Constraints on surface deformation in the Seattle, WA, urban corridor from satellite radar interferometry time-series analysis
Constraints on surface deformation in the Seattle, WA, urban corridor from satellite radar interferometry time-series analysis
Geophys. J. Int. (2008) 174, 29–41 doi: 10.1111/j.1365-246X.2008.03822.x GJI Geodesy, potential ﬁeld and applied geophysics Constraints on surface deformation in the Seattle, WA, urban corridor from satellite radar interferometry time-series analysis Noah J. Finnegan,1 Matthew E. Pritchard,1 Rowena B. Lohman1 and Paul R. Lundgren2 1Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York, USA. E-mail: firstname.lastname@example.org 2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA Accepted 2008 April 8. Received 2008 April 8; in original form 2007 November 2 S U M M A R Y We apply differential InSAR (DInSAR) time-series techniques to the urban corridor between Tacoma, Seattle and Everett, WA, using 93 interferograms from three satellites (ERS 1, ERS 2 and RADARSAT-1) between 1992 and 2007.
Our goal is to study local tectonic, geomorphic and groundwater processes. Consequently, we remove long-wavelength (>50– 100 km) deformation signals from unwrapped interferograms. By comparing surface velocities generated via the time-series technique at more than two million points within the overlapping region between two independent ERS tracks, we estimate the uncertainty of relative surface velocity measurements to be ∼0.5 mm yr−1 in the vertical. We estimate the uncertainty of relative displacement measurements to be ∼5.4 mm, given our comparisons of DInSAR- derived time-series to GPS data, a result that is consistent both with previous DInSAR time- series analysis and with the uncertainty expected from GPS displacements projected onto the radar line-of-sight.
Active tectonic deformation at shallow depths on the region’s numerous east–west structures is absent over the ∼11.5 yr of SAR data examined. Assuming that the south-dipping thrust beneath Seattle and Tacoma takes up 3 mm yr−1 of north–south shortening, our data indicate that the fault must be currently locked to a depth of greater than 10 km. We also document extensive groundwater-related deformation throughout much of the study region. Most notably, we identify sharp, linear deformation gradients near Federal Way, WA, and running between Sumner, WA, and Steilacoom, WA. These features may mark the locations of previously unmapped fault splays that locally control groundwater movement.
We find no slow landslide deformation on any of the numerous mapped slide complexes within Seattle, although regions of known active landsliding, such as along Perkins Lane in Seattle, exhibit radar phase de-correlation. These observations are consistent with relatively infrequent and rapid landslide deformation within Seattle.
Key words: Time series analysis; Radar interferometry; Hydrology; Intra-plate processes; Continental tectonics: compressional; North America. 1 I N T RO D U C T I O N Differential interferometric synthetic aperture radar (DInSAR) time-series analysis can resolve mm-scale vertical deformation and reveal rich patterns of deformation in both space and time (e.g. Ferretti et al. 2001; Lundgren et al. 2001; Berardino et al. 2002; Schmidt & Bürgmann 2003; Lanari et al. 2004; Casu et al. 2006; Kwoun et al. 2006; Pritchard & Simons 2006; Shanker & Zebker 2007). Here, we apply DInSAR time-series techniques from three satellites (ERS 1, ERS 2 and RADARSAT-1) to the urban corridor between Tacoma, Seattle and Everett, WA (Figs 1a and b), over the time-period 1992–2007.
The goals of our work are twofold, as follows.
First, in order to assess the utility of DInSAR time-series analysis in the Pacific Northwest, a scientifically alluring but challenging location for conventional radar interferometry, we determine the magnitude of the uncertainty in our time-series techniques that results both from atmospheric noise and from our assumptions about the contribution of vertical versus horizontal motion to the DInSAR observations. To this end, we compare DInSAR-derived surface elevation time-series data and GPS-derived surface elevation time- series data to determine the uncertainty of DInSAR relative to GPS.
Additionally, we compare two contemporaneous vertical velocity maps generated from overlapping ERS satellite tracks in order to quantify the uncertainty of mean relative vertical surface velocities generated via independent time-series analyses.
The second goal of this paper is to apply time-series meth- ods to establish new geodetic constraints within the densely pop- ulated study area. Specifically, our targets are: (1) to define patterns and magnitudes of groundwater-related deformation in C 2008 The Authors 29 Journal compilation C 2008 RAS
30 Noah J. Finnegan et al. regional aquifers; (2) to better characterize the location of and activity on faults within the Puget Sound Lowland; (3) to mea- sure rates of creeping deformation on mapped landslides in Seattle; and (4) to independently quantify how short-wavelength deforma- tion may be contaminating GPS data collected within the study area.
Figure 1. (a) Tectonic and geomorphic overview of the study area. Fault locations in A–D are taken from US. Geological Survey (2006) and Johnson et al. (1999, 2004b). Geophysical anomaly data are based on the interpretations in Brocher et al. (2001) and Brocher et al. (2004). The locations of GPS stations are indicated by the black dots accompanied by a four-letter station identifier (www.geodesy.cwu.edu/). SFZ = Seattle fault zone, TFZ = Tacoma fault zone. (b) Patterns and magnitudes of mean radar LOS surface velocity calculated from 38 RADARSAT-1 Finebeam 1 interferograms spanning the period 2002.18–2006.19.
(c) Patterns and magnitudes of mean radar LOS surface velocity calculated from 24 ERS track 156 interferograms spanning the period 1992.52–1999.97. (d) Patterns and magnitudes of mean radar LOS surface velocity calculated from 31 ERS track 428 interferograms spanning the peri- od 1992.58–1999.83. In (a)–(d), the topographic backdrop is generated from 1-arcsec SRTM data.
2 M E T H O D S A N D DATA The Pacific Northwest poses challenges to researchers applying DInSAR methods due to its extensive and seasonally variable vege- tative cover. However, within the urban corridor containing the cities of Tacoma, Seattle and Everett (Fig. 1b), we find that radar scattering C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
Constraints on surface deformation, Seattle, WA 31 properties for C-band radar (about 5.6 cm wavelength) are stable enough to permit the creation of coherent interferograms with tem- poral baselines shorter than 3 yr.
In this study, we present results from both the ERS 1/2 satellites of the European Space Agency, for which we have data from two tracks that overlap by ∼50 km, and from the RADARSAT-1 satellite (Finebeam 1) of the Canadian Space Agency, which overlaps with both ERS tracks (Tables 1 and 2 and Fig. 1a).
To process the ERS 1/2 data, we use the Caltech/JPL ROI_PAC software package (Rosen et al. 2004) with precise satellite orbits from Scharroo and Visser (1998). To process the RADARSAT-1 data, we use a modified version of ROI_PAC Table 1. Summary of the SAR data coverage. Sensor Track/mode Time span # Acquisitions # Interferograms Incidence angle over Seattle ERS 1/2 156 1992–2000 21 24 25.5◦ ERS 1/2 428 1992–2000 27 31 19.6◦ RADARSAT-1 Finebeam 1 2002–2006 18 38 39.5◦ Table 2. Summary of DInSAR data used in the analysis. RADARSAT-1 Finebeam 1 ERS Track 428 ERS Track 156 Start date End date Perpendicular Start date End date Perpendicular Start date End date Perpendicular baseline (m) baseline (m) baseline (m) 2/9/2002 2/28/2003 −310 7/5/1992 1/31/1993 106 8/25/1992 6/16/1992 26 2/9/2002 3/24/2003 −47 7/5/1992 8/29/1993 −99 9/29/1992 8/25/1992 2 2/9/2002 4/17/2003 −282 12/27/1992 1/31/1993 −210 1/12/1993 6/16/1992 −17 2/28/2003 4/17/2003 28 1/31/1993 3/7/1993 14 1/12/1993 8/25/1992 149 3/24/2003 4/17/2003 −235 3/7/1993 5/16/1993 −76 3/23/1993 9/29/1992 −105 3/24/2003 8/15/2003 −161 5/16/1993 7/25/1993 −14 3/23/1993 12/8/1992 148 4/17/2003 8/15/2003 74 5/16/1993 8/29/1993 76 4/20/1995 1/12/1993 −146 3/24/2003 10/2/2003 −124 7/25/1993 8/29/1993 −71 5/25/1995 1/12/1993 −163 8/15/2003 10/2/2003 37 7/25/1993 7/18/1995 −7 5/25/1995 4/20/1995 3 8/15/2003 12/13/2003 −7 8/29/1993 10/3/1993 14 1/26/1996 12/8/1992 −33 10/2/2003 12/13/2003 −44 8/29/1993 4/4/1995 −23 4/5/1996 4/20/1995 76 4/17/2003 4/11/2004 121 4/4/1995 5/29/1996 103 4/6/1996 5/25/1995 −1 8/15/2003 4/11/2004 47 6/13/1995 12/5/1995 −170 8/8/1997 1/25/1996 10 10/2/2003 4/11/2004 10 6/13/1995 12/6/1995 30 8/8/1997 1/26/1996 100 12/13/2003 4/11/2004 54 7/18/1995 9/26/1995 53 9/12/1997 1/25/1996 24 2/28/2003 7/16/2004 −183 7/18/1995 12/5/1995 −82 9/12/1997 1/26/1996 −253 6/22/2004 7/16/2004 75 7/18/1995 7/23/1997 88 9/12/1997 8/8/1997 114 8/15/2003 8/9/2004 50 9/26/1995 12/5/1995 −261 8/28/1998 8/8/1997 28 4/11/2004 8/9/2004 3 10/31/1995 11/1/1995 −2 8/28/1998 9/12/1997 −190 12/13/2003 11/13/2004 96 12/5/1995 12/6/1995 −71 9/17/1999 4/5/1996 11 4/11/2004 11/13/2004 42 12/5/1995 1/9/1996 −34 11/26/1999 1/25/1996 89 8/9/2004 11/13/2004 39 1/9/1996 8/27/1997 −164 11/26/1999 8/8/1997 −61 2/28/2003 12/7/2004 −54 5/29/1996 3/10/1999 −361 11/26/1999 8/28/1998 85 12/13/2003 12/7/2004 −149 7/23/1997 8/27/1997 −29 11/26/1999 9/17/1999 −275 2/28/2003 2/17/2005 −18 7/8/1998 9/16/1998 137 – 4/17/2003 2/17/2005 −46 7/8/1998 12/30/1998 166 – 12/7/2004 2/17/2005 36 9/16/1998 12/30/1998 −44 – 2/28/2003 3/13/2005 273 12/30/1998 3/10/1999 −408 – 3/24/2003 3/13/2005 10 2/3/1999 3/10/1999 116 – 11/13/2004 3/13/2005 82 2/3/1999 10/6/1999 84 – 8/15/2003 8/28/2005 143 3/10/1999 10/6/1999 −32 – 8/9/2004 8/28/2005 93 – 3/13/2005 8/28/2005 −28 – 3/13/2005 12/26/2005 −65 – 8/28/2005 12/26/2005 −37 – 8/9/2004 2/12/2006 −8 – 2/17/2005 2/12/2006 162 – 8/28/2005 2/12/2006 −101 – (www.roipac.org/Radarsat).
Interferograms were filtered using ROI_PAC’s non-linear spectral filter (Goldstein & Werner 1998). We use 1-arcsec (approximately 30-m resolution) Shuttle Radar Topography Mission (SRTM) digital elevation models (DEMs) to remove the topographic signal embedded within the InSAR phase (Farr & Kobrick 2000). Processed interferograms were unwrapped using SNAPHU (Chen & Zebker 2002), and then for each of the three data sets the unwrapped interferograms were co-registered to a master scene in radar coordinates. The spatial resolution of the raw ERS interferograms is ∼20 m pixel−1 and for the RADARSAT-1 Finebeam 1 interferograms ∼5 m pixel−1 ; however, we applied spa- tial averaging to reduce noise and therefore achieved a final spatial C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
32 Noah J. Finnegan et al. resolution of 90–100 m pixel−1 . We subtract a second-order poly- nomial, best-fitting surface from all processed, unwrapped interfer- ograms in order to remove apparent long-wavelength deformation introduced due to uncertainties in satellite orbits (particularly for RADARSAT-1). We note that because of this necessary process- ing step, the three time-series described below are sensitive only to short-wavelength deformation at spatial scales smaller than the dimensions of the study area itself. Because the dimensions of our study region are not square (∼50 km east–west by ∼100 km north– south), the spatial wavelength of the removed polynomial surface and, therefore, the shape of deformation signal that could be re- moved along with it, depends on the orientation with respect to the study region dimensions.
For north–south striking deformation, the smallest wavelength signal that could be removed during processing would be a parabolic deformation pattern with a width correspond- ing to the ∼50 km east–west width of the study area itself. Alter- natively, for east–west striking deformation, parabolic deformation patterns with widths larger than the ∼100 km north–south length of the study area would be removed by our processing. Hence, the methods applied in this paper are sensitive to deformation at spatial scales less than 50–100 km and are insensitive to long-wavelength deformation due to, for instance, interseismic deformation or slow slip events (Wang et al.
2003; Melbourne et al. 2005) associated with the subduction zone interface.
To put the individual interferograms within a comparable ref- erence frame, we fix the average deformation of each unwrapped interferogram to be zero. We favour this approach over fixing all deformation relative to a single reference point (e.g. Schmidt & Bürgmann 2003) because of the uncertainty in regional deforma- tion and therefore in our inability to locate with confidence a single stable reference point. However, it is worth noting that when we calculate deformation relative to a single reference point near down- town Seattle, our results are essentially identical to those obtained by simply assuming that the mean deformation across the study area is zero (Appendix A).
Therefore, we are confident that the results presented below are insensitive to the method used for calculat- ing relative deformation. We emphasize that due to our choice of calculating relative deformation, all of the deformation discussed below should be considered as local, relative deformation. In other words, areas identified as subsiding or uplifting are doing so only in relation to their immediate surroundings. Such an approach is appropriate for measuring local, short-wavelength deformation sig- nals. However, we acknowledge that before using our results in a more regional analysis, they would need to be tied to an indepen- dently determined stable reference.
The temporal resolution of our analysis is determined by the interval between time-adjacent SAR acquisitions. Because of the large number of interferograms used in our analysis, there are mul- tiple constraints on deformation for many time-intervals. Therefore, after all of the interferograms from a particular satellite track are co-registered in radar coordinates to a single master scene, we apply a linear least-squares inversion scheme to each set of interferograms (e.g. Lundgren et al. 2001), solving for the deformation history that best fits the entire set of temporally overlapping interferograms.
The implicit assumption of the inversion is that deformation measured in any one interferogram is the sum of the deformation within each of the time-intervals encompassed by that interferogram. By mini- mizing the misfit between the modelled deformation and the actual deformation for each interferogram, we solve for the deformation over every time-interval spanning time-adjacent SAR acquisitions. By weighting the inversion with the overall phase variance of each unwrapped interferogram (e.g. Kwoun et al. 2006), we compensate for the fact that some interferograms are inherently noisier than others.
We convert the final time-series to geographic coordinates using the SRTM DEM.
Within the heavily urbanized region of the study area, radar phase coherence was high in essentially all the interferograms used in this study. However, depending on the temporal baseline of the pair and the seasons of the SAR acquisitions used, the phase coherence out- side urban centres was less consistent. In order to maximize the spatial coverage of the inversion, we linearly interpolated across incoherent areas in the unwrapped interferograms (e.g. Berardino et al. 2002). We then used the interpolated, unwrapped interfer- ograms in the inversion described above, introducing an implicit spatial smoothing relative to deformation rates calculated from the original set of points.
In the results presented below, we mask out pixels where more than a threshold percentage of observations were generated via interpolation. For ERS track 428 and RADARSAT-1 Finebeam 1, we used a threshold of 50%, and for ERS track 156 we used a threshold of 67%. The choice of the specific threshold value for each of the three sets of interferograms reflects a balance between, on the one hand, including as many areas that sometimes, but not always, are coherent in our analysis and, on the other hand, excluding regions with obvious unwrapping errors and/or unac- ceptable levels of noise. In general, we found that the choice of the specific threshold did not dramatically affect the results within the study region (Appendix B).
3 R E S U LT S Figs 1(c)–(e) depict the patterns of mean relative surface velocity in the direction of the radar line-of-sight (LOS) derived from the time-series inversions using the RADARSAT-1 (Fig. 1c) and ERS (Figs 1d and e) interferograms. Overlaid on the figures are mapped fault traces (US Geological Survey 2006; Johnson et al. 1999; 2004b), the inferred buried edges (wedge tips) of the Seattle up- lift (Brocher et al. 2004), linear geophysical anomaly patterns interpreted by Brocher et al. (2001, 2004), and the locations of active GPS stations in the study region (www.geodesy.cwu. edu).
Comparison of Figs 1(d) and (e) reveals a consistent pattern of relative subsidence at rates exceeding 3 mm/yr over much of the Green, Duwamish, and Puyallup River valleys from Seattle to Tacoma during the period 1992–2000.
Relative subsidence is partic- ularly high and clearly defined immediately to the south of Seattle, between Renton and Auburn, and within Tacoma. In one location near Federal Way, relative subsidence extends out of the Holocene sedimentary deposits in the Green, Duwamish, and Puyallup River valleys and into the older glacial and inter-glacial deposits that blanket the Puget Sound Lowland, ceasing abruptly at a sharp linear boundary near Federal Way. We also observe in both the track 428 and 156 data a clear spatial coupling of relative uplift and subsi- dence just to the north of the PCOL GPS station over the period 1992–2000.
An examination of Fig. 1(c) reveals that between 2002 and 2006 relative subsidence continued within the Green, Duwamish, and Puyallup River valleys. However, near Federal Way where we ob- serve relative subsidence between 1992 and 2000, we observe rela- tive uplift over the period 2002–2006. Notably, this zone of relative uplift is truncated along exactly the same linear feature marking the northward extent of subsidence near Federal Way during 1992 C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
Constraints on surface deformation, Seattle, WA 33 Figure 2.
(a)–(d): comparisons of RADARSAT-1 Finebeam 1 deformation time-series results to LOS projected, detrended time-series data for 4 GPS stations temporally and spatially overlapping the DInSAR data: THUN, SEAW, PCOL, SEAT. The time-series inversion we employ yields elevation values for every date with a SAR acquisition; these elevation values are denoted by the black triangles. In (a)–(d), the GPS data (grey solid line) are smoothed with a 10-d window. The propagated LOS uncertainty envelope (+/–1σ) for the GPS data is indicated with the dashed grey line. –2000. Between 2002 and 2006, the deformation pattern observed north of the PCOL GPS station is no longer detected.
We note that because all deformation is calculated relative to the mean in Figs 1(b)–(d), relative uplift is a requirement in all of our velocity maps due to all of the documented subsidence in the study area. We find that zones of relative uplift in Figs 1(b) and 2(d) are generally broad, noisy and lacking common spatial characteristics among the three velocity maps. Therefore, we do not focus on these patterns in this analysis.
4 U N C E RTA I N T Y A NA LY S I S Any interpretation of the DInSAR-derived time-series data requires an understanding of the contributions from atmospheric noise and an assessment of the significance of individual deformation fea- tures. In the following section, we assess in two ways the sensitivity of the DInSAR time-series method used here to surface deforma- tion within the study region. First, we compare DInSAR–derived deformation histories to independent GPS observations. Next, we compare inferred vertical deformation rates between overlapping DInSAR tracks.
In Figs 2(a)–(d), we compare GPS time-series data projected onto the satellite LOS direction to RADARSAT-derived surface elevation time-series data averaged over a 20–80 pixel area surrounding each of four GPS sites.
During large parts of the time-span of the ERS data, only a single GPS station is available, so a comparison between GPS and ERS is not shown. The figures show that RADARSAT- derived surface displacement is by and large within the range of propagated error for detrended continuous GPS data projected onto the radar LOS in the Puget Sound region (www.geodesy.cwu.edu). We choose to compare DInSAR to the detrended GPS data, instead of the GPS data corrected for periodic quasi-annual deformation (e.g. Szeliga et al. 2004), because we believe that the annual signal is spatially heterogeneous enough (Fig.
4) to appear in the DInSAR data even after we have removed a regional second-order poly- nomial, best-fitting surface from each interferogram (a procedure analogous to the detrending process only in space instead of time). We find that the standard deviation of the difference between rela- tive surface displacement measured by GPS and by DInSAR at these four stations is 5.4 mm. After propagating reported 1σ values for the GPS data (www.geodesy.cwu.edu) into our LOS projection calcula- tion, we find that the mean uncertainty for the radar LOS-projected GPS data for the four sites considered is 5.2 mm.
Therefore, the rms error of the DInSAR relative to GPS is only slightly higher than the uncertainty in the GPS measurements alone. This estimate of the uncertainty in the time-series inversion is similar to the value of 5.6 mm computed via direct comparison of DInSAR time-series data and GPS in the Los Angeles area (Casu et al. 2006). Although the total magnitude of surface change recorded at the 4 GPS stations in the Seattle area is relatively small (∼10 mm), the comparisons nevertheless confirm that DInSAR-derived displacement histories are sufficiently accurate to provide a useful complement to exist- ing continuous GPS networks, particularly when or where surface changes are more dramatic than those observed here.
We note that all of the detrended GPS station data in Puget Sound show a strong seasonal variability in surface elevation that is matched to a greater or lesser extent by DInSAR in the four comparisons shown in Fig. 2. In western Washington, peaks in ele- vation typically occur in late fall, and lows in elevation are typically observed in late spring (Fig. 2). In Japan, variability of a similar amplitude and period in vertical GPS data has been attributed to seasonal snow loading of the crust (Heki 2001). The mountains of western Washington have winter precipitation (mostly snow) in excess of 4 m of snow water equivalent (Daly & Taylor 1998) and the Puget Lowland itself stores significant groundwater during the winter (www.waterdata.usgs.gov/wa/nwis/).
Therefore, defor- mation of the crust from snow loading (Heki 2001), groundwater recharge and withdrawal (e.g. Lanari et al. 2004) and surface water loading (e.g. Cavalié et al. 2007) might all drive measurable and spatially complex seasonal deformation that could be resolved with the DInSAR methods employed herein, despite their insensitivity to long-wavelength flexural deformation.
Given the complications in comparing GPS and DInSAR di- rectly, as well as the large errors in vertical GPS measurements to begin with, the agreement between DInSAR and GPS observations is encouraging, but does not provide us with a rigorous, quantitative C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
34 Noah J. Finnegan et al. measure of the uncertainty in our DInSAR-derived deformation rate maps. Therefore, we also compare relative surface velocities from two independent ERS tracks that overlap in time and space across the urban regions of interest (Figs 1d and e).
A cursory examination of Figs 1(d) and (e) reveals that the two relative velocity maps share many features in common, despite the fact that they are derived from completely independent data sets and slightly different satellite or- bital geometries. To enable direct comparison of the measurements shown in Figs 1(d) and (e) and in Fig. 3a, we begin by making the assumption that the LOS length changes measured by the DInSAR observations result from vertical deformation. We plot the inferred relative vertical velocities derived from track 428 data versus the inferred relative vertical velocities derived from track 156 data for the cells where both tracks retain coherence (2033 442 individual cells).
Next, we employ a simulation in which we vary both the range of relative vertical velocity across the study region, as well as the uncertainty in our ability to measure vertical velocity. Our goal is to match the residuals shown in Fig. 3(a) by comparing many sets of synthetically generated relative velocity distributions with synthetically generated uncertainties, and thereby estimate the ac- tual measurement uncertainty of our techniques. We best match the data distribution and residuals in Fig. 3(a) using a model where Figure 3. (a): inferred vertical deformation rate calculated from ERS track 428 data versus inferred vertical deformation rate calculated from ERS track 156 data over the study area.
Line of 1:1 agreement is shown in grey. (b): modelling the signal and noise in (a). Each axis represents 2 000 001 data points sampled from a uniformly distributed velocity field ranging between –3 and 1 mm yr−1 with a Gaussian noise component of standard deviation 0.45 mm yr−1. When plotted against one another, as shown here, the data range and scatter match (a) well, suggesting that the error associated with measurements of vertical velocity using ERS data is ∼0.5 mm yr−1. the relative vertical surface velocity signal within the study area ranges between –3 and 1 mm yr−1 and the error associated with the measurement of that velocity is Gaussian and has a standard deviation of 0.45 mm yr−1 (Fig.
3b). We note that 0.45 mm yr−1 represents a measure of the uncertainty in relative vertical surface velocity within the study area. Because our focus in this study is on relative deformation, systematic offsets between the two ERS data sets will therefore impact neither the results of our analysis nor our uncertainty estimates. A comparison of DInSAR time-series data with surface levelling data in Naples, Italy (Casu et al. 2006) sug- gests similar magnitude velocity uncertainties (1.0 mm yr−1 ), while uncertainties in surface velocity measured via a comparison of GPS and InSAR permanent scatterers have been assessed at less than 2 mm yr−1 in New Orleans (Dixon et al.
2006). Because we have assumed only vertical deformation in our un- certainty analysis, the ∼0.5 mm yr−1 vertical velocity uncertainty reported above likely reflects an upper bound on the uncertainty in LOS deformation (Figs 1d and e). This is because in the absence of significant horizontal motion, the satellite LOS captures ∼90% of vertical deformation in ERS data, and ∼80% of vertical deforma- tion in RADARSAT-1 data (Table 1), suggesting that some of the scatter in Fig. 3(a) might be reduced for an equivalent figure using LOS deformation. Additionally, systematic differences in the two velocity inversions shown in Figs 1(d) and (e) due to the different spread of dates used in the two velocity estimates, and suggested by the slight asymmetry about the 1:1 line in Fig.
3(a) might further contribute to inflation of the uncertainty calculated above relative to the actual uncertainty in LOS relative velocity. Fig. 3(a) thus indicates that over the 7+ yr of ERS measure- ments used in the time-series analysis, computations of average relative vertical velocity within the study area have an uncertainty of likely less than 0.45 mm yr−1 , which is sufficient to resolve with confidence the relatively subtle patterns of surface velocity within the study area. Fig. 2, in turn, indicates that surface displacement determined via DInSAR time-series analysis from RADARSAT-1 Finebeam 1 data has an uncertainty of approximately 5.4 mm rela- tive to GPS.
5 D I S C U S S I O N A N D C O N C LU S I O N S 5.1 Groundwater Surface deformation driven by the balance between groundwater pumping and recharge is commonly observed with DInSAR over shallow aquifers (e.g. Hoffman et al. 2001; Schmidt & Bürgmann 2003; Lanari et al. 2004). This is primarily due to the fact that net changes in groundwater storage alter the ratio of pore fluid pressure to lithostatic pressure within an aquifer, which in turn drives strain that can be detected at the Earth’s surface (Hoffman et al. 2001). If groundwater drawdown in an aquifer results in deviatoric (i.e. lithostatic—pore fluid) stresses above historical values, non- recoverable aquifer compaction can occur (Hoffman et al.
2001) and this typically results in surface subsidence of the order of tens of centimetres to metres (Hoffman et al. 2001; Schmidt & Bürgmann 2003). Otherwise, aquifer deformation is elastic and will typically exhibit strong millimetre- to centimetre-scale annual or inter-annual variability (e.g. Hoffman et al. 2001; Lanari et al. 2004; Bürgmann et al. 2006). As the rates associated with elastic deformation in aquifers are of the same magnitude as typical tectonic deformation rates, it is important to identify deformation related to groundwater movement before using DInSAR for tectonic applications.
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Constraints on surface deformation, Seattle, WA 35 Figure 4. Standard deviation of the residual surface displacement after subtracting the component of displacement due to the mean surface velocity (Figs 1b–d) for RADARSAT-1 Finebeam 1 (b), ERS Track 156 (c), and ERS Track 428 (d). The small white dots denote the locations of municipal wells in King County with greater than 15 connections (www.metrokc.gov/gis). The white dashed lines show the boundaries of King County. The arrows point to the locations of linear deformation gradients apparent in the residual displacement data. The figure reveals seasonal deformation related to groundwater removal and recharge.
We test whether relative deformation patterns in the study area are related to groundwater by plotting the standard devia- tion of the residuals of surface displacement (Figs 4b–d) after we subtract from the time-series the component of surface change due to the mean surface velocities shown in Figs 1(c)–(e). Our assumption in making Figs 4(b)–(d) is that (in the absence of seis- mic activity) tectonic deformation will drive monotonic deforma- tion, whereas elastic aquifer changes can be identified based on strongly annual or inter-annual deformation (e.g. Lanari et al. 2004). Figs 4(b)–(d) therefore provide a measure of surface elevation fluc- tuation over the time-period examined and, importantly, illustrate that regions in Figs 1(c)–(e) characterized by high rates of rela- tive subsidence or uplift are also almost uniformly characterized by high surface elevation variability.
This correlation suggests that the interplay of groundwater recharge and withdrawal within shallow aquifers drives much of the observed deformation within the study area. This interpretation is also supported by the close correspon- dence of regions of apparent groundwater deformation revealed by the RADARSAT-1 data from 2002 to 2006, and the locations of large municipal water wells in King County (Fig 4b). Additionally, C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
36 Noah J. Finnegan et al. the observed transition from subsidence to uplift between 1992– 2000 and 2002–2006 over Federal Way may reflect a change from net groundwater removal to storage in the Mirror Lake aquifer underlying this region. During the mid-1990s, water levels in this aquifer were depressed by as much as 20 m, after which time pump- ing rates declined and water levels within the aquifer increased (www.ecy.wa.gov/programs/wr/wstf/images/pdf/asr-bman.pdf). The fact that relative subsidence dominates the net deformation observed over most of Holocene deposits in the Green, Duwamish, and Puyallup River valleys, however, also suggests that groundwa- ter deformation patterns are superimposed on regional subsidence within Holocene deposits.
Because of the young age of the sedi- ments in these valley fills and the profound hydrological alterations over the last century to the Green, Duwamish, and Puyallup River valleys (Collins et al. 2003), we interpret subsidence as an indica- tion of sediment compaction combined with sediment starvation in valley bottoms.
5.2 Near surface faults A series of faults (Fig. 1b) in the Puget Sound Lowland accommo- date convergence between southern Washington State and southern British Columbia caused by the clockwise rotation of the Oregon block (e.g. Johnson et al. 1994; Wells et al. 1998). The total north– south convergence across the Puget Sound Lowland measured over geologic timescales is about 4–7 mm yr−1 (e.g. Wells & Simpson 2001), and the sparse measurements available from GPS may be consistent with this rate if corrections are made for interseismic deformation from the subduction megathrust (e.g. Mazzotti et al.
2002). However, how convergence is partitioned across the numer- ous active faults in the Puget Sound Lowland is an open question (e.g. Johnson et al. 2004a). Recent work suggests that much of the convergence (2–3 mm yr−1 ) may be accommodated by complicated faulting and folding between the Seattle Fault and just south of the Tacoma Fault (Johnson et al. 2004b), the two key structures bounding the Seattle Uplift (Brocher et al. 2004). However, even in this area, it is difficult to quantify which specific subfaults, faults or splays may be active, and their subsurface geometry is controversial (Johnson et al.
In order to better characterize the nature of faulting in this compli- cated area, dense deployments of GPS stations have been proposed (Johnson et al. 2004b). As an alternative to such a dense GPS de- ployment, here we compare patterns of spatially continuous mean relative surface velocity measurements derived from DInSAR to the locations of known faults and structures throughout the Puget Sound Lowland. Our goal is to determine if any of the structures in the region are actively accommodating observable aseismic de- formation resulting from fault creep. After an examination of both synoptic data presented in Figs 1(c)–(e) and detailed vertical de- formation rate profiles across the Seattle and Tacoma faults zones (Figs 5a–c), however, we find that the patterns of observed surface deformation do not align with known structures or faults.
Instead, in both detailed cross-sections the deformation appears related to the groundwater and sediment compaction effects described above. Specifically, across the Seattle fault the pattern of relative surface velocity is controlled primarily by the location of Holocene val- ley bottom deposits in the Duwamish River valley, where both the variability and amplitude of vertical deformation are greatest. The mapped traces of the Seattle fault do not visibly influence deforma- tion in the cross-section line shown in Fig 5(c). Across the Tacoma fault, we observe subsidence in the Puyallup River valley and the transition from subsidence to uplift above the Mirror Lake aquifer near Federal Way between 1992–2000 and 2002–2006 (Fig.
5b). Additionally, the sharp transition marking the northward extent of inferred groundwater-related deformation in Federal Way is evident in the velocity cross-sections (solid red arrow in Fig. 5b). However, although surface motion along the Tacoma fault transect is aligned generally to the regional tectonic fabric, the high temporal vari- ability of surface elevation across the Tacoma fault led us to infer that ground movements across the Tacoma fault zone are related to groundwater-deformation, not tectonic uplift.
The main thrust beneath the Seattle Uplift dips southward at ∼20◦ , and the fault may accommodate as much as 3 mm yr−1 north–south compression at depth (Pratt et al. 1997; Johnson et al. 2004b). Using these constraints in an elastic dislocation model (Sav- age 1983; Okada 1985), we calculate that the thrust beneath the Seat- tle Uplift must be locked currently to a depth greater than 10 km. Otherwise, 3 mm yr−1 of north–south shortening would drive defor- mation at the surface of both sufficiently large magnitude and short wavelength to be detected with the techniques employed herein. Al- ternatively, if fault slip is occurring at depths of less than 10 km, it must be distributed across numerous faults such that vertical uplift is less than 0.5 mm yr−1 (and therefore undetectable) for a given structure.
In the absence of direct observations of motion on faults, insight into the geometry of near-surface faults can still be gained by ob- serving patterns of deformation due to groundwater movements. Because faults often juxtapose rocks of differing permeability, pat- terns of deformation driven by groundwater pumping and recharge commonly reveal fault locations in individual interferograms and time-series data (e.g. Hoffman et al. 2001; Schmidt & Bürgmann 2003; Lanari et al. 2004). As discussed in Section 5.1, spatial pat- terns of the magnitude of surface elevation fluctuations, as opposed to their rates, more directly reveal patterns in groundwater motion.
Therefore, we use patterns in surface elevation fluctuations shown in Figs 4(b)–(d) to search for linear deformation gradients potentially marking the locations of near surface faults.
Figs 4(b)–(d) resolve two sharp deformation gradients in the vicinity of the Tacoma fault zone (indicated by the black arrows in Figs 4b–d). The first, located near Federal way, is also evident in the velocity data plotted in Figs 1(c)–(e) and 5(b). Although the trace of this feature does not conform to the location of a known fault, several lines of evidence indicate that this deformation gradient marks the location of an unmapped near-surface fault. The feature is located within deposits crossed by several parallel magnetic anomalies in- terpreted to reflect possible fault locations (Brocher et al.
2004), is parallel and just to the north of the Tacoma fault zone (Figs 1b–e), and clearly controls local groundwater movements (Figs 4b–d). In light of these results, and especially given the strong motivation for further understanding the activity and geometry of faults in the Puget Lowland, we identify Federal Way as a region to concen- trate on in future geophysical investigations aimed at revealing the geometry and activity on subsurface faults.
In Figs 4(b)–(d), we also identify a south-west–north-east ori- ented deformation gradient south of Tacoma, running approxi- mately from Steilacoom on the coast of Puget Sound east to Sumner. Although this feature is only crisply resolved in the RADARSAT- 1 data, it is also visible in the ERS data. Additionally, the linear deformation gradient corresponds to a strikingly linear valley wall section along the south side of the Puyallup River valley (Fig. 4a). We acknowledge that this feature is less clear than that observed near Federal Way. However, its length, orientation and potential ex- pression in the topography led us, tentatively, to identify this feature C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
Constraints on surface deformation, Seattle, WA 37 Figure 5. (a): location map of the Tacoma and Seattle fault zones showing cross-section lines in (b) and (c). (b): inferred vertical deformation rates across the Tacoma fault zone from the three DInSAR inversions. The red solid arrow indicates the location of the sharp deformation gradient near Federal Way seen in Figs 1(c)–(e) and 4(b)–(d). The dotted lines indicate the locations of geophysical anomalies, and the dashed lines indicate mapped faults that have been projected into the cross-section line. (c): inferred vertical deformation rates across the Seattle fault zone from the three inversions.
The dashed lines indicate mapped faults that have been projected into the cross-section line, and the solid lines indicate mapped thrust faults intersecting the cross-section line. as marking the location of another near-surface fault located to the south of the Tacoma Fault and striking essentially parallel to the Seattle fault zone. We therefore also point to the uplands south of Tacoma as a region to concentrate on in future geophysical investi- gations aimed at constraining near-surface fault geometries. 5.3 Landslide deformation Since de-glaciation in Puget Sound 16 000–17 000 yr BP (Porter & Swanson 1998), bluff retreat driven primarily by landslides has resulted in 150–900 m of coastline retreat within the unconsoli- dated glacial sediments blanketing much of Puget Sound (Galster & Laprade 1991).
Landslides occur regularly during the winter as high precipitation saturates weakly consolidated sediments and thereby increases pore fluid pressures and reduces normal stresses (Schulz 2004). In the last decade, landslides have derailed trains, dumped houses into Puget Sound, and resulted in several deaths and tens of millions of dollars of property damage (Baum et al. 1998). LiDAR-based mapping has identified 173 slides and slide complexes just within Seattle city limits (Baum et al. 2000; Schulz 2004).
As catastrophic sliding can be preceded by slow or creeping de- formation (Iverson 2005; Jibson 2005), monitoring landslides with DInSAR represents a potentially useful way to identify specific slides that may be prone to future catastrophic failure. Additionally, creeping landslide deformation may be interpreted as an indication of strain-induced dilation of pore spaces—a negative feedback on catastrophic landslide deformation (Iverson 2005). Alternatively, where strain-induced contraction of pore spaces occurs (a positive feedback on catastrophic landslide deformation), creeping defor- mation may be absent (Iverson 2005), and deformation inferred to be primarily rapid and catastrophic.
Thus, the presence or absence of slow deformation can also provide an important clue into the mechanics governing landslide deformation at a given location. Comparing the results of our surface velocity analysis to LiDAR maps of landslide complexes within Seattle city limits (Figs 6a–d) reveals that between 1992 and 2007 there was no slow landslide deformation on any of the mapped slide complexes within Seattle. This is especially significant as radar phase coherence was retained over most of the areas of mapped landslide activity. The few mapped slide complexes with documented rapid landslides over this period, such as along Perkins Lane in Seattle during the extremely wet win- ter of 1996–1997, exhibit radar phase de-correlation.
We presume this because the high deformation rates and surface disruption as- sociated with these slides changed radar scattering properties to the point where conventional interferometry was not possible. Based on the fact that slow deformation was not detected on any mapped slides during the periods 1992–2000 or 2002–2006, we infer that within the Seattle area landslide deformation is relatively infrequent and, when it occurs, catastrophic. Additionally, we speculate that the lack of observed slow deformation on mapped slides indicates that strain-induced changes in soil pore spaces do not provide a negative feedback on slide deformation here.
Otherwise, we would antic- ipate measuring slow deformation on some of the mapped slide complexes in the study region.
5.4 GPS contamination GPS data in the Puget Sound Lowland have been used primarily as a tool for understanding broad wavelength deformation associ- ated with the Cascadia subduction zone (e.g. Melbourne et al. 2003). For such applications, regional deformation solutions should be cor- rected for local short-wavelength deformation present at individual C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
38 Noah J. Finnegan et al. Figure 6. (a): locations of mapped landslides, denuded regions and landslide headscarps within Seattle city limits (Schulz 2004).
(b)–(d): radar LOS velocity maps generated from the time-series analysis. The circles in (c) and (d) identify the location of the highly destructive Perkins Lane landslide during the winter of 1996–1997. Table 3. Mean radar LOS and inferred vertical velocity calculated from the time-series analyses for eight GPS stations within the study area. Station LOS deformation LOS deformation LOS deformation Vertical deformation Vertical deformation Vertical deformation ERS Track156 ERS Track 428 RADARSAT-1 Finebeam-1 ERS Track 156 ERS Track 428 RADARSAT-1 Finebeam-1 (1992.52–1999.97) (1992.58–1999.83) (2002.18–2006.19) (1992.52–1999.97) (1992.58–1999.83) (2002.18–2006.19) (mm yr−1) (mm yr−1) (mm yr−1) (mm yr−1) (mm yr−1) (mm yr−1) PFLD −1.53 0.41 0.33 −1.69 0.44 −0.40 SEAW 0.08 0.29 −0.61 0.09 0.31 0.56 SSHO 0.37 0.39 −0.57 0.41 0.42 0.55 SMAI 0.34 0.03 −0.69 0.38 0.03 0.80 KNTC −1.17 −0.71 0.11 −1.28 −0.76 0.08 THUN 1.16 0.12 −1.29 1.27 0.13 1.12 PCOL −0.76 −0.92 0.97 −0.84 −1.00 0.09 SEAT −0.07 0.61 −1.68 −0.07 0.65 1.30 GPS stations when possible (e.g.
Bawden et al. 2001). Here, we use the results of our surface velocity mapping to identify GPS sta- tions that may be impacted by the short-wavelength deformational features identified above. Table 3 lists the GPS stations located within the study region along with LOS deformation rates and cor- responding vertical deformation rates computed from within visu- ally identified patches of pixels (20–80 pixels in area) surrounding each GPS station.
An examination of Table 3 shows that the stations located within the study area do not appear to be substantially impacted by the C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS
Constraints on surface deformation, Seattle, WA 39 localized deformation patterns documented above. All of the sta- tions have mean local surface LOS deformation rates ranging be- tween 0.03 and 1.5 mm yr−1 . Therefore, long-term deformation rates calculated at any of these eight stations should be contami- nated between 0.03 and 1.7 mm yr−1 of equivalent vertical defor- mation, depending on the station.
Additionally, we note that the average difference between the estimates of vertical surface veloc- ity computed in Table 2 between ERS tracks 428 and 156 is 0.16 mm yr−1 , well within the ∼0.5 mm yr−1 uncertainty calculated in Section 4. Finally, we note that although in Table 3 neither PCOL nor KNTC shows significant contamination from local deforma- tion computed from DInSAR, the sites are nevertheless located on the edges of clear deformational features identified in our velocity maps. KNTC is situated on the edge of the relatively rapidly sub- siding zone between Renton and Auburn, WA.
PCOL is located on the edge of the region impacted by pumping from a pulp mill and a gravel pit (B. Clothier, private communication, 2007). Thus, future GPS work involving these stations should consider the possibility of local deformation impacting data from these sites. AC K N OW L E D G M E N T S We are extremely grateful to B. Clothier at Robinson, Noble & Saltbush, Inc. for sharing his knowledge of the groundwater hy- drology of Pierce County. We acknowledge helpful reviews from two anonymous reviewers and the associate editor John Beavan. We also thank E. Fielding and E. Price for the software used to pro- cess the RADARSAT-1 data.
SAR data were acquired through the Alaska Satellite Facilty (ASF). Research supported in part by the US Geological Survey (USGS), Department of the Interior under USGS National Earthquake Hazards Reduction Program (NEHRP) awards number 08HQGR0012 (MEP) and 06HQGR0035 (RBL). The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily repre- senting the official policies, either expressed or implied, of the US Government.
R E F E R E N C E S Baum, R.L., Chleborad, A.F. & Schuster, R.L., 1998. Landslides triggered by the winter 1996–97 storms in the Puget Lowland, Washington, U.S. Geol. Surv. Open-File Rep., 16, 98–239. Baum, R.L., Harp, E.L. & Hultman, W.A., 2000. Map showing recent and historic landslide activity on coastal bluffs of Puget Sound between Shils- hole Bay and Everett, Washington, U.S. Geol. Surv. Misc. Field Studies Map MF-2346, 1 sheet. Berardino, P., Fornaro, G., Lanari, R. & Sansosti, E., 2002. A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms, IEEE Trans.
Geosci. Remote Sens., 40, 2375–2383. Bawden, G.W., Thatcher, W., Stein, R.S., Hudnut, K.W. & Peltzer, G., 2001. Tectonic contraction across Los Angeles after removal of groundwater pumping effects, Nature, 412, 812–815.
Brocher, T.M., Parsons, T., Blakely, R.J., Christensen, N.I., Fisher, M.A., Wells, R.E. & the Ships Working Group, 2001. Upper crustal structure in Puget Sound, Washington: Results from the 1998 Seismic Hazards Investigation in Puget Sound, J. Geophys. Res., 106, 13 541–13 564. Brocher, T.M., Blakely, R.J. & Wells, R.E., 2004. Interpretation of the Seattle Uplift, Washington, as a passive-roof duplex, Bull. Seismol. Soc. Am., 94, 1379–1401. Bürgmann, R., Hilley, G., Ferretti, A. & Novali, F., 2006. Resolving vertical tectonics in the San Francisco Bay Area from permanent scatterer InSAR and GPS analysis, Geology, 34, 221–224.
Cavalié, O., Doin, M.-P., Lasserre, C. & Briole, P., 2007. Ground motion measurement in the Lake Mead area, Nevada, by differential synthetic aperture radar interferometry time series analysis: Probing the lithosphere rheological structure, J. Geophys. Res., 112, doi:10.1029/2006JB004344. Casu, F., Manzo, M. & Lanari, R., 2006. A quantitative assessment of the SBAS algorithm performance for surface deformation retrieval from DInSAR data, Remote Sens. Env., 102, 195–210. Chen, C.W. & Zebker, H.A., 2002. Phase unwrapping for large SAR in- terferograms: statistical segmentation and generalized network models, IEEE Trans.
Geosci. Remote Sens., 40, 1709–1719. Collins, B.D., Montgomery, D.R. & Sheikh, A.J., 2003. Reconstructing the historical riverine landscape of the Puget Lowland, in Restoration of Puget Sound Rivers, 79–128 eds Montgomery D.R., Bolton S.M., Booth D.B., & Wall L., University of Washington Press, Seattle, WA. Daly, C. & Taylor, G., 1998. Washington Average Annual Precipitation, 1961–90, Water and Climate Center of the Natural Resources Conserva- tion Service, Portland, Oregon, USA, 1 sheet.
Dixon, T.H. et al., 2006. Space geodesy: Subsidence and flooding in New Orleans, Nature, 441, 587–588. Farr, T.G. & Kobrick, M., 2000. Shuttle Radar Topography Mission produces a wealth of data, EOS, Trans., AGU, 81, 583–585. Ferretti, A., Prati, C. & Rocca, F., 2001. Permanent Scatterers in SAR Interferometry, IEEE Trans. Geosci. Remote Sens., 39, 8–20. Galster, R.W. & Laprade, W.T., 1991. Geology of Seattle, Washington, United States of America, Bull. Assoc. Eng. Geol., 28, 235–302. Goldstein, R.M. & Werner, C.L., 1998. Radar interferogram filtering for geophysical applications, Geophys.
Res. Lett., 25, 4035–4038. Heki, K., 2001. Seasonal Modulation of Interseismic Strain Buildup in Northeastern Japan Driven by Snow Loads, Science, 293, 89–92. Hoffmann, J., Zebker, H.A., Galloway, D.L. & Amelung, F., 2001. Sea- sonal subsidence and rebound in Las Vegas Valley, Nevada, observed by synthetic aperture radar interferometry, Water Resour. Res., 37, 1551– 1566.
Iverson, R.M., 2005. Regulation of landslide motion by dilatancy and pore pressure feedback, J. Geophys. Res., 110, F02015, doi:10.1029/2004JF000268. Jibson, R.W., 2005. Landslide Hazards at La Conchita, California: U.S. Geol. Surv. Open–File Report 05–1067, 12 pp. Johnson, S.Y., Potter, C.J. & Armentrout, J.M., 1994. Origin and evolu- tion of the Seattle fault and Seattle basin, Washington, Geology, 22, 71– 74. Johnson, S.Y. et al., 2004a. Evidence for late Holocene earthquakes on the Utsalady Point Fault, northern Puget Lowland, Washington, Bull. Seismol. Soc. Am., 94, 2299–2316.
Johnson, S.Y., Blakely, R.J., Stephenson, W.J., Dadisman, S.V .
& Fisher, M.A., 2004b. Active shortening of the Cascadia forearc and impli- cations for seismic hazards of the Puget Lowland, Tectonics, 23, doi:10.1029/2003TC001507. Kwoun, O.-L., Lu, Z., Neal, C. & Wicks, Jr, C., 2006. Quiescent deformation of Aniakchak Caldera, Alaska, mapped by InSAR, Geology, 34, 5–8. Lanari, R., Ludgren, P., Manzo, M. & Casu, F., 2004. Satellite radar inter- ferometry time series analysis of surface deformation for Los Angeles, California, Geophys. Res. Lett., 31, doi:10.1029/2004GL021294. Lundgren, P., Usai, S., Sansosti, E., Lanari, R., Tesauro, M., Fornaro, G. & Berardino, P., 2001.
Modeling surface deformation observed with syn- thetic aperture radar interferometry at Campi Flegrei caldera, J. Geophys. Res., 106, 19 355–19 366.
Mazzotti, S., Dragert, H., Hyndman, R.D., Miller, M.M. & Jenton, J.A., 2002. GPS deformation in a region of high crustal seismicity: North Cascadia Forearc, Earth Planet. Sci. Lett., 198, 41–48. Melbourne, T.I., Szeliga, W.M., Miller, M.M. & Santillan, V .M., 2005. Ex- tent and duration of the 2003 Cascadia slow earthquake, Geophys. Res. Lett., 32, L04301, doi:10.1029/2004GL021790. Okada, Y., 1985. Surface deformation due to shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 75, 1135–1154. Porter, S.C. & Swanson, T.W., 1998. Radiocarbon age constraints on rates of advance and retreat of the Puget Lobe of the Cordilleran ice sheet during the last glaciation, Quat.
Res., 50, 205–213.
C 2008 The Authors, GJI, 174, 29–41 Journal compilation C 2008 RAS