contains solutions for events with magnitude about and greater 
than 5.5. There are 275 earthquakes (Mox1*10?) for the study 
area and the August 17 earthquake was excluded since it 
decreases the strain rates. Thus earthquakes input file includes 
274 earthquakes in a time interval of 30 years. For the creation 
of the earthquake focal mechanisms input file, a Java program 
was created and these data updated periodically in the 
application. Global CMT catalog uses dyne-cm unit. 1 dyne- 
centimeter is equal to 1E-007 Newton-meter. Sparse coordinate 
system for moment tensor components is different from this 
catalog and also from [6]. Therefore conversion is needed for 
both notation and direction of the axis (mxx- mpp, myy- mtt, 
mxy--mtp). 
2.3 Strain Algorithm 
Strain is relative movement of the points on the Earth's surface 
and caused by continental plate movement. 
In two dimension, two lines form the axes of the strain ellipse. 
The principal axes of strain £i and Es are given by: 
  
1 € 
EE; = 2€» +e, )* 
(1) 
with directions Ÿ and O+(x/2), with 9 given by: 
26. 
tan(20) z — ——— 
€ L6. 
xx yy (2) 
£i and ^2 can be positive or negative. In graphical 
illustration, these values are pointed by arrows. There are 
different kinds of methods to obtain strain parameters. The 
method, which was developed [4] in order to estimate a strain 
rate and velocity model, is followed to carry out this research. A 
comprehensive overview of the methodology can be found in 
[5]. According to [4], the horizontal velocity field u(r) for the 
spherical Earth expressed as 
u(X) 2 rW(X)xx Q) 
where r is the radius of the Earth and Ÿ is the position vector 
on the Earth's surface. It determines W(x) at the nodes of a 
rectangular grid using bi-cubic spline interpolation. These 
values are obtained from least-squares inversion between 
observed and predicted values of strain rate and velocity. 
Depending on the data distribution on the study region, 
smoothing between neighbouring grid cells is required. No 
smoothing takes no account of how the strain rates are 
distributed in neighbouring rectangles, in which the strain rates 
may be significantly higher or lower. In the case of seismic data 
inversion, strain rates are estimated from Kostrov summation 
[7]: 
1 
&, ETT Mom, 
HT (4) 
where H is the shear modulus, V is the cell volume (the grid 
area times the seismogenic thickness), T is the time period of 
the earthquake record, M, is the scalar seismic moment, and mj 
is the unit moment tensor. Shear modulus is taken as 
3.5x10" Nm” and seismogenic thickness is 30 km. These 
chosen values affect the magnitude but not the style of the 
estimated strain rates. Programs to calculate strain rate consist 
of over 20 open source FORTRAN programs which run on 
Linux operating system. Content of the input files vary 
depending on the inversion type, selected area and data used. 
Creation of these files which may contain over hundreds of 
lines requires programming. These initial files include data 
pertaining to geometry, earthquakes and GPS. In addition, 
programs need some other input files which created during the 
run process. The geometry file is to create a rectangular grid for 
the area of interest. A sample of the content of the geometry file 
is as follows: 
50 30 4 
0-0.3 0.3 
30 20 
10303 
30 20.5 
20303 
30 21 
30303 
30 .21.5 
Header line has the maximum number of knot points in X 
direction, maximum number of knot points in Y direction and 
number of rotation value while other lines include the number 
of X coordinate, number of Y coordinate, and three indices 
(number of rotation value, index for xy derivatives of rotation 
value, index for xy derivatives of latitude-longitude). The knot 
points of the grid are the points where x and y have integer 
values. The model is calculated on a regular grid structure, 
which each grid area is in 0.5x0.5 degree size (50 grids between 
20 « longitude (E) (X) « 45 and 30 grids between 30 « latitude 
(N) (Y) « 45). So the total number of grid areas is 1500 and the 
number of deforming grid areas is 1081. In other definition, the 
total number of knot points is 1581 and the number of 
deformation points is 1053. The results are velocities at 1581 
points and strain rates at 1081 points. The number of rigid 
blocks is 3, and it is assumed that rigid plates are not deforming. 
34 grids cover AR rigid block, 135 grids cover AF rigid block, 
and 250 grids cover EU rigid block in the study (Figure 2). 
Na. v a 4 
o » 
ee ee et v^ 
x T" Tv 
€ 9 COM S 0 4 4 4 0 9 9 9 td t ng + +... ++ #44 + ttt reg 
1244 CELLES dans ass nu 0 CC 
ti tr 
+ he 4 SNS T4 640 000000000005 0000000 UN nt + 4000 
» L2 
* 
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N estan 008 TTL, 
t Ma 
: 
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SL I Raa EI M 
t. 
eret n . . . 
B E À 
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ned Ta 
aeg... pipi fult .. . 
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1:0 
Ky 
Figure 2. Grid geometry for the study area with known active 
faults of the region 
The extent of the rigid blocks is based on the seismicity [8], [9]. 
[10]. Strain programs assigns “rotation value numbers” in a 
236 
  
€) "r3 C, — — — 9 vc N A MN C0 s Un