International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
1 Introduction 
Synthetic Aperture Radar (SAR) is an active remote sens- 
ing system, operating in the microwave region of the elec- 
tromagnetic spectrum. It emits a series of coherent, pulsed 
electromagnetic waves from an antenna mounted on an 
airborne or spaceborne vehicle, and records amplitude 
and phase of backscattered signals from objects on the 
ground (Hanssen 2001; Zhou et al., 2003). In this sense, 
SAR systems acquire complex images. The deformation 
of the ground surface, such as earthquake displacements, 
land subsidence caused by groundwater, natural gas, or 
oil extraction, can be quantified by comparing the phase 
information of two complex SAR images of which the 
first is recorded before deformation, and the second there- 
after. This is done using differential SAR interferometry 
(D-InSAR). D-InSAR provides a deformation image on a 
pixel-by-pixel basis over an area of thousands of square 
kilometers. 
Traditionally, leveling is used for measuring vertical 
deformation, i.e. subsidence and uplift, at a spatially dis- 
crete set of locations along trajectories. It is followed by 
interpolation to get a continuous two-dimensional cover- 
age. The accuracy is high at measurement points, but 
may be low at non-measured points. Besides, for a non- 
homogeneous deformation pattern, point-wise leveling mea- 
surements may not always be effective to represent defor- 
mation, unless points are measured at a very high density. 
So far, D-InSAR has not been as widely used as level- 
ing. The main reason is that it produces noise and causes 
artifacts during data acquisition and processing. Noise 
is created by decorrelation between two or more images 
acquired at different times, whereas spatial and temporal 
variation in the atmosphere creates artifacts that are dif- 
ficult to distinguish from ground deformation. For these 
reasons, D-InSAR accuracy may be too low to detect 
small deformations. Although error sources are inevitable 
in differential SAR interferometry, their effects can be re- 
duced. 
Several studies show an agreement between DInSAR 
measurements and leveling results in detecting land sub- 
sidence (e.g., Carnec and Fabriol 1999), but both can be 
ineffective if used alone. If only vertical deformation oc- 
curs, à solution is to combine D-InSAR with leveling as 
recommended by Van der Kooij (1995) and Van Bree et al. 
(1999). As an alternative, Zhou et al. (2000) use a set of 
sparsely distributed leveling measurements as the ground 
truth, and fit a polynomial model to the differences be- 
tween the two kinds of measurements at test points 
In this study we further integrate data obtained with 
InSAR and those obtained with leveling. The objective is 
to correct the errors contained in D-InSAR measurements 
by using measurements as the ground truth to improve 
their accuracy. We propose the use of geostatistics to in- 
un 
tegrate leveling with D-InSAR. Geostatistics is well suited 
to deal with data that are neither deterministic nor. purely 
random, and show spatial correlation. The spatial corre- 
lation is estimated by variograms, which in turn are used 
to estimate deformation at non-measured locations (Chils 
and Delfiner 1999). The proposed method is applied to 
data collected in Tianjin Municipality. China. where land 
subsidence occurs due to groundwater extraction. 
2 Materials and Methods 
2.1 Height change measurements by dif- 
ferential SAR interferometry 
Differential SAR interferometry creates two interferograms 
(phase differences) from single look complex (SLC) SAR 
images. The first interferogram results from two images 
spanning a relatively long time interval. If the inter- 
ferogram is used to detect land subsidence between two 
image acquisitions, it contains fringes due to both topo- 
graphic effects and height changes. The second interfero- 
gram comes from two SAR images spanning a relatively 
short time interval, say, one day, or is calculated from 
an external Digital Elevation Model (DEM). and contains 
topographic fringes only. By differencing the two interfer- 
ograms, topographic effects are removed, and only height 
change effects remain. 
2.2 Integration of leveling and D-InSAR 
measurements using geostatistics 
Let Dhg(z) be a height change measurement obtained 
with D-InSAR at a two-dimensional coordinate vector r 
(the center of a pixel). Taking the different types of errors 
in the measurement into account, we model DA,(x) by the 
expression 
Dh,(x) = Dh{x) + ms(x) + es (x) - e,(x) (1) 
where Dh(x) denotes the true height change at x, 
and m;(xr) and e(x) constitute the systematic distortion. 
The term ms(x) models the bias mainly due to mean 
atinospheric effects and possible indetermination of the 
orbital parameters, e(x) is the spatially correlated error 
caused by local atmospheric effects and uncertainty in 
topographic correction. We assume that Cov(e(x), e(x * 
h) — C(h), C.(h) being a covariance function, depend- 
ing only on distance A. Systematic distortion is estimated 
during post-processing, yielding an estimate for the true 
height change and additive white noise after subtraction. 
A calibrated raster height change map is generated on 
the basis of height change measurements corrected for 
systematic distortion. 
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