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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B8, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
The second row figures show a similar cross section of surface 
but indicate the relative location of both first and second order 
of momentums to be used in direction finding procedure. It is 
obvious that both orders points in the normal shape are 
coincident while there is a displacement of both of them in the 
inclined and affected state. The vector connecting first to 
second order point introduces the inclination direction of 
wave's peak in a 3 dimensional space. Portraying this vector on 
the X-Y plane gives the direction of the current in the local 
coordinate system, which will be transferred in the specific 
coordinate system for further use. Here are the equations to 
compute the first and second order surface momentum having 
the coordinates of points Eq3. 
  
  
  
em 
ym d 
Wired Direc Lun 3 
  
  
Figure 3. a) First order of surface momentum point of resulted 
surface of a normal wave in a cross section of a plane 
perpendicular to the X-Y plane (Most top). b) Distance vector 
between surface points and First order of surface momentum 
point of resulted surface of a deformed wave in a cross section 
of a plane perpendicular to the X-Y plane (Top). c) Second 
order of surface momentum point of resulted surface of a 
normal wave in a cross section of a plane perpendicular to the 
X-Y plane (Lower). d) First and Second order of surface 
momentum point of resulted surface of a deformed wave in a 
cross section of a plane perpendicular to the X-Y plane 
(bottom). 
G) 
  
Where r(i) Distance between the first momentum and 
surface Points 
O(k) First surface momentum point of kth maximum 
point 
O’(k) Second surface momentum point of kth 
maximum point 
P(i) The ith point of surface peak 
The second order surface momentum inclines toward the 
sharpness tip of a deformed shape. Finally to get a better and 
more reliable result out of this method, the surface model can be 
accompanied with the bathymetric models of the area. 
3. THE DATA USED AND RESULTS 
The method described above must be applied on a dataset in 
order to see its impact and results in a real case. For some 
reasons the TerraSAR-X dataset was not accessible and we were 
obliged to use another satellite data. The data used in this paper 
is from Jason] satellite altimeter and was taken from the NOAA 
(4| website. Hope to use the TerraSAR-X data in the future 
works. The Surface model is determined using the Delaunay 
triangulation method. This surface has been used in our method 
and the results which were in the local datum have been 
transferred in to the UTM system. For better demonstration and 
use of dataset results, the vector field has been exported in the 
KML format to be shown in the Google Earth Environment. 
The location of data set is over the Hormuz strait connecting 
The Persian Gulf and The Oman Sea. Vector field over the 
Hormuz Strait is shown in the Figures (4, 5 and 6). 
    
    
Figure 4. Surface current vector field Over the Coastal area of 
Hormuz Strait in an overall view and low resolution but high 
density. 
Figure 5. Surface current vector field Over the Coastal area of 
Hormuz Strait in detailed view and high resolution and vector 
density.