Novozhilov Mean Rotation as a scalar earth surface deformation measure in local scale (Case study: N-W of Iran)

The regions of northwestern Iran, eastern Turkey and Caucasus are one of the most intriguing regions of the Arabia-Eurasia collision. It is a pure intercontinental collision zone with the highest elevation in western Asia. This region is known for a spatial separation of sub-parallel thrusts and strike-slip faults. Iranian plateau includes two major mountain belts, hence Alborz in the north and Zagros in the south and west of Iran. Azerbaijan includes Alborz mountains, Talesh and Lesser Caucasus along with mountains in the Azerbaijan plateau. Azerbaijan is between great mountains of Caucasus in the north and Alborz in the east and distance away from Zagros in the south. A lot number of faults including Tabriz fault and Aras fault meet in the west of the study area.
One of the most fundamental and important a new area of research in geodesy is earth surface deformation modeling at local and global scales. Also, check out the effective factors in deformation, and offers various computation methods in order to determine the movement of the earth's crust are considered as a recent development in geodesy. In recent years, space geodetic techniques with high precision and reliability have provided new sources of information to determine the geodetic positions. This information used for the detection and quantification of surface deformations. In this paper, Novozhilov method has been studied for mean rotation calculation with finite difference approach on earth surface in N-W of Iran especially north Tabriz fault. To achieve this goal, linear strain and rotation tensors on earth surface based on shell theory in continuum mechanics will be calculated using finite difference approach and then the mean rotation is extracted using linear strain and rotation tensors. Finite difference method is numerical methods based on mathematical discretization of the equations of boundary problems. By using this method, continuous process is studied in a finite number of sufficiently small time intervals. So it is possible, in these small intervals, the function approximated by approximate expressions. In each elementary interval is the integration, with the results of integration in the previous interval are taken as initial for the next time interval.
In the fourth decade of the 20th century Novozhilov obtained a measure of the mean rotation by modifying a previous definition produced by Cauchy. In the literature, this measure has been named Novozhilov's mean rotation measure ever since. The measure introduced by Novozhilov for the mean rotation indicates the importance of the infinitesimal rotation tensors.
The results obtained from linear strain and rotation tensors that computed using geodetic observations (GPS) in 2005, have good agreement with the results of previous work. The results of Novozhilov’s mean rotation criteria in the part of the Azerbaijan plateau shows that the highest right turn rotation is related to YKKZ station (2.975±0.631deg/Myr). An important feature of Novozhilov’s mean rotation analysis on earth surface than analysis of this parameter in Cartesian system is that the results of this measure on earth surface is very close to the results of previous studies on blocks rotation in different areas in Iran. Accuracy of this measure on earth surface is acceptable in most parts of the case study.