Deprem kayıtlarının istatistiksel analizi

Abstract

Deprem neden olduğu sonuçlar açısından en önemli doğal afetlerden biridir. Deprem yer hareketi, çok karmaşık bir fiziksel yapıya sahiptir. Yerkabuğunu oluşturan zemin tabakalarının homojen dağılmaması ( topografik, jeolojik ve yerel zemin koşullan ), deprem hareketinin merkezden yayılması sırasında tabakalar arasındaki sınırlarda dalgaların kırılma ve yansıması ile oluş mekanizmalarında ( fay mekanizması, manyitüd, odak derinliği, dışmerkez uzaklığı vb. ) görülen çeşitli farklılık ve belirsizlikler deprem hareketini tanımlamayı zorlaştırmaktadır. Yüzeyde ki deprem hareketini birçok faktör etkilemekte, çoğu zaman hareketin fiziksel etkisini ifade eden parametreler sınırlı veya yetersiz kalmaktadır. İnşaat mühendisliğinin temel amaçlarından biri insanların içinde yaşadıkları mekanları daha güvenli, daha dayanıklı ve uzun ömürlü olacak şekilde tasarlamak ve inşa etmektir. Aynı düşünce, deprem olayı için de benzer bir bakış açısını gerektirmektedir. Amaç depremi engellemek olamayacağına göre, mühendislik uygulaması açısından tasarıma ve inşaata yönelik hasarları olumsuz şekilde etkileyen çeşitli belirsizliklerin, gerekli inceleme ve araştırmaların yapılarak mümkün olduğunca en aza indirilmesi ve istatistiksel yaklaşımlar yaparak olasılık ilişkilerinin bulunması olacaktır. Bu düşünceler doğrultusunda, orta ve büyük şiddetli bazı geçmiş deprem kayıtlarının mevcut veriler ışığında çeşitli parametreleri ( dışmerkez uzaklığı, en büyük zemin ivmesi, manyitüd, odak derinliği ) derlenmiş, kayıtların özelliklerin daha detaylı belirleyebilmek amacıyla iki yeni parametre ( Eşdeğer Çevrim Sayısı, Ortalama Darbe İvmesi ) tanımlanarak, istatistiksel analizler kullanılarak, ilgili parametreler arasındaki ilişkiler belirlenmeye çalışılmıştır.

The shaking of the surface of the ground during an earthquake is produced by the passage of stress waves. These seismic waves emanate from a region of Earth 1 s crust where stress failure has resulted in a sudden change in the equilibrium stress state. The size of earthquakes and the frequency of occurence depend on the state of stress in the Earth' s crust. By far the most important earthquakes from an engineering standpoint are of tectonic origin, that is, those associated with large scale strains in the crust of Earth. One of the theories describing this phenomenon is called as Elastic Rebound Theory. It explains that the strain energy that accumulates due to the deformation in the Earth mass, gets released when the resilience of the strong material is exceeded. The energy released through a rapture propogates in the form of waves which are called as seismic waves. According to the theory above, the raptures originate in the discontnhraes of Earth' s crust which are called as faults. Faults are not only the causes but also the results of earthquakes. A major tectonic earthquake is never an isolated phenomenon. The violent and destructive main shocks may be proceeded by preliminary tremors or foreshocks, which are less severe and few in number, but important to study in order to predict shocks and take protective measures. Parameters were proposed to describe an earthquakea as done in many physical events. These parameters are as follows ; a) The time of event : This is the time when the first rupture on the fault is originated. In many surveys, the date of an eartquake and the time according to GMT is necessary for it is used in archivement in many physical or statistical studies, b) The focal depth (D^ ) : The point inside the Earth mass where slipping or fracture begins is termed as focus or hypocenter. The depth between that point and surface is called as focal depth. Earthquakes may be classified according to their focal depths. Shallow earthquakes have focal depth less than 60 km., intermediate earthquakes have focal depth between 60 - 300 km., the deep earthquakes have focal depth more than 300 km. c) The coordinate of epicenter : The point just above the focus on the Earth' s surface is termed as epicenter. The coordinate of this point is given in terms of the latitude and longtitude. d) The size of earthquakes : It is important for engineering purposes to be able to describe in a quantative way, the size of the earthquake. In 1935, C.F. VI Richter of the California Inst, of Technology defined the magnitude of an erthquake for shallow shocks as, ML-Loglp(A/A.) (1) where ML is local magnitude, A is the maximum amplitude recorded by a Wood- Anderson seismograph of a distance of 100 km. from the center of the disturbance and A,, is an amplitude of one thousandth of a milimeter. Because of the remarkable success of the M^ scale, Beno Gutenberg, defined another magnitude scale, M^ called the surface - wave magnitude, using the amplitude of surface waves with a period of 20 seconds. Gutenberg also used seismic body waves, primary (P) and secondary (S) to define another scale, MB, which is called the body - wave magnitude. Other magnitude scales were also developed such as the moment magnitude, Mw and the Japan Meteorological Agency magnitude, M,.. The relationships between magnitude scales explained above can be given as follows ; Ms = 1.59 Mb- 3.97 (2) MS = MW = ML (3) The magnitude M is related to the energy released at the focus of the earthquake by the following approximate formula, Log E (ergs) = 11.8 + 1.5 M (4) Macroseismic investigation depends an evaluation of the intensity of an earthquake at a given point. Many scales of intensity have been used, among them are the Rossi - Forel scale (RF) of 10 degrees, which is still used in several countries, and the Mercalli Modified Scale (MM) of 12 degrees, which is used, in particular, in USA. The most recent is the MSK scale, proposed in 1964 by Medvedev, Sponheuer and Kamik. In the previous years, many researchers, proposed various intensity parameters to model and take into account the damage distribution and earthquake characteristics. Most of these parameters are directly related to the strong motion records. The square root intensity ( 1^) and the effective duration ( t"g.) from ths group. Housner* s intensity ( SI<>2 ) and the effective acceleration (a^ ) VII will be compound function of deterministic dynamic properties and input motion characteristics which involve random nature. Basically, two types of instruments are used to record earthquake motions. The instruments used by seismologists are generally sensitive and meant for recording weak motions of earth, which are called as seismographs. For engineering measurements, the instruments generally operate when the ground motion excceeds a threshold value ( say, a ground acceleration of 0.03 g. ) and are expected to record the strongest ground motion. These kinds are called as Strong Motion Accelerographs. These instruments are important for getting the basic data needed for design of engineering structures. A typical strong motion accelerograph would have three accelerometers- two horizontal to record motion in North-South (Ns) and East-West (Ew) directions respectively and one vertical. Using the acceleration records obtained by such instruments provides researchers a rich data base so that the engineering properties of the eathquakes can be studied in detailed way. Acceleration records obtained in previous earthquakes based on the data base from various active fault zones such as California, Alaska, Mexico, New Zeland, China, Canada, Japan and Turkey were compiled according to their magnitude, epicentral distance and peak ground acceleration. Using the equations (2), (3) all the magnitudes were reverted to common scale Mg. Statistical distributions and correlations between these parameters are determined The measured peak acceleration Ap and predominant period of ground T0 computed from the response spectrums would be used to a limited degree, in the determination of the effect and the severity of the strong motion which depends upon complicated source and local conditions. So to describe an earthquake motion with long duration consisting of a lrge number of cyclic stresses in a more realistic way, the time duration of the records must be defined with an engineering parameter. At this point of view, two different parameters were determined. These are Equivalent Number Of Cycles ( NEQ ) and Averege Stroke Acceleration ( Aj ). Considering a linear damage relation, the non-uniform time histories with an acceptance of A=100 gals, were converted to uniform equivalent cycles. Then these equivalent cycles were computed for horizontal directions for various records. The equivalent number of cycles were determined by a spreadsheet computer program that was developed a the method suggested by Seed et al (1975). The other parameter Ag was determined by associating the records obtained at two horizontal components (NS-EW) in a pair of X-Y axis. It xas assumed that, the figure based upon plotting the points of time accelerations shows the effect of earthquake in horizontal plane. In such figure the sets of consecutive points vra following each other with the angle smaller than 10° ( a < 10") was considered as strokes that effects building at any instant. These strokes were also computed by a spreadsheet program for all values of the records. Then the averege of these values were computed and The Averege Stroke Acceleration were determined for each record. Finally, the distribution of these new parameters and correlations with the other parameters were studied and their statistical relationships for analysis were determined based upon a linear regression. The purpose for suggesting such parameters is to develop new parameters to define an earthquake more accurately for engineering purposes. It is considered that NEQ and Aj should be given in addition to peak acceleration, Ap, as engineering parameters. RESULTS mâ CONCLUSION The brief summary of results found is given as follows ; a ) The earthquake ground motion is generated very complicated source mechanisms and local conditions and a coupled effects of a motion for engineering purposes is considered not sufficient to represent the motion with presently used parameters to describe an erthquake for engineering purposes. b) After Determining the relations between the Magnitude, which is one of the source parameters, and intensities (MMI) showed that this parameter (Mj) can not be accepted as the only parameter describing an earthquake. c) The attenuation relationships for peak ground acceleration Ap determined with respect to M<. and DF0C indicated that Ap may not be regarded as single definite engineering parameter representing the acceleration record. Because this value is effective only for a short instant and may not define the equivalent value of all amplitudes through the record. d) The statistical relationships between these new parameters obtained by a detailed study of the records, and Ap showed well linear regressional relationships. On the other hand, the linear attenuation relationships of these parameters with the DEPL gave poor correlations. This result suggested tahat NEQ and \_ should also be defined with Ap. to give the engineering properties of earthquakes. rx e) The non-linear multiple regression of predominant period T0 and amplification factor (Sacc. / Ap) with D,^ and Mg showed that, it is more realistic to assume a nonlinear relationship between these parameters. Consequently, it appears necessary to define earthquake characteristics more accurately in order to compute earthquake forces and leads to accomplish a safer structural design. For this purpose, more detailed studies of strong ground motion records is needed. Moreover, in the possibility of an earthquake threat, the concerning region must be studied in terms of tectonic and geotechnical surveys ( Microzonation ).