A numerical model of extensional tectonics for estimating the stress required for the collapse of normal fault blocks

Introduction
In gravity earthquakes that are affected by extensional tectonics in the crust, contrary to the dominance of elastic energy over gravity in strike-slip and compressional mechanisms, gravity is responsible for hanging wall collapse and earthquake occurrence. Therefore, in normal faulting, the release of energy in the form of elastic waves after the interseismic period is different from other faulting mechanisms. With the increase in the volume of the involved mass and the dip of the normal fault, the vertical displacement becomes larger, which leads to a larger released seismic energy and, consequently, an increase in the intensity of the earthquake. Although normally, the dip angle of activation of normal faults is considered to be around 60 degrees, if the internal friction of the rock is low, a lower dip is expected. Therefore, in this situation, the released gravitational energy will not have the ability to emit much seismic energy. The natural examples of the numerical model resulting from this study can be compatible with geodynamic situations that are characterized by the broad and well-known activity of extensional tectonics and related earthquakes. In addition, energy partitioning is important in earthquakes, and the potential energy stored by the volume involved during coseismic collapse can be compared and analyzed with the energy deduced from the magnitude of the earthquake. Regardless of the origin of the earthquake, potential energy indicates the energy allocation ratio, i.e., the ratio of the available energy to the energy released by the earthquake waves. Therefore, the issue of energy emission from other geological phenomena can be raised, according to previous studies. In this research, the estimation of the stress required for the occurrence of block collapse in normal faults has been investigated through the modeling of a two-layered block with brittle upper crust conditions. Therefore, the thinning of the lower crust during the interseismic stationary periods has been considered, and therefore, along with the extensional tectonics, continuous shearing deformation has also been applied. By knowing the extension rate in the interseismic stage, the stress required to break the entire thickness of the tested brittle crust is estimated.
Materials and Methods
In this article, in continuation of Doglioni's work (Doglioni, 2015), assuming the transfer of the constant deformation of the lower ductile crust upwards, but the different characteristics of the rock materials and the brittle range due to expansion in a conjugate wedge with the main active normal fault, the behavior of faults was investigated through block modeling consisting of a simple double layer with brittle upper crust conditions. It is assumed that the lateral changes in mantle deag with viscous-plastic behavior control the tectonic conditions at the plate boundaries and deformation is transferred from the base of the lithosphere to the earth's surface. Due to the brittle behavior of the upper crust, shallow deformation occurs periodically and the energy accumulated over hundreds of years is released in a very short period of time.
Results and Discussion
In this study, the order of the model elements is based on a non-structured network in such a way that it prevents the influence of the structure of Sparse matrices on the performance of linear algebra operations. While the lower crust continuously has a shearing behavior, the upper brittle crust is locked, and according to the results, an expansion wedge is imagined, and the width of this triangle is depicted here in such a way that it affects the locked fault with a thickness of about 3.5 km. As the ductile lower crust is thinned by viscous flow during the interseismic stationary period, the brittle-ductile transition zone (BDT) is characterized by a pressure gradient, while the viscous-plastic lower crust shows continuous shear deformation.
 
Conclusion
Continuous shear in the lower crust of the finite element model can indicate the locking of the brittle upper crust in the interseismic period of a seismic cycle. By applying tension of 2 mm per year in the interseismic stage, the brittle crust with a thickness of about 12 km needs about 160 MPa to break under tension. Therefore, the increase of accumulated slip from the boundary of two layers, i.e. BDT, towards the mainshock, 50% of the fractures resulting from the interseismic period are closed again (recovery). Considering the lower extension rate in the current model compared to the previous models, the difference in the result of stress required to break the brittle crust can have a significant relationship with the extension rate.