominal radar look angle of about 23° along the descending orbits. With a pixel size of 7.9 m in slant range by 4.0 m in azimuth, each image covers the same area of about 100×100 km whose central location is 121°28′E, 31°10TN. To optimize the interferometric combination, we determined the unique master image by maximizing radar coherence of the entire dataset by

To generate interferograms, all the slave images were co-registered onto the sampling grids of the master image.

Existing studies indicate that the most serious subsidence in Shanghai has been taking place around the downtown area, and reached a remarkable value of 2.63 m accumulated from 1921 to 1965 [

The PS candidates were detected on a pixel-by-pixel basis by the statistical computation of time series of amplitude values at each pixel. The pixel is determined as a PS candidate based on the criteria of inequality (3). ^{2}) appears in the area with dense buildings, while the PSs are rare in some farmlands due to serious temporal decorrelation. We formed a very strong network by freely connecting each PS and all the others if their distance is less than 1 km, as defined in inequality (4), resulting in 4202 arcs.

The increments of both linear subsidence velocities and elevation errors between two adjacent PSs of each arc were then estimated by maximizing MC with

It should be pointed out that the FCN used in our approach is more advantageous than TIN used elsewhere in terms of accuracy and reliability for estimating subsidence rates and elevation errors at PSs, although the former incurs much heavier computation burden than the latter. The reliability with FCN is significantly enhanced because it has much more connections (arcs) between adjacent PSs than TIN. In other words, the total number of redundant observations in FCN is much larger than that in TIN. Hence the LS estimator for FCN is less disturbed by outliers. Our testing results derived with simulated data indicated that the FCN-based LS estimation can efficiently resist against a small portion of outliers in measurements (Δε, Δ

The atmospheric delay and nonlinear subsidence in the study area were finally separated by a time-space filtering method as discussed in section 3.3. Prior to such separation, the residual phases in each differential interferogram were extracted by detrending both linear subsidence and topographic effect. The atmospheric phases of the master image (by ERS-2 on May 5, 1998) were derived by a LP space filtering applied onto the mean of 25 residual-phase images (see

After deriving atmospheric phases,

In recent years, both precise leveling and GPS survey have been carried out to monitor subsidence in Shanghai by some authorities [

To mitigate the negative impacts of both temporal decorrelation and atmospheric delay on mapping deformation with conventional DInSAR, this paper has presented an approach called PS-networking SAR interferometry for detection of land subsidence in Shanghai, China. With use of 26 ERS-1/2 SAR images acquired 1992 through 2002 over Shanghai, the time series of land subsidence is analyzed with a very strong network which is formed by freely connecting neighboring PSs according to a given distance threshold. The mathematical models and computing methods are addressed systematically by considering spatial autocorrelation and LS parameter estimation. The linear and nonlinear subsidence, atmospheric effect as well as topographic error were separated effectively in this way. The subsidence velocity field in 10 years over Shanghai was also derived. It was found that the annual subsidence rates in the study area range from -2.1 to -0.6 cm/yr, and the averaged subsidence rate reaches -1.1 cm/yr. The maximum subsidence accumulated in 10 years is up to -18 cm. These are generally in good agreement with the leveling subsidence results reported elsewhere. In addition, the testing results indicated that the FCN proposed in this study is more advantageous than the TIN used elsewhere in terms of reliability for estimating subsidence rates and elevation errors at PSs, although the former incurs much heavier computation burden than the latter.

With further improvement, it is anticipated that PS-networking SAR interferometry would become an operational tool to monitor the slowly-accumulated urban subsidence, and thus complementing the conventional geodetic tools such as GPS and leveling. In China, there are a number of cities which are suffering from land subsidence. Besides Shanghai, the other typical sinking cities include Tianjin and Taiyuan. The reliable and prompt measurements reflecting land subsidence evolution are valuable for assessing and mitigating some geological hazards related to land sinking.

The work presented here was partially supported by three grants from the National Natural Science Foundation of China (Project No. 40774004, 40374003, 40474008) and ESA Category-1 Data Use Program. The authors would like to thank State Bureau of Surveying and Mapping in China and the Delft University of Technology for providing topographic maps and precise orbital data, respectively. In addition, the authors are also very thankful to two anonymous reviewers for their valuable comments.

Flowchart of PS-networking SAR interferometry.

An example of PS network.

The study area marked by a box onto the master amplitude image.

All the detected PSs superimposed onto an optical orthoimage.

The classed map of linear subsidence rates at all the PSs.

The atmospheric phases in the partial AOI for the master image.

Time series of subsidence at 5 PSs as marked in

Perspective view of the subsidence field accumulated between June 1992 and August 2002.

The parameters of 26 ERS-1/2 SAR images used in this study.

No. | Platform -orbit | Imaging Date | ^{⊥}(m) |
No. | Platform –orbit | Imaging Date | (m) | ||
---|---|---|---|---|---|---|---|---|---|

1 | E1-04657 | 1992.06.06 | 504 | −2159 | 14 | E2-14887 | 1998.02.24 | −1239 | −70 |

2 | E1-06160 | 1992.09.19 | 146 | −2054 | 15 | E2-15388 | 1998.03.31 | −487 | −35 |

3 | E1-09166 | 1993.04.17 | -36 | −1844 | 16 | E2-15889 | 1998.05.05 | 0 | 0 |

4 | E1-10669 | 1993.07.31 | 274 | −1739 | 17 | E2-20899 | 1999.04.20 | 247 | 350 |

5 | E1-12172 | 1993.11.13 | −639 | −1634 | 18 | E2-23905 | 1999.11.16 | −348 | 560 |

6 | E1-19530 | 1995.04.10 | −207 | −1121 | 19 | E2-24406 | 1999.12.21 | −141 | 595 |

7 | E1-22035 | 1995.10.02 | 178 | −946 | 20 | E2-26410 | 2000.05.09 | 303 | 735 |

8 | E1-24039 | 1996.02.19 | 505 | −806 | 21 | E2-26911 | 2000.06.13 | −158 | 770 |

9 | E1-24540 | 1996.03.25 | −1144 | −771 | 22 | E2-28414 | 2000.09.26 | 290 | 875 |

10 | E2-04867 | 1996.03.26 | −1000 | −770 | 23 | E2-34426 | 2001.11.20 | −198 | 1295 |

11 | E1-25542 | 1996.06.03 | −1253 | −701 | 24 | E2-37432 | 2002.06.18 | 1048 | 1505 |

12 | E2-05869 | 1996.06.04 | −1104 | −700 | 25 | E2-37933 | 2002.07.23 | 144 | 1540 |

13 | E2-13384 | 1997.11.11 | −762 | −175 | 26 | E2-38434 | 2002.08.27 | −1021 | 1575 |

Note: the B^{⊥} and