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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
In situ leveling height change measurements at a set
of points from the same area can be used for calibration.
Let Dhr(x) be the leveling height change at location x,
then
Dh, (x) = Dh(x) t ej (x) (2)
where er (x) is the error term modeling errors from
leveling surveying. We apply a somewhat simpler model
for these data as the bias is negligible and errors are
mainly non-spatial in nature. If leveling and D-InSAR
height change measurements are available at the same
location, then from equations 1 and 2 we obtain:
A = Dhg(x) — Dhix) = ma(z)-Fe.(z)-e(r) (3)
where e(z) — es(x) — eg (x) is the independent error
part. In terms of geostatistics, the term rns(x) in equa-
tion 3 is the trend (or drift) that can be modeled by a
kth-order polynomial, e(z) is a zero-mean stationary pro-
cess, and e(x) is the error related to measurement errors
in data collection and/or micro variations.
If sufficient number of well distributed leveling points
are available, mg(x) and es(r) can be modeled based on
their leveling and D-InSAR measurements using a geosta-
tistical approach. This is then followed by a geostatistical
interpolation to create a map.
3 Applications and results
3.1 Data
The proposed method is applied to data collected in Tian-
jin Municipality, China. The city is located at the coast
of Bohai Gulf, and has experienced the most serious sub-
sidence in China since 1959 due to groundwater extrac-
tion. The total subsidence area is approximately equal
to 13.000 km? and consists of five subsidence centers. In
the urban area, the maximum accumulative subsidence
between 1959 and 1986 exceeds 2.5m. whereas the av-
erage rate of subsidence between 1980 and 1986 equals
13.5 emyr~1. By adopting water conservation measures,
including closing some wells and refilling water into un-
derground layers, the rate of subsidence reduced to 2
emyr !. Further industrial development, however, has
stimulated groundwater extraction in the suburban arca,
leading in those areas to a subsidence rate of 5-8 emyr- !.
To monitor subsidence, an claborate network of monitor-
ing sites was established in 1986 (figure 1). Since then,
à leveling campaign has been carried out once every year
mostly in the month of October. In total. six phases of
leveling measurements (1992 - 1997) of the network have
been collected. They indicate a set of points with pla-
nar coordinates in au arbitrary coordinate system and a
CA
/\_/ Boundary of study area
+ Leveling points
Figure 1: The leveling network established in Tianjin to
monitor land subsidence. The total length of the leveling
routes equals 3,000 km. The study area is indicated by a
rectangular boundary.
f I I I.
97/10/02 97/10/03 96/01/11 96/01/12
ERS-1 ERS-2 ERS-1 ERS-2
32499 12826 23481 03808
0 -228/-329 -190/-252 -148/-150
Table 1: Differential SAR interferometric images I . . . iy
collected at several dates (first row), by two satellites
(second line), at different orbits (third line) and differ-
ent baselines (B, / By) (fourth line).
series of height values measured at different times. Two
tandem pairs of ERS-1/2 SLC SAR images covering the
urban area of the city, acquired in 1996 and 1997. respec-
tively, have been collected as well. The spatial baselines
as well as time differences of the images are listed in table
j.
3.2 Integration
Among the 399 leveling points, 173 points selected at ran-
dom are used as test points, and 226 others are used as
control using cross-validation. At all leveling locations
the discrepancies between D-InSAR and leveling mea-
surements are calculated using equation 3. Systematic
distortion is predicted for each extracted coherent. pixel,
and subtracted from the original D-InSAR measurements.
The contour map based on the calibrated D-InSAR mea-
surements is shown in figure 2. À comparison using box-
plots and residual variograms is made with (a) original D-
InSAR. measurements and (b) error-detrended measure-
ments. Box plots of discrepancies at 226 control points
9
