Probable earthquake magnitude prognosis By Ergodic Method (case study: Yazd providence)

Since long ago, the process of fault genes in the earth’s crust is considered as a complex factor in the research performance within the earth at different scales. In simple terms, faults are created due to the transformation in the layers of earth crust and creating local tensions and rapture in the rocks (Wellman, 1978). One of the most original historic faults is the vibration parallel to rapture plate and happening hazards such as creating ability of seismicity in the region. This vibration can be either slow or sudden. Sudden vibrations are often the factor of creating earthquake which depends on the characteristic and dynamics of fault. Therefore, to perceive the physic of these faults it is necessary for the implementation of methods to predict earthquakes. The fault networks and earthquake follows a series of natural non-linear system and driving threshold system (Ferguson et al., 1996. Kay, C et al., 1961, White et al, 1965). The numerical simulation is used to predict how the faults perform (Ergodicity). Ergo in Greek means work or energy and Hodos means path (Pain, 1985). In simple terms, Ergodicity consist of evolutionary and historical changes of phenomenon so that changes can be classified in different phases. The most important features of this classification are based on the uniform average change level during each session of the development (Vernott et al, 2006). In 1993, for the first time Ergodic idea were formulated in a non-linear driving systems (natural fault) by fluctuation metric Thriumalai-Mountain (TM). According to the theory of metric (TM) Ferguson et al, on the bases of available observation assessed the function of several natural fault system (California between 1932 and 2004 in the region of 32 to 40 degree latitude and -115 to -125 degree longitude, Iberian Peninsula and North west America at 35 degree latitude and 45 degree North and between longitude of 5 degree to -15 degree and East Canada at 42 degree to 51 degree latitude and -60 degree to -85 degree longitude) using the data from Southern California Earthquake Center (SCES) and Northern California Seismic Network (NCSN). The result obtained examined the natural fault system for long period of time having magnitude M 4 Ergodic and large seismic events that can directly remove the system from ergodicity identified that this very large event eliminates the system out of balance for a time period and after that a quasi-equilibrium state is created. This case is called as outstanding balance or oscillatory mode (Ferguson et al, 2003). This article aims to study the Ergodicity threshold in the fault system of Yazd Province and distinguish the presence of marked equilibrium according to the characteristics of earthquake process which is the function of extent and data accuracy and seismology catalogs. Of course, testing the recent hypothesis of Ergodic method used is known as the Thirumalai-Mountain (TM) metric method.

With this method, the ability to release energy by the regional fault is assessed by using fluctuation metric (TM) Thirumalai-Mountain method according to the number of seismic events with specific or greater magnitude for a time period, quantitative and their influence on the Ergodic features occurred in the region under investigation. Fluctuation Metric mentioned by Thirumalai-Mountain (TM) is the relationship shown in equation 1, (Thirumalai-Mountain, 1993) and (Homes et al, 1996). Eq. 1.

In this study, for understanding the behavior of fault of Yazd Province (faults of Dehshir, Anar, Poshtebadam and ShehrBabak, …) and assessing the ability of seismicity based on evidence or statistical distribution of events during a specified time period the following information were used from Geophysic institute and International Institute for Earthquake Engineering and Seismology (IIEES) and Russian Institute of Seismology Center (ISC). Therefore, from the scope and specification of faults catalogs were prepared where each one is used for review and Ergodic probability in the region based on the number of events that occurred in a time period with specific or greater magnitude m 2, m 3. The region was analyzed with fault quantitative (temporal – spatial) and assessed by fluctuation metric (TM) Thirumalai-Mountain method. Initially by catalog and Gutenberg-Richter law the regions seismic parameter value (a, b) and N(t) value per year was calculated. Later, after using the produced catalog, the diagram of number of events per year based on different magnitude was prepared and inverse TM value was calculated. To calculate the average time of faults, equation (2) is used by selecting the increasing intervals of a year for integration and substituting the size of event N(t) per year, the average time period for specific magnitude M m were obtained respectively. Then the same mean was calculated in the whole system using equation (3) which is related to the average time period for the duration. Accordingly, the values calculated by the mentioned formula is substituted in equation (1) and (TM) metric value and its inverse were calculated for each year and its graph was drawn based on duration of time period for magnitude of m 2, m 3. Consequently, based on graphs Ergodic probability and prediction of probable earthquake magnitude in the region were considered. In order to calculate the seismic parameters (a, b) in Yazd Province the Gutenberg-Richter law were used. Therefore, for radical range of 200 kilometers from the central location of the Province (31.896, 54.368) is used from the information and specification of earthquake catalog with specific magnitude (m 3, m 2). Therefore, the events were classified according to the magnitude and then frequency and cumulative frequency of each category were calculated. another equation is used to obtain the parameters of earthquake (a, b) of Yazd region with specific magnitude m 2 and m 3 and time period 1927 to 2010. With the desired parameters of the seismic region the N(t) value for the event per year can be obtained and its value can be substituted instead of Et(t) in equation (2). Conclusion With regard to the studies done by Thirumalai-Mountain metric method to identify and define the existence of Ergodic probability in the fault system of the region (Dehshir, Anar, Poshte Badam, ShahrBabak and Shirkooh) and taking advantage from the specification and seismic data of Dehshir fault by using full spatial range from the coordinate range of Dehshir fault, it was found that the structural behavior of this fault is Ergodic for the magnitude m 2 in 1996 to 2001 and 2002 to 2005 and 2006 to 2010 and the magnitude m 3 for the whole period from 1996 to 2010. It is not Ergodic due to the lack of coherence time for magnitude greater than M 4.