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Yueqin Zhou 
  
It can be seen from (5) that the accuracy of the height change relies on the accuracy of the differential interferometric phase, 
which means if the differential interferometric phase values contain errors due to random phase noise and systematic 
artefacts, the derived height changes contain also errors. 
3. ERROR ANALYSIS AND MODELLING 
(1) and (2) have been based on the assumption that the interfero metric phase is only related to the slant range change due to 
the topography and the surface motion. In fact, several other factors have the influence on the interferometric phase, either 
result in noise that degrade the quality of the interferogram, or ca use extra phase differences, which are so -called artefacts. 
The main factors that cause phase noise are radar thermal noise, image misregistration, and temporal decorrelation etc. It 
has been proven that the radar thermal noise is too small that can be neg lected. On the other hand, the image misregistration 
can be avoided through precise registration up to 1/10 pixel. The most important factor, therefore, is the temporal 
decorrelation, which is inevitable especially in the case of monitoring very slow land subsidence since in this case a big 
. time interval (on the scale of years) is often required. The phase noise make the phase unwrapping very difficult, which in 
turn leads errors to the unwrapped phase values. 
Among others, the most important factors that may result in the artefacts are the atmospheric effect as well as inaccurate 
orbital parameters, and inaccurate topographic information used for removing topographic effects. The artefacts due to 
inaccurate orbital parameters can be corrected if enough ac curate ground control points are used. The effect of inaccurate 
topographic information may be avoided by using the image pair with very small perpendicular baseline, or very accurate 
reference DEM. The atmospheric effect, therefore, is the major limiting factor for the repeat-pass interferometry (Goldstein, 
1995). It can result in up to three extra fringes in the interferogram. These fringes appear to be similar to ground 
deformation, and hence might be interpreted as the ground deformation. 
One way to separate out the atmospheric effect from the true movements is to use multiple observations and average the 
derived products (Zebker et al., 1997). The other method is to model the atmospheric effects by using the meteorological 
data at the time of image ac quisitions (Hanssen and Feijt, 1996). The use of above two methods is sometimes limited by the 
data availability. 
The approach applied in this paper is to integrate the ground levelling measurements into the differential SAR 
interferometry. Assume that the overall effects of errors contained in hD -InSAR height change values can be grouped into 
three parts: blunders, additive random errors, and systematic errors. Under the assumption that land subsidence has a 
smooth pattern, the blunders are eliminated in the first by low-pass filtering. Then, at a given point, the following equation 
is assumed: 
dh = dh'+d +u (6) 
Where dh indicates the true valve of height change at the given point, while dh'is denoted as the computed height change 
from the differential SAR interferometry. The last two terms of (6) are the systematic error and the random noise, 
respectively. A simple but efficient model to fit the systematic error is polynomial: 
d=a,+ax+a,y+axy+ax’+ay’ +- (7) 
in which, a,,a,,--- are called polynomial coefficients, X,y are the coordinates of the given point. Assuming the random 
error is the white noise, the polynomial coefficients in (7) can be estimated using the linear regression analysis by means of 
a certain number of levelling point measurements. Then the height change values are calibrated based on (6) and (7). 
4. DATA PROCESSING AND RESULTS 
4.1 Test site 
Tianjin City, which has experienced the most serious subsidence in China since 1959 due to over exploitation of 
groundwater, is selected as the test site. The total subsidence area exceeded 13,000 km >. Five subsidence centers were 
identified, marked with cycle in Figure 2. In the urban area, the maximum accumulative subsidence from 1959 to 1986 
exceeded 2.5m. The average subsidence rate in 1980-1986 reached to 135mm per year. By adopting water conservation 
measures in 1986-1988, including closing parts of the wells and refilling water into underground, the rate of subsidence has 
been significantly reduced down to 20mm/yr. However, the further industrial development has pushed up extraction of 
groundwater in the suburban area, and the subsidence rate to 50-80mm per year. In order to monitor subsidence, an 
elaborate network of monitoring sites, shown in Fig.3, has been established since 1986. The levelling survey is carried out 
once a year in October. Six phase levelling measure ments spanning from 1992 1997 were used for the test. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 355