Ecv ice Sheets Technical Proposal

3.2WP2000 - Development and validation

3.2.1WP2100 - Multitemporal MAI development

A dedicated WP shall be devoted to investigating the feasibility of measuring deformation time-series from InSAR data stacks in the azimuth direction, i.e. the ground projection of the satellite flight-path. The latter is roughly 10° away from the north-south direction at mid-latitudes, thus offering an excellent sensitivity to motion in this direction. Within the scope of the project, the challenge lies in achieving sufficiently high measurement accuracies to retrieve even small interseismic deformation rates (a few mm/yr in the areas of interest of this study). If these accuracies could be obtained, maintaining spatial resolutions between 1 km and 10 km, it would be a very useful result for the project, which would allow to better resolve individual seismic sources in areas of high fault density like the central Appenines. In fact the only other source for north-south motion is GPS, with an average distance between the stations of about 30 km in Italy.

Two SAR-based techniques have been proposed in literature to measure azimuth displacement: the first (chronologically) is rather a family of techniques, which comprises so-called speckle or intensity tracking (Gray et al. 1998), complex cross-correlation (Joughin, 2002) and coherence tracking (Derauw, 1999). The second method is known as Spectral-Diversity (Scheiber and Moreira, 2000), Multi Aperture Interferometry (MAI), (Bechor & Zebker 2006; Jung et al. 2009) or azimuth Split-Bandwidth Interferometry (SBI), owing to the similarity with the concepts originally proposed by Madsen and Zebker, (1992) and later reformulated by Bamler and Eineder, (2005).

A multi-temporal version of intensity tracking was proposed by Casu et al., (2011), by generalizing the SBAS approach of Berardino et al., (2002). They applied this method to retrieve the 2D deformation (range and azimuth) within the volcanic crater of Sierra Negra in the Galapagos archipelago. On areas within the caldera, where coherence was so low for conventional SBAS to fail, the azimuth error standard deviations with respect to GPS data were <10 cm. These accuracies are an order of magnitude worse than multi-temporal DInSAR methods and are unusable for any interseismic deformation measurement worldwide.

We propose to investigate a novel multi-temporal approach based on MAI. Compared to classical DInSAR, although MAI is typically less accurate by a factor 4 on single-pair measurements, for a given coherence level (Bechor and Zebker, 2006; Jung et al., 2009), it is not affected by the main error sources of DInSAR, namely tropospheric propagation and phase unwrapping, which is not required unless displacements comparable to the antenna length are sought. Compared to the offset-tracking techniques mentioned above, MAI has a higher spatial resolution as well as a higher measurement accuracy for a given coherence level. Furthermore, being a phase-based technique, more powerful filtering approaches can be applied (Goldstein and Werner, 1998).

In the proposed algorithm, a stack of unfiltered full-resolution MAI interferograms is formed and provided as an input to the combined Persistent Scatterer (PS) and Small Baseline (SB) approach of Hooper, (2008) and Hooper et al., (2007). The PS and SB-point selection approaches are in fact methods for phase stability estimation, under the assumptions that the sought deformation is spatially correlated and one of the error terms is correlated with the perpendicular baseline. These assumptions hold for conventional DInSAR, but also for MAI (Jung et al., 2009). It is therefore expected that the coherent point selection approach will be directly applicable, although new values more suitable for MAI will most likely have to be established for the applied thresholds. The subsequent steps of the multi-temporal analysis shall be equally applicable, with the important exeption of phase unwrapping, which is not required for the sought displacement rates (Bechor and Zebker, 2006). It is to be verified whether an additional filtering step will have to be introduced, to improve measurement accuracy. In this case, the averaging of statistically homogeneous pixels should be considered (Ferretti et al., 2011).

3.2.2WP2200 - Multitemporal DInSAR enhancements

The Small Baseline Subset (SBAS) (Berardino et al. 2002) is a technique used to extract deformation time series from stacks of interferometric acquisitions over wide areas. It carries out an analysis of the data based on the generation of an interferogram stack obtained by pairing the acquisition to form a redundant network in the acquisition domain defined by the spatial and temporal offsets (spatial and temporal baseline) with respect to a master, reference image. Differently from Persistent Scatterers Interferometry (PSI) (Ferretti 2001), multilooking (i.e., spatial averaging) and spatial and temporal baseline limitation is applied in SBAS to mitigate the effects of decorrelation of radar echoes. The spatial decorrelation is an effect which increases with the (numerical) value of the range resolution. The spatial averaging reduces the interferometric noise at the expense of a spatial resolution loss; it provides at the same time an estimate of the coherence. Phase unwrapping, via modern multitemporal algorithms, which may imbed also the models as better explained in the following, is then applied on a sparse grid of coherent pixels (Fornaro 2009). The monitoring of deformation is finally achieved, at low resolution, by separating in a joint estimation framework the signal components based on specific deterministic or statistical characterizations. Deterministic modeling allows first the estimation of the (temporally) linear motion (deformation mean velocity) and of the residual topography: atmospheric phase delay is then also estimated due to its uncorrelated nature along the time and then subtracted to access the final time series. Modeling in terms of deformation mean velocity and residual topography can be also used to improve the performances of unwrapping (Fornaro 2009, Fornaro 2011). The selection of the processing sparse grid is a fundamental step in multipass DInSAR processing to separate reliable and unreliable phase components at the wrapped interferogram level to perform reliable phase unwrapping. A commonly adopted strategy is to select a grid of pixels showing an average spatial coherence degree above a convenient threshold.

The choice of a minimum grid of pixel for all the interferograms is mandatory to perform the extraction of time series and to apply advanced phase unwrapping approached. Nevertheless, if the spatial density of the deformation measurement is the main aim, alternative solutions can be implemented.

Data filtering is a viable way to increase the coherence and recently a new, powerful approach has been proposed based on the analysis of the data covariance matrix, namely SQUEESAR (Ferretti 2011), that allows extracting an equivalent persistent scatterers mechanism showing higher coherence. More recently (Fornaro 2013) this filtering approach has been extended by relaxing the constant amplitude constraint.

A different very simple solution, recently proposed in the literature (Sowter 2013), to increase the spatial density is based on the use of a reduced subset of interferograms, not necessarily characterized by a large redundancy, but rather by a low degree of connectivity between the acquisitions at the interferogram generation stage. More specifically, by limiting the interest only to the deformation mean velocity, it is possible to keep only interferograms which are characterized by high level of coherence even if this implies the use of a considerably reduced subset of interferograms with respect to that commonly used in classical SBAS approaches. This solution allows retaining coverage on pixels that appear intermittently coherent and is therefore called intermittent SBAS.

With reference to application to seismic hazard the intermittent SBAS solutions for mean deformation velocity measurement with reduced (most coherent) interferogram stacking will be implemented and compared to the advanced version of the SBAS technique that includes a spatially-adaptive covariance based filtering module which is able to reconstruct the whole time series deformation based on the processing of redundant interferogram stacks. In particular it is of interest to verify whether an significant increase in measurement coverage is observed, as reported in (Sowter et al., 2013), and if the price to pay in terms of measurement accuracy is still acceptable for interseismic deformation measurement applications. Increased coverage, if achieved, would ease the interpretation of the deformation patterns and improve the reliability of the phase unwrapping process.

3.2.3WP2300 - SAR and GPS integration

Current continuous GPS measurements allow the determination of distances at sub-cm accuracy level for receiver separations of tens to hundreds of kilometers, however the cost of GPS receivers is quite high thus posing a limit to the spatial density of GPS networks. Conversely DInSAR is capable of measuring deformations with high spatial resolution but poor temporal resolution. Thus it is of a great interest to combine GPS and DInSAR data in order to correct for long-wavelength systematic errors, typically caused by the inaccurate knowledge of the SAR sensor orbit and other poorly characterized error sources (e.g. oscillator drift and long-wavelength atmospheric propagation effects). For this reason a dense GPS network can provide the ancillary spatial and temporal information useful to mitigate and possibly remove possible orbital artifacts from the interferograms. It must be further considered that large-scale tectonic deformations might appear as signal ramps, which can be easily confused and removed as orbital artifacts.

For these reasons we developed in 2009, after L’Aquila earthquake, a robust system to “tune” InSAR maps with GPS results. Firstly, we generated the GPS solutions of cumulated displacement with the same time span of the interferometric pairs. We then calculate the parameters of a first or second, whether permitted by data, order surface such that the discrepancies between InSAR and GPS, at GPS locations, are minimized. The comparison is made after projecting the 3D GPS measurements into the InSAR LoS. Against its simplicity, a strong effort has been put in the GPS and InSAR data handling accounting for their uncertainties in the most rigorous way. Full matrices of variance/covariance are provided for SAR and GPS; the minimization of their misfit is carried out with a linear weighted inversion to retrieve the orbital surface parameters. Moreover, the SAR value at the GPS location is retrieved with a local Kriging interpolation where the algorithm parameters are tuned with the covariance autocorrelation function of SAR data related to the same region.

A different task pertains to the estimation of three components of the velocity vector at a given location of the Earth surface from three known datasets: ascending and descending one-dimensional LOS range rate and GPS three-dimensional velocity vectors. The GPS velocities are known only at a few sparse locations, whereas DInSAR velocities are inferred at PS positions. Some interpolation technique such as kriging must be used in order to interpolate the GPS and DInSAR values on given grid points and subsequently the joint inversion of the velocity data provides the estimate of the tree-dimensional velocity vector at any grid point. Alternatively, appropriate weighting functions of the GPS and DInSAR data could be used in the joint inversion. A new approach will be explored in which the optimal grid resolution results from a given user requirement, e.g. for a given level of precision or correlation of the velocity estimates.

3.2.4WP2400 - Integration of deformation measurements for hazard modelling

Innovative methods to assess seismic hazard using velocity (or equivalently strain rate) maps were presented by Bird et al. (2009) , Bird et al. (2010) and Carafa and Kastelic (in press). To convert any velocity map or any part of off-fault deformation to a forecast of long-term shallow seismicity, the aforementioned studies applied the hypotheses, assumptions, and equations of Bird and Liu (2007), who referred to them as the “seismic hazard inferred from tectonics” (SHIFT) hypotheses: 1) The long-term seismic moment rate of any tectonic fault, or any large volume of permanently deforming lithosphere, is approximately that computed using the coupled seismogenic thickness (i.e., the seismic coupling coefficient times the seismogenic thickness) of the most comparable plate boundary-type; and 2) The long-term rate of earthquakes generated along any tectonic fault, or within any large volume of permanently deforming lithosphere, is approximately that computed from its moment rate by using the frequency/magnitude distribution of the most comparable plate boundary-type.

In standard and consolidated approaches to PSHA, the seismic rates are defined for each source zone (faults or area) on the basis of the seismicity reported in the catalogue, once the catalogue is declustered and its time intervals of completeness are determined. In other words, the seismic rates depend strongly on the observed earthquakes. In this project the aim is to obtain the information on the earthquake recurrence model from geodetic survey, so that this approach can be applied in regions where historical seismicity is poorly constrained or absent. We will define the recurrence rates for each seismic source, being the sources, the faults or a regular grid that covers the investigated volume, as previously introduced by the SHIFT approach. For a given site, we: (1) calculate the annual frequencies of exceedance for a suite of ground motion levels (i.e., a hazard curve) due to the seismicity of each single source; and (2) estimate the maximum shaking that is expected to be exceeded for a range of probability of exceedance. For each site, step (1) is repeated for all sources in the source model, and step (2) is calculated by summing the results of step (1) to give the annual frequencies of exceedance for a suite of acceleration levels and spectral periods at the site due to all sources.