The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
162 
interferograms, on which the fringes caused by baseline errors 
is first estimated with FFT in range and azimuth direction and 
then eliminated. The nonlinear algorithm is performed in phase- 
unwrapped maps, where a quadratic surface function is used to 
fit the trend of unwrapped phase and then the trend is subtracted. 
The quadratic function can be described by: 
f\x,y) = a, + a 2 ■ x + a 3 • y + a 4 ■ xy + a 5 ■ x 2 + a 6 ■ y 2 (3) 
where a n (hi = 1 • • • 6) = polynomial coefficients 
x,y = coordinates in range and azimuth directions. 
3. RESULTS 
To verify the effectiveness of linear and nonlinear methods for 
mitigating the baseline errors, ESA Envisat ASAR data at Bam 
area are selected. The selected image pairs and baselines are as 
follows. 
Master 
Slave 
Temporal 
Perpendicular 
Baseline 
Baseline 
9192 
6687 
-175 days 
475 m 
9192 
9693 
475 days 
530 m 
Table 1. SAR images pair and baselines 
The data was processed by DORIS software with two-pass 
diffemential method, in which SRTM3 DEM was used to 
remove the topographic effects. The results are as follows. 
Figure 5. Figure 6. 
Figure 1. Interferogram (9192-6687,coarse orbit used) 
Figure 2. Residuals of Fig. 1 after subtracting bilinear fringes 
Figure 3. Interferogram (9192-6687,precise orbit used) 
Figure 4. Rresiduals of Fig.3 after subtracting bilinear fringes 
Figure 5. Interferogram (9192-9693,precise orbit used) 
Figure 6. Residuals of Fig.5 after subtracting bilinear fringes 
From the comparison of interferogram between Figure 1. and 
Figure 3., we can see that the pattern of fringes mainly takes on 
the characteristics of linear trend. The fringes on Figure 1 and 
Figure 3. are mainly ascribed to baseline errors, for no obvious 
deformation takes place during the 175 days of SAR images 
acquirement. The pattern difference between them are only due 
to the difference of the orbit accuracy: Figure 1. with precise 
orbit and Figure 3. with coarse one. Figure 1. is generated 
during BAM earthquakes, on which the batterfly-look fringes 
are very clear. However the three other linear fringes cannot be 
due to earthquakes, and they should be due to the baseline 
errors. If the linear fringes are not eliminated, they will affect 
the interpretation of the earthquakes. Maps Figure 2, Figure 4, 
and Figure 6 are respectively the results of Figure 1, Figure 3, 
Figure 5 after subtracting the linear fringes estimated from FFT 
spectrum. 
The fringes caused by baseline errors can be removed in two 
methods. One is bilinear method, which is performed on 
interferograms, the other is nolinear method performed on 
phase-unwrapped maps. The results of both methods are as 
follows. 
580 5M 58« 59.2 
sao m.4 m.2 
warn^ 
0 $ to t5 20 25 30 35 40 45 
Figure 7. 
58 0 584 58.8 562 
58.0 58,4 £*,» 50.2 
tO 8 «-4-2 0 2 4 
Figure 8. 
Figure 3. 
Figure 4.