# Deformation Trend Extraction Based on Multi-Temporal InSAR in Shanghai

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

^{m}denote radar wavelength, range from the master pixel to the sensor and the local incidence angle, respectively. B

_{⊥}and T are the perpendicular baseline and the temporal baseline, respectively. The height correction of point target x related to the reference point is Δh(x). The linear deformation rate of point target x related to the reference point is v(x), and ϕ

_{noise}is the combination of white noise and unmolded errors, which include baseline-related error, the atmospheric phase, and the non-linear deformation phase.

## 3. Experimental Result and Analysis

#### 3.1. Data Selection

#### 3.2. Subsidence Results

#### 3.3. Validation

_{i}is the difference between the leveling measurements l

_{i}and the MT-InSAR deformation estimates p

_{i}. So,

_{i}and p

_{i}obey a normal distribution, then d also obeys normal distribution, i.e., ${d}_{i}\sim N({\mu}_{{d}_{i},}{\sigma}_{{l}_{i}}^{2}+{\sigma}_{{m}_{i}}^{2})$. μ

_{di}denotes the mean of d

_{i}and μ

_{di}according to H

_{0}, while ${\sigma}_{{l}_{i}}^{2}$ and ${\sigma}_{{m}_{i}}^{2}$ denotes the variance of the leveling measurements and the MT-InSAR deformation estimates, respectively, which are known. Before calculating the statistic by Equation (4), d

_{i}should be normalized, i.e., ${{d}^{\prime}}_{i}=\frac{{d}_{i}}{\sqrt{{\sigma}_{{l}_{i}}^{2}+{\sigma}_{{m}_{i}}^{2}}}$.

_{i}:

- For ASAR, t = 0.38
- For CSK, t = 0.83

_{α/2}(152) = t

_{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.

## 4. Comparison and Discussion

^{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.

## 5. Conclusions

## Acknowledgments

## References

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**Figure 2.**Temporal and perpendicular baseline distribution of interferograms. The red circle denotes the master image while the blue ones denote the slave images.

**(a)**Envisat Advanced Synthetic Aperture Radar (ASAR),

**(b)**COSMO SkyMed (CSK) SAR.

**Figure 3.**Location of Shanghai. The study area is specified by the red square, the background is the averaged ASAR intensity image.

**Figure 4.**Linear deformation rates of point targets overlaid on the average amplitude SAR image.

**(a)**Deformation rate distribution obtained by ASAR images,

**(b)**deformation rate distribution obtained by CSK SAR images. The four blue lines denote four chosen profiles across the significant subsidence funnel, labeled as L1, L2, L3 and L4. The blue circles located near the middle bottom are the reference points.

**Figure 5.**Histogram of standard deviation of mean subsidence rates estimated.

**(a)**Obtained by ASAR images,

**(b)**obtained by CSK images.

**Figure 6.**Comparison of subsidence rates between Interferometric synthetic aperture radar (InSAR) and spirit leveling on bench marks.

**(a)**Is for ASAR results, while

**(b)**is for CSK results. SD denotes the standard deviation of subsidence rates in each searching window.

**Figure 7.**Comparison of subsidence rates along the four chosen profiles. (

**a**), (

**b**), (

**c**) and (

**d**) corresponding to profile L1, L2, L3, and L4, respectively. The red dots denote subsidence rates of the CSK point targets, while the blue squares denote the ASAR point targets.

**Table 1.**Root mean square error (RMSE) of the subsidence differences based on the four chosen profile lines.

L1 | L2 | L3 | L4 | |
---|---|---|---|---|

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

## Share and Cite

**MDPI and ACS Style**

Chen, J.; Wu, J.; Zhang, L.; Zou, J.; Liu, G.; Zhang, R.; Yu, B.
Deformation Trend Extraction Based on Multi-Temporal InSAR in Shanghai. *Remote Sens.* **2013**, *5*, 1774-1786.
https://doi.org/10.3390/rs5041774

**AMA Style**

Chen J, Wu J, Zhang L, Zou J, Liu G, Zhang R, Yu B.
Deformation Trend Extraction Based on Multi-Temporal InSAR in Shanghai. *Remote Sensing*. 2013; 5(4):1774-1786.
https://doi.org/10.3390/rs5041774

**Chicago/Turabian Style**

Chen, Jie, Jicang Wu, Lina Zhang, Junping Zou, Guoxiang Liu, Rui Zhang, and Bing Yu.
2013. "Deformation Trend Extraction Based on Multi-Temporal InSAR in Shanghai" *Remote Sensing* 5, no. 4: 1774-1786.
https://doi.org/10.3390/rs5041774