Measurement of coseismic deformation by satellite geodesy



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Volcanos

Volcanos continue to be the most fruitful target for INSAR studies. We know the location of the most active ones. We know that shield volcanos produce better fringe patterns than stratovolcanos [Massonnet and Sigmundsson, 2000; Zebker et al., 2000]. We know how to choose images to optimize radar correlation, by considering ground, weather, and orbit conditions. Techniques for separating tropospheric artifacts from deformation signals are are particularly useful in this case [e.g., Beauducel et al., 2000a].

For these reasons, INSAR on volcanos is now fully validated. The feasibility studies of the past few years have proven the concept. It works! Progress in the next few years will come from operational monitoring of many volcanos. This will require routine acquisitions every time the satellite passes over the volcano. Although some may argue against the utility of acquiring SAR images during the winter when there is snow on the ground, simple comparison of SAR images (without interferometry) has already revealed a subglacial eruption [Alsdorf and Smith, 1999].

Landslides and subsidence


[Carnec, 1996; Carnec and Delacourt, 2000; Carnec and Fabriol, 1999; Carnec et al., 1996; Delacourt, 1997; Delacourt et al., 2000; Fruneau et al., 1996].

Glaciers


[Joughin et al., 1996a; Joughin et al., 1996b; Joughin, 1995; Joughin et al., 1998; Joughin et al., 1995; Legresy et al., 2000; MacAyeal et al., 1998; Michel and Rignot, 1999; Rignot, 1996a; Rignot, 1996b; Rignot, 1997; Rignot et al., 1996; Rignot et al., 1995; Rignot, 1998].

Interseismic Deformation


Several studies have successfully applied INSAR to measure subtle deformation during the intersesimic interval between large earthquakes. [Rosen et al., 1998][Bürgmann et al., 2000].

[Peltzer, et al., 2001]

[Wright et al., 2000a].[Wright, et al., 2004a; Wright, et al., 2004b]

Postseismic Deformation


Studying the postseismic deformation in the months following a large earthquake can help understand mechanical behavior of the lithosphere. The mainshock provides a known impulse and satellite surveying, the response. By measuring and modelling these signals, we can construct a mechanical experiment to determine the relevant rheologic properties. This is one one of the few cases in solid-earth geophysics where we can access the time dependence of the the phenomenon. The time scales of both the phenomena and the measurements are short enough to make the problem tractable.

Landers provides a good case study, although earlier examples exist. Here, both GPS and INSAR also measured postseismic deformation [Bock et al., 1997; Massonnet and Feigl, 1995a; Massonnet et al., 1994; Massonnet et al., 1996b; Peltzer et al., 1996; Savage and Svarc, 1997; Shen et al., 1994]. See also: [Deng et al., 1998; Peltzer et al., 1998; Pollitz et al., 2000]. And more recently : [Jacobs, et al., 2002; Fialko, 2004a; 2004b].

The same arid conditions also favor INSAR for measuring postseismic deformation following the M ~ 7 earthquake at Hector Mines in 1999 [Sandwell et al., 2000].

Postseismic deformation involving afterslip down-dip from the coseismic slip was also captured following the Izmit earthquake using GPS [Ergintav et al., 2000; Reilinger et al., 2000].

Other studies using INSAR have improved our understanding of post-seismic deformation [Jonsson, et al., 2003; Chlieh, et al., 2004; Arnadottir, et al., 2005].

Troposphere


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. This effect was first observed as several concentric fringes in a 1-day interferogram on Mount Etna [Massonnet and Feigl, 1998]. One can recognize this subtle effect using pair-wise logic [Massonnet and Feigl, 1995a] or using a 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 earthquake near St. Paul de Fenouillet, France [Rigo and Massonnet, 1999].

The interferograms spanning the Izmit earthquake illustrate the dangers of interpreting tropospheric fringes as deformation. There, Reilinger et al. [2000] found that “both the ERS-1 and ERS-2 interferograms are significantly contaminated by tropospheric artifacts”. Accordingly, they chose not to include these INSAR results in their estimate of coseismic slip. The inversion procedure is particularly sensitive to gradients in the displacement field, which are in turn sensitive to errors in range along the steep radar lineof sight. In the far field, at 50 km from the fault, an error of one 28-mm fringe in range can alter the estimate of slip on the fault by several meters. This may explain why models based on these INSAR observations tend to find more slip on the fault, and thus a higher total moment, than does the GPS-only solution [Reilinger et al., 2000].

Left uncorrected, the tropospheric artifact appears as a residual of approximately 8 cm in range almost 50 km north of the fault when Delouis et al. [2001] include the ERS-2 interferogram in their inversion.

To mitigate the correlation of tropospheric delay with topographic elevation, we can estimate additional parameters in addition to the parameters of geophysical interest in our models. To do this, Feigl et al. [2001] implicitly assume a uniform troposphere. They then estimate the (negative) correlation between tropospheric delay along the radar line of site and the topographic elevation. This “tropo-topo” correlation coefficient thus adds a free “nuisance” parameter in their estimation procedure.This parameterization differs slightly from the layered tropospheric model employed by Beauducel et al. [2000a] at Etna. The single layer approach adds only one free parameter, the gradient, to the inversion. The layered model adds one parameter per tropospheric layer. Reducing the number of nuiscance parameters reduces the trade-off between the nuisance parameters and those of interest in the geophysical model for deformation.

For the ERS-1 coseismic interferogram at Izmit, Feigl et al. [2001] find a strong correlation between topographic relief and tropospheric delay, yielding a vertical gradient of –36 ± 6 mm in range per kilometer of elevation. This value is of the same order of magnitude as the worst cases observed in radiosonde profiles [Hanssen and Klees, 1999]. The INSAR estimate of the tropospheric gradient may be biased by the non-uniform distribution of measurements with respect to elevation [Beauducel et al., 2000a].

The strong tropospheric gradient produces over more than three fringes in the valley around Izmit, just as in the aseismic one-day interferogram (Figure 5). Estimating this nuisance parameter yields a moment of 2 x 1018 N.m lower than the value we find without it. This implies that tropospheric artifacts may have slightly increased the moment previous inversions using the ERS interferograms




Figure 5. Interferogram showing the phase difference between an ERS1 image acquired August 12, 1999 (orbit number 42229) and an ERS-2 image acquired August 13, 1999 (orbit number 22556). The altitude of ambiguity is 40 m, but the DEM used for this calculation has an estimated RMS accuracy of ~ 7 m. Orbital fringes have been modeled empirically with a linear gradient. As a result, the remaining fringes must be tropospheric in origin [Feigl et al., 2001].

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