بررسي ماهيت و پيش بيني سري هاي زماني زمين لرزه هاي شهر تهران

Nature Evaluation and Time Series Prediction of Tehran Earthquakes

با بررسي تاريخچه تلاش هاي بشر براي ايمن سازي در برابر اثرات زلزله، با حوادث تلخ و زيانبار بسياري مواجه مي شويم. با توجه به آنكه اغلب تصميم گيري هاي مرتبط با تاثير زمين لرزه، بر پايه ي تصادفي بودن آنها اتخاذ شده است، بررسي صحت اين فرض مي تواند گره بخشي از خطاها در مقدمات ايمن سازي را آشكار سازد. بررسي هاي اخير نشان داده است كه ساختار ديناميكي اين رخدادهاي پيچيده با استفاده از مفاهيم نظريه ي آشوب بيش از ساير تيوري ها قابل فهم مي باشد. در اين مقاله، 9 زمين لرزه رخ داده در محدوده شهر تهران انتخاب و مكانيزم رخداد زلزله ها از نقطه نظر تصادفي و يا غيرخطي بودن سري زماني مربوط به آنها، با استفاده از اصول نظريه آشوب مورد بررسي قرار گرفته است. به اين منظور بازسازي فضاي فاز براي تعيين زمان تاخير با استفاده از روش تابع ميانگين اطلاعات متقابل و همچنين روش نزديك ترين همسايه هاي كاذب جهت تخمين بعد محاط، بكار گرفته شده است. از روش بعد همبستگي براي بررسي حضور آشوب در ساختار زمين لرزه ها و از روش پيش بيني موضعي و شبكه عصبي مصنوعي، جهت بررسي ماهيت آشوبي و پيش بيني زمين لرزه هاي آشوبي استفاده شده است. نتايج تحقيق نشان مي دهد كه ديناميك حاكم بر زمين لرزه هاي اين منطقه تصادفي نيست. اين زلزله ها رفتار آشوبي با بعد بالا از خود نشان مي دهند. پيش بيني زلزله ها با استفاده از شبكه عصبي نتايج رضايت بخش دارد.

The history of the human efforts for safety against earthquakes shows the catastrophic and harmful events, even nowadays. The majority of decisions in seismic safety policy are based on randomness assumption for earthquake time series. The accuracy of this assumption assessment, can accurate the strategies and resulted in more secure decisions. Also in structural control context, seismic time series prediction in the feedback systems, can reduces the time of control system reaction and in subsequent decreases structural damages. Recent studies have shown that dynamical structure of these complex time series can be better understand using nonlinear dynamics theory. In the present paper, we evaluate randomness and nonlinear characteristics of 9 earthquakes time series from metropolitan Tehran earthquake database using chaos theory conceptions. These earthquakes are Arjomand, Bumahen, Damavand, Eshtehard, Firuzkooh, Taleqan 1, Taleqan 2, Taleqan 3 and Tehran earthquake. To this end, we reconstruct phase space for delay time calculation using average mutual information function. Embedding dimension is calculated based on false nearest neighbors. Correlation dimension is used for earthquake chaotic behavior assessment and local prediction algorithm and artificial neural network are employed for earthquake prediction. Results illustrate nonrandom nature of evaluated earthquakes. These earthquakes have high dimension chaotic behavior. Earthquake prediction is good and acceptable accuracy using chaos theory and artificial neural network. The existence of the specific attractors in a part of 2D reconstructed phase space for the earthquakes show the presence of a nonlinear processes. This is an evidence for no stochastic behavior of the earthquakes. Also, reduction in the false neighbors with embedding dimension increases, shows no stochastic time series. Lyapanov exponent positive gradient displays a nondeterministic process, although it cannot warranty the chaotic behavior. Correlation exponents have high values for Taleqan1 and Tehran earthquakes. So these earthquakes saturate in large quantities. Bumahen and Damavand earthquakes correlation exponents have increasing trend and do not saturate. These observations prove the chaotic behavior of high dimension or random process with inconsiderable chaos. So these earthquakes cannot be predicted properly. Performing the local prediction based on the selected embedding dimensions and the neighbor’s number, showed that the predicted time series are relatively good for the earthquakes of Arjomand, Eshtehard, Firuzkooh, Taleqan 2 and Taleqan 3. Proper anticipated of trends, upward and downward branches as well as amplitudes illustrate the chaotic nature of the earthquakes. The correlation coefficient for Arjomand, Eshtehard, Firuzkooh, Taleqan 2 and Taleqan 3 are 0.9541, 0.4494, 0.5124, 0.6600 and 0.3697 respectively. In the case of Talegan1 and Tehran earthquakes, time series amplitudes and peaks do not predicted appropriately, but the prediction is acceptable. Correlation coefficient of Taleqan1 and Tehran are 0.2452 and 0.1760 respectively. Bumahen and Damavand earthquakes do not trace properly. It should be noted that for each earthquake, 20% of the endpoints of accelerations are used to evaluate the prediction process. According to the results of the analysis and earthquakes prediction in Tehran region, using phase reconstruction and artificial neural networks, we can say that the dynamics governing the earthquakes in this region are not random, but, chaos with high dimension. Earthquake prediction is good and acceptable accuracy using chaos theory and artificial neural network.