# Efficient Ground Surface Displacement Monitoring Using Sentinel-1 Data: Integrating Distributed Scatterers (DS) Identified Using Two-Sample t-Test with Persistent Scatterers (PS)

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Pre-Processing

#### 2.2. DS Selection

#### 2.2.1. DS Candidate Selection

#### 2.2.2. Final DS Selection

#### 2.3. PS Selection

#### 2.4. Displacement Retrieval

## 3. Experimental Results

## 4. Discussion

#### 4.1. SHP Maps

#### 4.2. Despeckled Intensity

#### 4.3. Consistency Assessment of the Displacements

#### 4.4. Computational Time

#### 4.5. Different SAR Stack-Sizes

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**One example for SHPs selection, showing: (

**a**) all neighbors selected by applying the t-test; (

**b**) labeling the eight connected pixels, which are shown with different colors; and (

**c**) discarding those pixels with labels different from the label of the central pixel. The outline of the central pixel is shown with yellow.

**Figure 3.**Sentinel-2 satellite image of the Trondheim study area. The white rectangle shows the outline of the Sentinel-1 data processed in this study.

**Figure 4.**The PTA temporal coherence corresponding to the SHP map obtained by using the two-sample t-test

**Figure 5.**Mean line-of-sight velocity maps considering: (

**a**) only PS points; (

**b**) PS and DS pixels derived by our new method using the two-sample t-test; and (

**c**) PS and DS pixels identified by the two-sample KS-test. The triangles show the selected reference area. The vectors H and L represent the satellite heading and look angle. Negative implies away from satellite. For the point labeled A, the displacement time-series is shown in Figure 9a.BA indicates the location of the profile analyzed in Figure 9b. A zoomed in area around section BA from: (

**d**) the PS result; and (

**e**) the PS and DS pixels derived by the t-test.

**Figure 6.**The number of SHP identified considering a $15\times 21$ estimation window and performing the two-sample (

**a**) t-test and (

**b**) KS-test, both at 95% significance level, and (

**c**) the scatter plot of the number identified by the t-test versus the KS-test, color-coded by the smoothed density of pixels.

**Figure 7.**(

**a**) Amplitude image of the SLC on date 25 July 2015; and the filtered version using two-sample: (

**b**) t-test; and (

**c**) KS-test.

**Figure 8.**(

**a**) The line-of-sight displacement velocity derived using KS-test versus t-test, color-coded by the smoothed density of pixels; (

**b**) the histogram of the difference between the velocities; and (

**c**) the difference of the velocities versus the standard deviation, color-coded by the normalized smoothed density of pixels for each standard deviation bin with the width of 0.05. Dashed lines show region where absolute of the difference is less than twice the standard deviation.

**Figure 10.**Correlation coefficient between the number of SHPs found for all pixels, for the full 50 images and for fewer images.

**Figure 11.**An example of the SHPs (yellow points) identified by performing the two-sample KS-test, the two-sample t-test, and the one-sample t-test for the full 50 images and for fewer images. The central pixel is shown with red.

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**MDPI and ACS Style**

Shamshiri, R.; Nahavandchi, H.; Motagh, M.; Hooper, A. Efficient Ground Surface Displacement Monitoring Using Sentinel-1 Data: Integrating Distributed Scatterers (DS) Identified Using Two-Sample *t*-Test with Persistent Scatterers (PS). *Remote Sens.* **2018**, *10*, 794.
https://doi.org/10.3390/rs10050794

**AMA Style**

Shamshiri R, Nahavandchi H, Motagh M, Hooper A. Efficient Ground Surface Displacement Monitoring Using Sentinel-1 Data: Integrating Distributed Scatterers (DS) Identified Using Two-Sample *t*-Test with Persistent Scatterers (PS). *Remote Sensing*. 2018; 10(5):794.
https://doi.org/10.3390/rs10050794

**Chicago/Turabian Style**

Shamshiri, Roghayeh, Hossein Nahavandchi, Mahdi Motagh, and Andy Hooper. 2018. "Efficient Ground Surface Displacement Monitoring Using Sentinel-1 Data: Integrating Distributed Scatterers (DS) Identified Using Two-Sample *t*-Test with Persistent Scatterers (PS)" *Remote Sensing* 10, no. 5: 794.
https://doi.org/10.3390/rs10050794