**4. Experimental results**

This section shows some experimental results obtained by applying the PO-SBAS and the MinA techniques for the estimation of three-dimensional components of terrain displacements.

### **4.1. Sierra Negra PO-SBAS results**

The experiments carried out in this case were related to the area of Sierra Negra caldera, which is the most active among shield volcanoes located on Isabela Island, Galapagos Archipelago. Following an Mw 5.4 earthquake, in October 2005 Sierra Negra caldera erupted, interrupting a period of quiescence that lasted almost 30 years. The investigation of several analyses of the Sierra Negra caldera geodetic signals revealed Sierra Negra is almost continuously in an uplift phase, which started in 1992, and accelerated so as to reach about 5 m of cumulative ground displacement before the 2005 eruption. On the other hand, the October 2005 catastrophic event induced a subsidence of the inner caldera of more than 5 m [33].

Due to the large deformation dynamics affecting Sierra Negra caldera, the retrieval of ground displacements using DInSAR is a challenging task. Indeed, the application of conventional SBAS-DInSAR time series analysis on the 2003–2007 Galapagos dataset provides only a partial picture of the deformation field. In particular, a set of 25 ENVISAT SAR images were processed (see [27] for further details). **Figure 7(a)** and **(b)** shows the retrieved mean ground velocity maps relevant to the 2003–2007 period. The behavior of the northern flanks of the volcano, being the displacements still in the order of centimeters, is clearly imaged by the SBAS-DInSAR analysis, and it is in agreement with previous studies. However, due to the lack of coherence caused by the large deformation dynamics, the interferometric phase analysis is not able to measure displacements around the crater and inner caldera due to the lack of coherence caused by the large deformation dynamics.

In order to image the spatial and temporal evolution of the deformation in these areas, the SAR amplitude information was exploited. Thus, the PO-SBAS approach was applied to the same data pairs considered for the generation of the SBAS-DInSAR time series. Following the PO-SBAS steps explained, the offsets for each data pair were calculated, and a common mask of "good" pixels was selected by considering only those having a high QI value that were present at least in 70% of the whole dataset. At this stage, the PO-SBAS time-series were generated for each of the selected pixels. The accuracies for the PO-SBAS measurements, relevant to the herein analyzed test-case, were obtained by calculating the standard deviation of the measurements in an area that is known to be stable. Estimated accuracy values are in

Generation of Earth's Surface Three-Dimensional (3-D) Displacement Time-Series by Multiple-Platform SAR Data http://dx.doi.org/10.5772/intechopen.71329 69

**Figure 7.** SBAS-DInSAR results. (a) Mean deformation velocity map of the Galapagos Islands retrieved by applying the SBAS technique and (b) zoom of the study area, (c) Comparison between PO-SBAS and GPS measurements corresponding to the GV01 station.

the order of 1/20th of pixel, in agreement with those expected. However, since the aim of this analysis is to emphasize the areas characterized by large deformations, the pixels whose dynamics are smaller than 1/10th of pixel were masked out. **Figure 8** shows the PO-SBAS time-series and the comparison with external GPS measurements available in the area.

### **4.2. Piton de La Fournaise MinA results**

monitored, being the accuracy of these methods is on the order of 10 cm (or larger). In this case, the strategy here adopted can be extended using AZPO and RGPO time-series of deformation, instead of the LOS deformation measurements, and applying the minimum-acceler-

This section shows some experimental results obtained by applying the PO-SBAS and the MinA techniques for the estimation of three-dimensional components of terrain

The experiments carried out in this case were related to the area of Sierra Negra caldera, which is the most active among shield volcanoes located on Isabela Island, Galapagos Archipelago. Following an Mw 5.4 earthquake, in October 2005 Sierra Negra caldera erupted, interrupting a period of quiescence that lasted almost 30 years. The investigation of several analyses of the Sierra Negra caldera geodetic signals revealed Sierra Negra is almost continuously in an uplift phase, which started in 1992, and accelerated so as to reach about 5 m of cumulative ground displacement before the 2005 eruption. On the other hand, the October 2005 cata-

Due to the large deformation dynamics affecting Sierra Negra caldera, the retrieval of ground displacements using DInSAR is a challenging task. Indeed, the application of conventional SBAS-DInSAR time series analysis on the 2003–2007 Galapagos dataset provides only a partial picture of the deformation field. In particular, a set of 25 ENVISAT SAR images were processed (see [27] for further details). **Figure 7(a)** and **(b)** shows the retrieved mean ground velocity maps relevant to the 2003–2007 period. The behavior of the northern flanks of the volcano, being the displacements still in the order of centimeters, is clearly imaged by the SBAS-DInSAR analysis, and it is in agreement with previous studies. However, due to the lack of coherence caused by the large deformation dynamics, the interferometric phase analysis is not able to measure displacements around the crater and inner caldera due to the

In order to image the spatial and temporal evolution of the deformation in these areas, the SAR amplitude information was exploited. Thus, the PO-SBAS approach was applied to the same data pairs considered for the generation of the SBAS-DInSAR time series. Following the PO-SBAS steps explained, the offsets for each data pair were calculated, and a common mask of "good" pixels was selected by considering only those having a high QI value that were present at least in 70% of the whole dataset. At this stage, the PO-SBAS time-series were generated for each of the selected pixels. The accuracies for the PO-SBAS measurements, relevant to the herein analyzed test-case, were obtained by calculating the standard deviation of the measurements in an area that is known to be stable. Estimated accuracy values are in

strophic event induced a subsidence of the inner caldera of more than 5 m [33].

lack of coherence caused by the large deformation dynamics.

The diagram block of the MinA algorithm is shown in **Figure 6**.

ation (MA) regularization.

68 Time Series Analysis and Applications

**4. Experimental results**

**4.1. Sierra Negra PO-SBAS results**

displacements.

To further demonstrate the capabilities of the DInSAR-driven minimum-acceleration combination algorithm, it has been applied for studying the settlements of the area of Piton de La Fournaise (Reunion Islands), which is characterized by the presence of a large volcanic system that erupted on April 3, 2007 and lead to large fractures on the ground. Such volcanic system has extensively been studied [34], however new data can provide additional information on the state of volcanism of the island. The presented experiments are based on processing three independent sets of SAR images collected by the ENVISAT/ASAR (C-band) radar instrument along ascending (48 images) and descending passes (35 images) as well as by the ALOS-1/PALSAR (L-band) sensor (11 images), spanning the 2003–2010 time interval (see Table III in [23]). These three SAR datasets were independently processed by the

**Figure 8.** Examples of PO-SBAS time-series in azimuth (right) and range (left) directions, respectively. (a)-(f) Comparison between PO-SBAS and GPS measurements in the proximity of selected GPS stations. (g)-(h) AZO and RGO displacement mean velocity maps. The figure is adapted from [27].

SBAS-DInSAR processing chain, and corresponding LOS-projected displacement time-series (and mean deformation maps) were generated. The MinA combination method is applied (as a post-processing stage) only to those pixels that remain coherent in all three independent SBAS-DInSAR processing analyses, and this permitted discriminating from the LOSprojected deformations the time-series of the 3D deformation components.

**Figure 9(a)**–**(c)** shows the maps of retrieved E-W, U-D, and N-S mean deformation velocity maps, superimposed to a gray-scale SAR amplitude image of the zone common to all the three SAR data-tracks. Also, one point, labeled to as P in **Figure 9** and located in the summit Generation of Earth's Surface Three-Dimensional (3-D) Displacement Time-Series by Multiple-Platform SAR Data http://dx.doi.org/10.5772/intechopen.71329 71

**Figure 9.** Geocoded maps of the Up-Down (a), east–west (b), and north–south (c) mean velocity deformation.

SBAS-DInSAR processing chain, and corresponding LOS-projected displacement time-series (and mean deformation maps) were generated. The MinA combination method is applied (as a post-processing stage) only to those pixels that remain coherent in all three independent SBAS-DInSAR processing analyses, and this permitted discriminating from the LOS-

**Figure 8.** Examples of PO-SBAS time-series in azimuth (right) and range (left) directions, respectively. (a)-(f) Comparison between PO-SBAS and GPS measurements in the proximity of selected GPS stations. (g)-(h) AZO and RGO displacement

**Figure 9(a)**–**(c)** shows the maps of retrieved E-W, U-D, and N-S mean deformation velocity maps, superimposed to a gray-scale SAR amplitude image of the zone common to all the three SAR data-tracks. Also, one point, labeled to as P in **Figure 9** and located in the summit

projected deformations the time-series of the 3D deformation components.

mean velocity maps. The figure is adapted from [27].

70 Time Series Analysis and Applications

area of the crater, was selected. The inherent (combined) E-W and Up-Down deformation time-series relevant to this point are shown in the plots of **Figure 10**. They make it evident the large cumulative E-W displacement, moving mostly eastward, affects the upper part of the Eastern flank with velocity of about 10 cm/year. This trend is abruptly interrupted by a jump of about 40 cm in correspondence of the April 2, 2007 eruption, which induced a widespread flank movement starting at the time of dike injection to feed an initial eruption, a few days before the main eruptive event; also a significant U-D signal was active even with a more moderate deformation value (around 8 cm).

**Figure 10.** DInSAR results retrieved for the Piton de la Fournaise study area. Zoom view of the Up-Down (a) and East-West (b) mean deformation displacement maps. (c) and (d) are the MinA-driven time-series obtained by combining the LOS time-series for the Up (c) and East-West (d) components, respectively.

## **5. Conclusions**

In this chapter, a review of some existing DInSAR methods for the retrieval of the 3-D (2-D) deformation time-series is first provided. In particular, we review some recently published methods and then we focus on the MinA method. With respect to previous works, this method has the advantage to be a post-processing algorithm, thus it does not require the simultaneous processing of hundreds of differential SAR interferograms. Information on the quality of LOS-projected deformation time-series (e.g., the temporal coherence maps) as well as the *a priori* identification of very coherent targets is very proficient for the discrimination of the 3-D deformation components. One strength of the algorithm is represented by the opportunity to complement LOS measurements with other external sources of information (such as GPS/leveling data). This technique has primarily been developed as an ultimate extension of the SBAS processing chain; however, it can be used, without any further modification, to work with other general-purpose DInSAR toolboxes. Several examples are provided, thus also clarifying how this method can be easily integrated in the currently available DInSAR toolboxes.
