Interseismic behavior of active faults estimation based on geodetic observation, the case study: north Tehran fault

 Studying active faults behavior for earthquake prediction and recognition is a concentrated subject in earth science. Precise measurements of earthsurface deformation by geodetic observation provide a good reference for studying different geodynamic phenomena.  Applying geodetic measurements in postseismic and interseismic intervals is an important tool for estimating strain accumulation and rheological properties of the faults. However, the geodetic measurements only describe the movement of selected points and therefore are not a direct estimation of the rheological properties of the region. To derive the values of those parameters, assumptions on the behavior and on the properties of the lithosphere surrounding the fault should be introduced and then by applying geodetic displacement field as boundary value of elastic and viscoelastic formulation, the inverse problem could be solved. The important problem in these inversions is the complex non-linearity of this formulation which classic inversion methods cannot solve them well. Global optimization methods are usually applied to solve these inversions.
In this study, we estimate the interseimic behavior of North Tehran fault. North Tehran fault is a north-dipping thrust fault marking the boundary between Eocene rock formation and alluvium. It is the general term for the abrupt change of elevation between Tehran’s piedmont and rock formation raising over 2.5 km above it. The North Tehran Fault is located at the southernmost piedmont of Central Alborz. It stands out as a major active fault menacing directly the city of Tehran, a 12 million inhabitants mega pole, and would have been the source of several major historical earthquakes in the past. The fault zone extends within the 110 km and corresponds mainly to a reverse fault crossing the northern suburbs of the Tehran metropolis.
In order to investigate the recent crustal movements in Tehran north fault, the design of a leveling network containing three leveling circuits across the fault was taken in 1997. The main corrections to the data is applied including gravity irregularities, rod miscalibrations, residual refraction and rod scale expansion because of temperature differences. Another leveling observation was performed in 2005 in three distinct lines. We used these observations for assessing North Tehran interseimic behavior. The methodology of geometrical modeling of surface vertical deformation is applied to fix the datum of leveling observation in non-deformed region. For this, Mean and Gaussian curvature differences were introduced as scalar invariants associated with the tensor of change of curvature.
Using precise leveling observations, Okada relations are inverted applying simulated annealing algorithm in Bayesian framework. Simulated annealing is a procedure analogous to thermodynamic annealing where the chaotic motions of atoms of a molten solid settle down to form a crystal with minimal energy under certain suitable conditions. With a similar analogy, the unknown model parameters constitute the molecules of a molten solid in which the chaotic motion of them during temperature reduction gradually ceases and the state corresponding to the global minimum of the cost function becomes highly probable at a very low temperature.
The inversion results show the uplift of the hanging wall and subsidence of the footwall of the fault. The estimated slip rate is 1.9±0.2 for the eastern part and 5.7±0.04  for the western part of the faults in 1997-2005 period.