Measurement of coseismic deformation by satellite geodesy

SAR interferometry

This geodetic technique calculates the interference pattern caused by the phase difference between two images acquired by a spaceborne synthetic aperture radar (SAR) at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. Each fringe represents a range change of half the wavelength. Thus, the contour interval is 28 mm for C-band radars such as ERS and RADARSAT and roughly four times larger, 125 mm for the L-band JERS satellite. These maps provide an unsurpassed spatial sampling density (~100 pixels/km²), a competitive precision (~1 cm) and a useful observation cadence (1 pass/month), as described in a review article by Massonnet and Feigl [1998], which I paraphrase here.

To capture an earthquake, INSAR requires three data sets: a SAR image before the earthquake, one after, and topographic information. The SAR images themselves are rich data sets well documented in the remote sensing literature [Curlander and McDonough, 1991; Henderson and Lewis, 1998]

The topographic information is necessary to model and remove the interferometric fringes caused by topographic relief as “seen in stereo” from slightly different points of view. To handle the topographic contribution, we can choose between the “two-pass” approach, [e.g., Massonnet and Feigl, 1998] and the “three-pass” or “double-difference” approach [e.g., Zebker et al., 1994]. For tectonic studies, there is usually a trade-off between the two-pass approach, which requires a digital elevation model (DEM), and the three-pass approach, which requires a third SAR acquisition. Further discussion of relative merits of the two- and three-pass approaches are beyond the scope of this chapter.

To interpret an interferogram, one must understand how different effects contribute to the fringe pattern. Many instructive examples appear in review papers by Massonnet and Feigl [1998] and Madsen and Zebker [1998]. The mathematical details appear in another review [Bamler and Hartl, 1998]. For earthquake studies, the most important effects involve topographic relief, orbital trajectories, and tropospheric refraction, usually in combination.

If the topographic information (a DEM for two-pass, or the “topo pair” in three-pass INSAR) is in error, the interferogram will contain artifactual fringes. They appear in the same location in every interferogram produced using that topographic model. To quantify this effect, Massonnet and Rabaute [1993] define the altitude of ambiguity h_a , or the shift in altitude needed to produce one topographic fringe. Indeed, this parameter is inversely proportional to the perpendicular component of the (“baseline”) vector separating the two orbital trajectories, conventionally written B, pronounced “B-perp”, and given in meters [Zebker and Goldstein, 1986]. The number of “topographic” fringes is proportional to B_ and inversely proportional to h_a. Thus we seek pairs of orbital trajectories with a small separation, that is, with small (absolute) values of B_ and large (absolute) values of h_a for earthquake studies. It turns out that for the ERS satellites, an acceptably good orbital pair has both B_ and h_a approximately equal to 100 m.

A topographic error of  meters in the DEM will produce a phase error of  /h_a fringes in the resulting interferogram. Errors in typical DEMs range from 10 to 30 m [Wolf and Wingham, 1992], implying that choosing a pair of images with |h_a | between 20 and 60 m will yield an interferometric measurement with an error better than  /h_a = ± 1/2 cycle, or ± 14 mm for ERS. Small values of |h_a | can mask even large signals with artifactual topographic fringes. In an extreme (and rare) case, Massonnet and Feigl [1995a] uncovered a topographic error of  ~250 m, roughly 8 times larger than the published precision for the DEM. This artifact resembles the fringe pattern produced by a small earthquake. Avoiding such confusion requires looking at several interferograms with different values of h_a . For an earthquake, the number of coseismic fringes does not depend on h_a.

Atmospheric effects can also complicate the interpretation of an interferogram. Indeed, variations in the refractive index of the troposphere are the current limiting source of error in the INSAR technique [Delacourt et al., 1998; Goldstein, 1995; Hanssen, 1998; Massonnet and Feigl, 1995a; Rosen et al., 1996; Tarayre and Massonnet, 1996; Williams et al., 1998; Zebker et al., 1997]. Potentially, one could confuse a topographic signature with a displacement, if propagation effects create fringes which "hug" the topography like contour lines, but which measure the change in tropospheric delay, as first observed as several concentric fringes on a 1-day interferogram on Mount Etna [Massonnet and Feigl, 1998];. One can recognize this subtle effect by pair-wise logic [Massonnet and Feigl, 1995a] or using the DEM and local meteorological observations [Delacourt et al., 1998; Williams et al., 1998]. Yet separating the tropospheric noise from the deformation signal can be challenging, particularly when the signal is small, e.g. the magnitude 5.2 St. Paul de Fenouillet earthquake [Rigo and Massonnet, 1999].

Correlation of two optical images acquired by optical satellites such as SPOT

It is also possible to detect (large) coseismic displacements by correlating two optical images. The “lag” vectors estimated between the corresponding sub-pixel cells of a pre-quake and a post-quake image yields the horizontal components of the coseismic displacement vector with sub-meter precision and hectometer resolution [Crippen, 1992; Crippen and Blom, 1992; Vadon and Massonnet, 2000; Van Puymbroeck et al., 2000]. To capture the Izmit earthquake of August 17, two groups have correlated optical images acquired by the SPOT4 satellite on July 9 and the SPOT2 satellite on September 16, after anti-aliasing resampling [Michel and Avouac, 2000; Vadon and Massonnet, 2000].

The result is a measurement of the offset between the two images at each 20-meter pixel where the correlation succeeds. In this case, lines of the SPOT images are almost parallel to the fault, we use only the offset in columns to determine the horizontal component of displacement in the direction S77°E. Although the two images were acquired in very similar geometric configurations, the correlation map still shows the effects of slight differences in spacecraft position and sensor attitude. Michel and Avouac [2000] model these explicitly, while Vadon and Massonnet [2000] model them empirically with a biquadratic polynomial fit. These results are shown in Error: Reference source not found and Figure 2, respectively. As Michel and Avouac write, SPOT images can also be used to map accurately the fault zone and determine the slip distribution by sub-pixel correlation of images acquired before and after an earthquake. It reveals a less than 100m wide and very linear fault zone that can be traced for 70km from Gölcük to Akyazi. The obtained slip distribution compares well with the field measurements, and is consistent with ground deformation measured at some distance from the fault zone using SAR images. Very little slip was absorbed off the main fault plane.” [Michel and Avouac, 2000].

Both these maps show a discontinuity corresponding to the trace of surface rupture mapped between the east end of the bay at Izmit and Sapanca Lake. The mean offset between two 5-by-20-km blocks on opposite sides of the fault is 4.60 ± 0.24 m. After median filtering with a 2-by-2-km window, Feigl et al. [2001] retain 148 values.

Figure 2. Component at S77°E of the coseismic displacement field measured by correlation of SPOT images. As described by Vadon and Massonnet (2000), these images were acquired on July 9 and September 16, 1999. These original 20-m pixels have been filtered using a 2-dimensional median filter on a 100-by-100-m window [Feigl et al., 2001].

Berthier Izmit Figure

Figure 3. The left panel shows the offsets in longitude determined by correlating two SPOT images acquired on 9 July and 16 September 1999. A clear discontinuity in the offset field indicate the location of the surface rupture. Area where the correlation failed are displayed in grey. The location and co-sismic deformation recorded at 4 GPS stations are also added. The right panel represent the slip along the surface rupture as a function of longitude. The blue dots represent the mean slip every 300 meters; the red dots a running average over 3-km segments [Berthier, 2005].