*5.2. Effects of Overlap Rate on Result Precision and Time Consumption*

In the proposed partition strategy, partitioning the image is the first and most critical step. Different partition strategies provide different precision results, and different data processing efficiency. Because we adopt the even partition strategy, the size and overlap ratio of the blocks have a great impact on the results. To analyze the effects of the overlap ratio on the partition results, we set one block size and obtained the temporal deformation results of Changzhou using the overlap ratios of 10%, 20%, 30%, and 40%, separately. The results are shown in Figure A2. We evaluated the result precision (Table 4).

The precision of the deformation rates obtained by different overlap ratios is similar because the mean values of the high-quality homonymy points in the overlap region are used in adjustment, which is slightly influenced by the overlap region. As long as the block size is the same, the precision of the results obtained by different overlap ratios are similar. However, the time consumed by different overlap ratios is different. The larger the overlap ratio, the larger the number of blocks and the longer the processing. When the number of parallel processing is 5, the total time consumed by the four overlap ratios are 6.6 h, 7.6 h, 9.5 h, and 10.7 h, indicating that the consuming time increases with the increase of overlap ratio. The increase in the overlapping area brings larger double-counted areas and raises the reliability of the results. Considering the precision, reliability, and time consumption, we choose 20% as the best overlap ratio. The experiments show that overlap ratio 20% has similar result precision and time consumption with that of overlap ratio 10%, but it leads to more than 64% overlap area, which contributes to a significantly higher reliability.



#### *5.3. Implications of Data Partition Strategy for MT-InSAR*

The administrative boundary of a city is usually an irregular polygon, but the image coverage is a regular quadrangle. Thus, the image coverage contains many data unrelated to the study area. The traditional method will also process these data. If such data accounts for a large proportion of the image, the data processing will waste a lot of time. The proposed method only processes the block data inside the study area, which can improve the data processing efficiency. In Figure 4, the gray blocks do not need processing. Furthermore, the proposed method can refine the data processing for only the blocks with deformation, which further improves the efficiency of data processing.

The difference in the image coverage will definitely lead to the difference in the results. In this paper, we divide data into blocks, and process, correct, and splice the results of all blocks. The atmospheric delay in small range data is easier to remove than that in the data with large range. Studies have shown that the atmospheric phase in InSAR data measurements has a close correlation with spatial scale [35]. The atmospheric phase difference between two PS points with a distance less than 1 km is less than 0.1 rad2 [40], so the smaller the area, the better the atmospheric error removal according to the error propagation law. However, for large deformation areas, long-wavelength deformation may be removed as orbital errors, due to the polynomial fitting [21]. Thus, the proposed method is not fully applicable to the study area with long-wavelength deformation, such as interseismic deformation.

The correction of the partition results is based on the assumption that the deformation rates of the homonymy points are the same. However, the deformation acquired by InSAR is the line-of-sight (LOS) deformation, and the deformation direction at each point is related to the incidence angle. When the deformation of the homonymy point is obtained from the same orbit and has the same incidence angles, the deformation rates should be the same. If the partitioned data are acquired under different imaging geometries, there will be inconsistency in the incidence angles, resulting in different LOS deformation. Therefore, the incidence angle variation of the results should be considered when the partition data are acquired from different orbits.

Finally, the method does not use control points for the adjustment. Although the benchmarks between image blocks are unified, there may be a deviation between the unified benchmark and the real deformation result datum. We only make a simple correction to the result but using external data as control points may improve the correction.

#### **6. Conclusions**

In this paper, we propose to partition the data into blocks before obtaining the deformation, to save memory and time for large-scale data processing. To validate this method, we used the Sentinel-1 TOPS data covering Changzhou, a plain area, and Qijiang, a mountainous area in China. The time series deformation results were obtained in these two regions using the traditional processing method (the improved IPTA) and the partition processing method. The latter outperforms the former in precision, time consumption, and memory occupation. Taking Changzhou City as an example, the memory occupation of the traditional processing method is about 27.2 G, and the total time consumed by processing is about 20 h. During partition processing, the memory occupation of each block is only 1.3 G, and the consumed time is 8.7 h when the parallel number is 5. We also compared the precision of the results obtained by the two methods. The results obtained by the partition processing in Changzhou is as about 4.0 mm/yr, while the precision of the traditional processing is about 4.2 mm/yr. The correspondence in Qijiang is about 3.3 mm/yr and 3.9 mm/yr, respectively. The precision of the results obtained by the proposed method is higher than that obtained by traditional processing.

In general, the proposed method can significantly reduce the memory occupation and time consumption of data processing under the condition of sufficient parallelism, and the precision of the results is higher than that obtained by traditional processing. This method is suitable for monitoring the short-wavelength deformation in a large area, such as large-scale urban deformation monitoring and large-scale landslide deformation detection. However, further research is needed for the result splicing and its application to long-wavelength deformation.

**Author Contributions:** Conceptualization, Y.W. (Yuexin Wang) and G.F.; data curation, S.L.; formal analysis, Z.F. and Y.W. (Yuedong Wang); funding acquisition, Y.W. (Yuexin Wang) and G.F.; methodology, Y.W. (Yuexin Wang) and G.F.; resources, G.F.; Software, Y.W. (Yuexin Wang); supervision, S.L., Y.Z. and H.L.; validation, X.W.; writing—original draft, Y.W. (Yuexin Wang); writing—review and editing, Y.W. (Yuexin Wang), G.F., Z.F., Y.W. (Yuedong Wang), X.W., Y.Z. and H.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (No. 42174039), and the Fundamental Research Funds for the Central Universities of Central South University (No. 506021741).

**Acknowledgments:** The authors would like to thank the European Space Agency (ESA) for providing free Sentinel-1 data. The data were additionally retrieved from the Alaska Satellite Facility Distributed Active Archive Center. We also thank the contributors for the Generic Mapping Tools (Wessel et al., 2013) open-source software.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** Parameters of the images used in this study.



**Table A1.** *Cont.*

**Figure A1.** The detailed flowchart of the proposed method.

**Figure A2.** The deformation results in Changzhou obtained using the overlap ratio of (**a**) 10%, (**b**) 20%, (**c**) 30%, and (**d**) 40%. A1-C4 are the same areas as A–C described in Section 4.1.
