International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
In the primed interferogram, the phase @ is 
1 ÀE in 
$-2—(B*^o) — (9 
The surface displacement Ap adds to the topographic phase 
term, which could create confusion in the interpretation. 
However, if the data from the initial unprimed interferogram are 
; : : Bj, 
properly scaled with a proportional factor —L and subtracted 
// 
from the primed interferogram, we can obtain a solution 
dependent only on Ap , as follows: 
, B, dr 
dim A 
? 5," A p 9) 
Since the quantity on the left is determined entirely by the 
phases of the interferograms and the orbit geometries, the line- 
of-sight component of the displacement Ap is measurable for 
each point in the scene. 
For operational use, a common method is that the baseline 
parameters of primed interferogram are used to simulate the 
unprimed interferogram derived from only topography effects, 
which then is subtracted from primed interferogram. The 
resulted differential interferogram contains only the information 
related to surface deformation. 
It is important to assess the relative sensitivity of the phase 
measurement to topography and displacement since the 
topography itself may be poorly known. From the imaging 
geometry, it can be seen in Fig.1 that the height z of the point z 
(y) can be determined by: 
z = H — pcos0 (10) 
where H is the flying height. The relative sensitivity of the 
phase may be derived by differentiating Eq. (10) with respect to 
6: 
dz = psin dO (11) 
And also we can differentiate Eq. (8) with respect to Oand 
displacement Ap . Because of the irrelevance between Ap and 
B, and recalling Eq. (4), we can obtain Eq. (12) and Eq. (13): 
dg’ - D B'cos(0 — a°)d0 (12) 
d)! 4z 
d^p À 
(13) 
  
For the displacement case, we have Eq. (13). Combining Eq. 
(11) with (12), we can obtain Eq. (14): 
dé 4z B'cos(0 —') (14) 
dz À psin 
Since baseline length (a few hundred meters) is much less than 
p (a few hundred kilometers for a spacecraft system), it is 
. ~ ^ . / C , . 
evident from Equation (13) and (14) that — 1s much smaller 
dz 
, 
  
than . Thus, the measured phase is much less sensitive to 
d^p 
topography (Eq. (14)) compared to displacement (Eq. (13)). 
When the accuracy of measuring topography using SAR 
interferometry reaches the level of meter, the accuracy for 
measuring deformation displacement can reach the level of 
centimeter or Millimeter. Comparing the two results 
numerically for the case of ERS-1, 1 m of topography gives a 
phase signature of 4.3 degree (actually less than the real noise 
limit about 20 degree, implying that ERS-1 is not sensitive to 
topography at this level). However, for the same pass pair, a |- 
m surface displacement yields a phase signature of 12,800 
degree, or nearly 3000 times greater sensitivity. Since we seek 
to measure 1-cm surface changes, this implies that we require 
topographic data accurate to about 3000x 1 em, or +30m. 
3. CASE STUDY 
The Mani Earthquake occurred 10:02:55.4 a.m. (UTC) on Nov. 
8, 1997 around 150km away from Mani country in Naqu region, 
Tibet, China. The location of epicenter is 8733 E, .35.260?N.1 
the depth of 40km, the magnitude of Ms7.4 measured by China 
earthquake observation network. Concerning the earthquake, 
the data measured by NEIC (National Earthquake Information 
Center of America) are that: time is 10:02:54.9 a.m. (UTC) 
location of epicenter is 87.37^E/135.1 1?N the depth of 35km, 
and the magnitude of Ms7.9 (Feng Hao, 1997). 
Mani Earthquake is the strongest event in China since 90's in 
20 century. Investigation and research of its principle and 
geometry, dynamics related to surface rupture zone is very 
significant to analyze the development and evolution of China's 
earthquake in the future. In this study, we investigate the 
distribution of surface deformation and extract displacement 
information of the earthquake rupture zone using differential 
SAR (ERS1/2 SAR) interferometry. 
3.1 Site Background and Data Source 
The epicenter of Mani earthquake is located the nearly east to 
west Margaichace-Ruolacuo fault zone along the northern 
boundaries of Qiang-Tang block, south of Chaoyang lake. The 
Margaichace-Ruolacuo fault extends approximately 270km and 
has experienced strong events since Holocene epoch. Remote 
sensing images around this area are characterized by less 
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