A NEW PERSISTENT SCATTER NETWORK CONSTRUCTION ALGORITHM FOR PERSISTENT SCATTER INSAR AND ITS APPLICATION TO THE DETECTION OF URBAN SUBSIDENCE

To extremely eliminate atmospheric delays for improving the accuracy of persistent scatter InSAR, the algorithm for constructing three-dimensional Delaunay network of global positioning system (GPS) stations is introduced to construct three-dimensional persistent scatter Delaunay network. The comparison with two-dimensional persistent scatter network indicates that three-dimensional Delaunay network is stable and avoids the affect of landscape conversion from geography space to image space. The urban subsidence of Lujiazui in Shanghai during 1992-2002 was effectively detected with InSAR based on three-dimensional persistent scatter Delaunay network. The result shows that persistent scatter InSAR based on three-dimensional persistent scatter Delaunay network can be used to efficiently and accurately detect ground deformation. The comparison with Leveling and InSAR based on persistent scatter planar network indicates that the accuracy and reliability of InSAR based on three-dimensional persistent scatter Delaunay network are significantly improved.


INTRODUCTION
Differential synthetic aperture radar interferometry (DInSAR) is a potential technique for monitoring minor ground deformation because of its pantoscopic view and high spatial resolution.However, de-correlations and atmospheric delays mitigate the accuracy of DInSAR.persistent scatter InSAR promoted by Ferretti is at present regarded as one of the most efficient approach in overcoming both de-correlations and atmospheric delays (Zebker, 1992, Ferretti et al. 2000a, 2001b).In persistent scatter InSAR, the persistent scatters are first detected from time serial SAR images.Then the network of persistent scatters is constructed (Luo et al. 2008a, Liu et al. 2008).Based on the network, the neighbourhood of persistent scatters is defined along each arc, i.e., connection of the network and the increments of differential phases, called neighbouring differential phases (NDP) between two neighbouring persistent scatters are calculated.Finally, ground deformations and terrain errors are deduced from NDPs.Because of the homogeneity of atmosphere distribution in certain range, atmospheric delays are strongly correlative in small space scale such as 2km (Luo, 2007b).The NDPs accordingly eliminate most of the atmospheric delays, which is consistent with the fundament of differential GPS.Furthermore, the more closely the two persistent scatters are adjacent, the more clearly the atmospheric delays are removed from NDPs.To eliminate atmospheric effects to a maximum extent, the pair of persistent scatter decided by the network should be as far as possible to close.So it's crucial to persistent scatter InSAR to establish an appropriate persistent scatter network.The common simple persistent scatter network introduced first by Mora et al. (2003) is triangular irregular network (TIN) established with Delaunay algorithm.However, some isolated islands and singular points are easily generated while the arcs longer than 1km are cut from TIN (Ferretti et al. 2000a, Colesanti et al. 2003).The presence of isolated islands makes deformation detection difficult.To avoid the generation of isolated island in the network, an enhanced persistent scatter network called freely-connected network (FCN) was proposed by Liu et al. (2009).According to FCN algorithm, every persistent scatter is connected to all the others.Therefore more arcs than TIN are generated in FCN and the isolated islands and singular points are seldom formed though the FCN is optimized by cutting the arcs longer than 1km.Furthermore, more observations are obtained from the FCN which correspondingly is useful to the network adjustment and the improvement of deformation measurement accuracy.However, FCN is constructed at the cost of computation time.Both TIN and FCN are two-dimensional networks constructed based on the image planar coordinate system.As atmospheric delays change along both horizontal and vertical direction, the NDPs derived from the planar network mainly mitigate the horizontal atmospheric delays.Most of vertical atmospheric delays still remain in the NDPs.On the other hand, because of the special image distortion such as foreshortening in SAR, the distance on the earth surface, i.e., ground distance between two neighbouring persistent scatters is usually longer than the range decided by the image resolution.Which means that the ground distance with nominal 1km (the range threshold used to select persistent scatter pairs) in image calculated by image resolution may be much longer than 1km.So the NDPs derived from planar network can not completely eliminate the atmospheric effects.In order to improve the correction of atmospheric effects in persistent scatter InSAR, the algorithm for constructing three-dimensional Delaunay network of GPS stations (Zhou et al. 2007) is introduced in this paper to establish three-dimensional persistent scatter Delaunay network (TDPDN).The validation of TDPDN is confirmed by detecting ground subsidence over Lujiazui in Shanghai during 1992-2002.

FOUNDMENTAL OF PERSISTENT SCATTER INSAR
Given N+1 SAR images acquired at the ordered times over the same area, N interferograms will be generated if an image is specified as common master image.Suppose that M persistent scatters is identified from the N+1 time serial images, the M persistent scatters are combined to form a network with some algorithm.Then the pairs of persistent scatters are defined through the network and N time serial NDPs for any pair of adjacent persistent scatters are calculated.The NDP is function of the difference of terrain errors and the difference of linear is the difference of linear deformation velocities between neighboring PSs.
 is phase residues.
It's the contribution of residual atmospheric delays, no-linear deformations and decorrelations.For N time serial NDPs of every pair of persistent scatters, the sets of N equations such as (1) are generated.Because residual phase


changes with time, the equation sets are a nonlinear system, i.e., rank deficiency.Under the condition of , the equation sets can be resolved.The (Ferretti et al. 2000a, Colesanti et al. 2003) or solution-space search method (Luo et al. 2011c).Then the deformation velocities of all persistent scatters can be deduced with the network adjustment (Liu et al. 2008) or by integrating along the arc of network (Ferretti et al. 2000a, Colesanti et al. 2003).Furthermore, the nonlinear deformations of persistent scatters and atmospheric phase screen (APS) with respect to singular SAR image or interferogram are filtered out from the NDPs.Finally, the time serial deformations of all persistent scatters and regional deformation field can be deduced.The accuracy of deformations estimated from NDPs depends on the degree that atmospheric delays and decorrelations are removed from NDPs.As long as two neighbouring persistent scatters defined by network are adjacent to the greatest extent in the geography space, most of atmospheric delays and decorrelation errors will be eliminated from the two neighbouring persistent scatters.So an appropriate network and optimal neighbourhood are crucial to persistent scatter InSAR.In order to achieve this goal, the three-dimensional persistent scatter Delaunay network is presented.

The problem of persistent scatter planar network
Persistent scatter planar network is a two-dimensional network constructed based on image planar coordinates.The structure of planar network is seriously affected by SAR projection and image resolution.On the one hand, the azimuth resolution of SAR images is usually higher than slant range resolution.That means the real geography landscape will be stretched in radar flight direction, i.e., azimuth direction while landscape is imaged by SAR.By contrast, the target space relationship defined by the network established in geography space will be different from that derived from image space because the sites and space relationship of targets vary with the scene conversion from geography space to image space.Figure 1 indicates the variation of target relationship from geography space to image space.

Experimental dataest
In the last century, the urban area of Shanghai was found beginning to subside because of the excessive exploitation of underground water (Zhang, 2002, Zhang, 2005, Ye et al. 2005).InSAR based on three-dimensional persistent scatter network and two-dimensional network respectively is used to detect the ground subsidence of Lujiazui in Shanghai.Figure 4  25 differential interferograms were generated by the "two-pass" method (Gabriel et al. 1989, Massonnet et al. 1993, Zebker et al. 1994b).Table 1 lists the parameters of all the images, including spatial and temporal baseline with respect to the master image.(c) Three-dimensional Delaunay network with three-dimensional coordinates

Experimental results
By the procedures of persistent scatter InSAR, refined 1520 persistent scatters are detected from 26 radar images by the statistical computation of time series of amplitudes.Figure 5 displays the distribution of all the 1520 persistent scatters marked with yellow points and superimposed onto an optical orthoimage download from GoogleEarth.The two-dimensional Delaunay network and three-dimensional Delaunay network of 1520 persistent scatters are constructed based on image planar coordinates and Cartesian coordinates respectively.Figure 6 demonstrates the two-dimensional network reformed by 1km threshold.4092 arcs, i.e., 4092 NDP observations are obtained from the planar network.Figure 7 shows the planar projection of three-dimensional network optimized with 1km threshold.4502 arcs are generated in this network.The number of NDP observations of TDPDN is significantly more than that of planar network.Based on persistent scatter InSAR algorithm, the subsidence of persistent scatters is derived according to two-dimensional network and three-dimensional network respectively.The statistics of subsidence is displayed in table 2. The maximum subsidence velocity detected with two-dimensional network is 21.0 mm/a and the minimum is 6.0 mm/a, and the average subsidence velocity is 16.8 mm/a.The maximum and minimum subsidence velocities achieved by TDPDN are 18.3 mm/a and 7.8 mm/a respectively, and the average subsidence velocity is 13.7 mm/a.In recent years, both precise leveling and GPS survey have been carried out to monitor subsidence in Shanghai by some authorities (Liu et al. 1998a, Liu, 2000b).The leveling (see Table 2) shows the subsidence rates from 1992 to 2002 in the study area range from 12.0 to15.0 mm/a, and the averaged subsidence rate reaches 12.6 mm/a (Yan et al. 2002).Table 2 shows the annual subsidence rates estimated with InSAR based on TDPDN are in good agreement with the leveling subsidence results reported in some open literature (Liu et al. 1998a, Liu, 2000b).This indicates that InSAR with TDPDN is effective for detecting land subsidence in Shanghai.Furthermore, TDPDN is more advantageous than persistent scatter planar network in terms of accuracy and reliability of estimating subsidence rates at persistent scatters.subsidence field is shown in Figure 9, where the remarkable sinking parts can be better appreciated.
Maximum and minimum subsidence values are -18 and -9 cm, respectively.The current land sinking is highly related to the large-scale urban construction and the overuse of groundwater.Especially from 1992 to 1995, the skyscrapers' constructions are most remarkable (Liu et al. 1998a).It should be noted that the estimated vertical displacement may also contain the settlement of skyscrapers, and not purely the natural subsidence of the land surface.The annual subsidence rate is however much smaller than that occurring in the 1980's.This is primarily attributed to some mitigation strategies which include reducing groundwater withdrawal, increasing river water use, pumping water back into depleted aquifers, and utilizing light materials for construction.

CONCLUSIONS
In order to improve the accuracy of persistent scatter InSAR, the approach for constructing three-dimensional persistent scatter Delaunay network is promoted based on the algorithm for establishing three-dimensional GPS network.The TDPDN

Figure 2 .
Figure 2. The slant range projection illustration of SAR

Figure 3 .
Figure 3.The Delaunay networks generated respectively by planet coordinates and three-dimensional coordinates displays the experimental area of interest (AOI) marked by a box onto the master amplitude image, where the inset shows the enlarged multi-image reflectivity map derived by averaging all the image patches of the AOI.The AOI covers the rectangle geographic scope ranging from 121.44584°E to 121.58915°E and 31.20618°N to 31.288°N.The total area is about 33km 2 .26 single look complex (SLC) SAR images taken by ERS-1/2 during 1992 through 2002 are utilized.The SAR image taken by ERS-2 on Jun 4, 1996 was chosen as the common master image and the remaining 25 images were used as the slave images.Thus

Fig. 4 .
Fig. 4. The experiment area marked by a box onto the master amplitude image

Figure 5 .Figure 7 .Figure
Figure 5. PSs superimposed onto an optical orthoimage Figure 5) in the central part of the study area, where about 15-cm land sinking was accumulated from 1992 to 2002.For visualization, a perspective view of the entire

Figure 8 .
Figure 8.Time series of subsidence at 5PSs as marked in Figure5

Figure 9 .
Figure 9. Perspective view of the subsidence field accumulated between June 1992 and August 2002

Table 1 .
The parameters of 26 ERS-1/2 SAR images used in this study.