We present a case study for detecting the four-dimensional (4-D) displacement of rift zones affected by large-magnitude deformation, by using spaceborne synthetic aperture radar (SAR) data. Our method relies on the combination of displacement time series generated from pixel offset estimates on the amplitude information of multitemporal SAR images acquired from different orbit passes and with different looking geometries. We successfully applied the technique on advanced SAR (ASAR) Envisat data acquired from ascending and descending orbits over the Afar rift zone (Ethiopia) during the 2006–2010 time span. Our results demonstrate the effectiveness of the proposed technique to retrieve the full 4-D (i.e., north, east, up, and time) displacement field associated with active rifting affected by very large-magnitude deformation.

Continental rifting is one of the most fascinating and debated geological phenomena observable on Earth and other planets of the solar system (Ernst et al., 2001, and references therein). The mutual occurrence of extension, faulting, and magmatic intrusion generally causes rapid modifications of the lithospheric crust and produces permanent surface deformation. Recently, remote sensing studies have demonstrated their capability to observe and monitor ground displacements caused by active rifting (Hollingsworth et al., 2013; Ebinger et al., 2010; Wright et al., 2006). Among diverse methods, spaceborne differential synthetic aperture radar (SAR) interferometry (DInSAR) allows accurate measurement of ground deformation by properly analyzing the phase difference between two SAR acquisitions over the same region of interest (Massonnet et al., 1993). The main advantage of DInSAR is the possibility of generating surface displacement maps at regional scales (on the order of 103–105 km2) and achieving accuracies at the sub-centimeter level. An intrinsic limitation of DInSAR analyses is that measurement of the surface displacements is one-dimensional, because only the projection of such displacements along the satellite’s line of sight (LOS) can be retrieved. In particular conditions, the combination of LOS results obtained from image pairs of the same area and spanning the same time interval but taken from different acquisition geometries (e.g., the ascending and descending orbits of the satellite) allows retrieval of the vertical and east-west components of the surface deformation field (Manzo et al., 2006). However, the north-south (mainly along-track) component of the ground motion is usually hindered by the satellite’s acquisition geometry (Fialko et al., 2001; Manzo et al., 2006).

An additional limitation of standard DInSAR is loss of coherence due to large surface displacements when analyzing SAR data relevant to large earthquakes, volcanic eruptions, and mass wasting, the “impulsive” nature of these phenomena being the cause of high-fringe-rate interferograms, which could lead to difficulties in the correct phase retrieval (Casu et al., 2011). When the deformation introduces geometric distortions without significantly disturbing the SAR image reflectivity, displacements can be observed by comparing the amplitudes of SAR image pairs acquired before and after an event (Fialko et al., 2001). Compared with DInSAR, this approach (hereafter generally referred to as pixel offset, PO) achieves accuracies on surface displacements significantly lower (typically on the order of 1/20th of pixel; see Casu et al., 2011). By contrast, PO analyses have the advantage of providing two-dimensional displacement information, i.e., on the deformation components occurring across and along the satellite’s track (the range and azimuth directions, respectively). Moreover, by jointly considering PO estimated on ascending and descending acquisitions over the same area of study, it is possible to retrieve the full three-dimensional deformation field (Fialko et al., 2001; Wright et al., 2004).

The latter information can be crucial when investigating complex geological and geophysical phenomena. However, not only the spatial configuration but also the temporal evolution of surface displacements assume a great relevance for the accurate understanding of the ongoing phenomena. To this end, several methods have been proposed for processing multitemporal DInSAR data and thus passing from a static representation of the deformation field to displacement time series (Ferretti et al. 2001; Berardino et al., 2002). Among them, the small baseline subset (SBAS) algorithm is well established and thoroughly tested in diverse scenarios (Lanari et al., 2007). SBAS is standardly applied to the phase information of properly selected SAR image pairs; nevertheless, by applying the same SBAS rationale to process PO measurements, it has been demonstrated that it is also possible to generate surface displacement time series from the SAR amplitude information, i.e., POs, through the technique referred to as PO-SBAS (Casu et al., 2011).

In this work, we propose an algorithm to retrieve the four-dimensional (4-D) (i.e., along north, east, up, and time) surface deformation field over zones affected by active rifting, by exploiting the PO-SBAS technique. In the following, we first describe the method’s theoretical background. Secondly, we combine the PO-SBAS time series results obtained from both ascending and descending passes of the advanced SAR (ASAR) Envisat sensor to retrieve the 4-D deformation field in the Afar depression, Ethiopia, during the 2006–2010 period. There, a rifting episode associated with dike intrusions on the Dabbahu segment of the Nubia-Arabia plate boundary has produced large surface deformation starting from 2005, and thus represents an interesting and challenging case study to test and validate the herein-proposed approach.

As mentioned above, the PO-SBAS technique allows us to generate displacement time series from a set of POs computed along the range and azimuth directions of SAR image pairs, respectively. Therefore, the retrieved measurements represent the projections of the actual displacements along both the LOS (range), as in the conventional DInSAR, and the orbit direction (azimuth). The availability of PO-SBAS time series obtained from different orbit geometries can be then used to retrieve the full 4-D deformation field (east, north, up, and time) of the investigated area.

Let us first consider two sets of ground points (pixels), one relative to ascending and one to descending orbits, for which we have computed the PO-SBAS displacement time series according to Casu et al. (2011). Among them, we select those that are common to both orbital passes on a unique geographic grid. We remark that, as a first-order approximation, ascending and descending measurements relative to such common pixels can be related to the same radar targets. This assumption is valid when spatial averaging and smoothing have been applied to PO estimates to reduce noise.

For each investigated pixel, we then consider four elements, two retrieved from the ascending passes and two from the descending ones. More specifically:
where daz and drg are the projections of the actual displacement d (see Fig. 1) along the azimuth and range directions, respectively, and t is the vector of acquisition epochs (time). Subscripts A and D indicate measurements obtained from ascending or descending orbits, respectively. Note that tA and tD take into account the different temporal sampling of the ascending and descending acquisitions. This aspect has to be carefully considered when combining measurements generated from different orbit passes, with the aim of extracting the actual displacement components. Indeed, to accomplish this task, in principle we require acquisitions taken at the same epochs, thus implying that tAtDt. However, apart from rare exceptions, ascending and descending orbit acquisitions are not coeval over the same region; therefore, a criterion to consider a unique temporal sampling t between ascending and descending passes has to be defined. A possible way is to pair ascending and descending acquisitions that are as close as possible in time—i.e., to consider them as acquired at the same time—assuming that the relative deformation between them is negligible. This is generally true when the expected measure error is bigger than the actual deformation that occurred between the two acquisitions, as is the case with the PO-SBAS measurements, for which the expected accuracy is on the order of 1/30th of pixel (Casu et al., 2011). Following this assumption, we can pair the ascending and descending acquisitions using an ad hoc strategy and taking into account possible events punctuating the time series, such as earthquakes and dike intrusions. For the sake of completeness, we could consider a model of the deformation among subsequent acquisitions (Pepe et al., 2015), so that the two ascending and descending time series could be evaluated and combined at the same epochs, t = ∪(tA, tD). However, such a solution may not be appropriate in the case of complex deformation behaviors (e.g., large and continuous dike intrusions) that cannot be accurately modeled.
Independently of the pairing method selected and assuming a unique time sampling for the PO-SBAS time series combination, we can derive from Equation 1, neglecting the time dependency, the following relation:
where d is the actual 4-D displacement vector; dN, dE, and dU represent the components along the north, east, and up directions, respectively; ϑ indicates the look angle; and α is the heading (see Fig. 1, which depicts the system geometry).
Equation 2 can be rewritten in matrix form as:
where forumla is the system coordinate conversion matrix and dNEU is the displacement vector expressed in terms of its north, east, and up components (see Fig. 1).

The system of equations in Equation 3 is over-determined (being that the number of equations is greater than the number of unknowns), and can be solved pixel by pixel via a least squares method, to finally obtain the 4-D dNEU(t) ground displacement. It is worth noting that the herein-presented approach, which has been carried out only for one ascending and one descending orbit, can be easily extended to multiple orbits.

The Afar depression system is one of the locations worldwide where active rifting processes can be observed (Hayward and Ebinger, 1996). In September 2005, a major basaltic dike with an estimated length of ∼60–65 km started intruding, causing hundreds of earthquakes, magma eruptions, and tectonic offsets (Wright et al., 2006; Ayele et al., 2009). In the period 2005–2010, most of the magma erupted from the central part of the Dabbahu–Manda Hararo system, counting as many as 12 distinct intrusion events (Ebinger et al., 2010). Starting from the initial stages of the rifting episode, this area has been focus of intense scientific investigation, performed with several techniques ranging from in situ observations to remote sensing analyses (Wright et al., 2006; Ferguson et al., 2010; Grandin et al., 2010; Nobile et al., 2012; Hamling et al., 2014).

The Afar depression has been repeatedly imaged by the Envisat satellite since 2005, thus a large SAR archive is nowadays available on that area. However, the phase information of the SAR signal is heavily affected by the large modifications occurring at surface, and the interferograms usually present high fringe rates (Fig. 2B), which lead to severe difficulties in the phase unwrapping and/or to complete loss of coherence due to significant misregistration errors. This occurs mainly in the near field of the rifting zone, where the expected deformation is on the order of several meters.

Instead, we exploited the amplitude information acquired from ascending (Track 300, Swath IS2) and descending (Track 464, Swath IS6) Envisat tracks (see Table 1 for the exploited data set) in order to retrieve the near-field deformation that occurred in the Afar rift region. First, we applied the PO-SBAS algorithm independently to the ascending and descending parts of the data set to generate displacement time series (Fig. 3). Secondly, we combined these results in order to retrieve the full 4-D deformation field on the common areas of the ascending and descending frames by considering the approach outlined in the Methods section and pairing the acquisitions according to Table 1 and Figure 4. We note that no temporal filtering was applied to the retrieved PO-SBAS time series, to avoid smoothing of sudden deformation. The results are shown in Figure 5, where a displacement pattern across the rift segment is remarkable, relevant to the repeated intrusive events affecting the Afar rift area. The cumulative displacements measured across the rift segment in the period 2006–2010 were >4 m in the east-west direction and ∼2 m in the north-south direction. Moreover, two clear subsidence lobes with maximum values of ∼1 m were revealed at the tips of the main faulting area, while uplift of 60–80 cm was measured across the rift. For all measurements, we estimated standard deviations ranging from 10 to 30 cm for the PO-SBAS measurements calculated in the far-field areas, i.e., not affected by significant deformation. This is in agreement with previous findings obtained in active volcanic regions (Casu et al., 2011).

Analyzing the evolution over time of the displacements, our results show an exponential decay, punctuated by the occurrence of 12 subsequent dike intrusions (Figs. 6A, 6B, and 6C; solid red lines in Fig. 6A; see Grandin et al., 2010). The revealed exponential decay agrees, in both amplitude and degree, with independent analyses on the deformation field (e.g., Nooner et al., 2009). Accordingly, a linear model fitting of the three-dimensional time series for point 2 of Figure 6 (close to the area of maximum deformation) leads to R2 = 0.8, while an exponential model has R2 = 0.94. Root mean square error between the signal and the model also supports the exponential decay hypothesis, being 28.3 cm and 16.7 cm for the linear and the exponential model, respectively (Fig. 7).

We computed the displacement time series in the Afar depression by exploiting the amplitude of SAR data acquired by Envisat satellite in the 2006–2010 period, retrieving information in areas where no deformation data were available through DInSAR and/or GPS measurements. We have shown how to retrieve the 4-D displacement field in active rift zones through the joint use of results, obtained independently on ascending and descending orbits, of the PO-SBAS algorithm. Our method demonstrates its validity in complex situations such as rifting episodes, where the deformation associated with repeated intrusions, faulting, and lithospheric extension might overlap in space and time.

Accurate, dense spatial and temporal information on displacements is crucial for the correct interpretation of geological phenomena, as well as for modeling purposes. In addition, the use of far-field (retrieved via the SBAS analysis) and near-field (retrieved via the PO-SBAS) displacement data may be considered in future studies as a convenient tool to better constrain analytical and numerical models in active volcanic areas (Manconi and Casu, 2012) and to better analyze the characteristics of the rifting and post-rifting periods (Hamling et al., 2014; Pagli et al., 2014). Indeed, the SAR phase may provide accurate information in areas not affected by large displacement dynamics (far field). On the contrary, the SAR amplitude permits measurement of displacements (although with less accuracy with respect to the SAR phase) where they are on the order of the SAR image pixel dimension, typically occurring in the near field. We are aware that while achievable accuracies of SBAS applied to the SAR phase are on the order of 1 mm/year for mean surface deformation velocities and 5 mm for surface displacement time series (Casu et al., 2006), realistic accuracies with PO-SBAS are on the order of 1/30th of the SAR image pixel size (Casu et al., 2011). However, in many cases, where large-magnitude and/or rapid deformation occurs, the analysis of the SAR amplitude information can be the only data that provides valuable results (Raucoules et al., 2013; Manconi et al., 2014).

Finally, the application of this method to SAR data acquired by high-resolution and short-revisit-time satellites, such as COSMO-SkyMed and TerraSAR-X, will further enhance the possibility of achieving better spatial and temporal sampling of the deformation field, opening new scenarios for the use of SAR data to monitor the Earth’s crust in active rift zones and elsewhere.

This work has been partially supported by MIUR (“Progetto Bandiera RITMARE”), and the Italian Department of Civil Protection. Part of the presented research has been carried out through the I-AMICA (Infrastructure of High Technology for Remote Sens. 2015, 7 15648 Environmental and Climate Monitoring-PONa3_00363) project of Structural improvement financed under the National Operational Programme (NOP) for “Research and Competitiveness 2007–2013,” co-funded with European Regional Development Fund (ERDF) and National resources. Envisat data are copyrighted by ESA. The DEM of the investigated zone was acquired through the SRTM archive. We are indebted to Carolina Pagli who encouraged the submission of the manuscript and professionally managed its review process as Guest Associate Editor. We also thank Hua Wang and one anonymous reviewer whose reviews helped to improve the final version of the manuscript.