Sismik moment tansör ters çözümüyle Türkiye depremlerin analizi

Abstract

Klâsik fay düzlemi çözümleri ya da kaynakla ilgili bilgi edinme yöntemleri, genellikle, deprem kaynağının bir ikili kuvvet-çifti (double couple) olduğu varsayımına dayanır. Halbuki bu tür sismik kaynakların tamamen ikili kuvvet-çifti olmadığı da en azından kuramsal bir gerçektir. Alternatif olarak, deprem kaynağındaki kuvvetler bir tansör olarak yorumlanabilir. Deprem kaynağını bir moment tansör ile tanımlamak, hem sismik kaynağı karakterize eden tüm kuvvetlerin belirlenmesini, hem de deprem kaynağının özelliklerinin daha iyi anlaşılmasını sağlayacaktır. Bu amaçla, bu çalışmada, doğrusal moment tansör ters çözümü ve moment tansörün analizini yapan bir bilgisayar yazılımı hazırlanmış ve gözlemsel telesismik deprem kayıtlarına uygulanmıştır. Türkiye'de olmuş, magnitüdleri (mı>) 6 civarında olan 6 adet telesismik deprem için, WWSSN istasyonlarında kaydedilmiş P dalgası fazlarının kullanıldığı bu çözümler, iki aşamadan oluşmaktadır. Önce, her depremin dalga-şekli tersçözümü yapılmış, sonra da Doğrusal Moment Tansör Tersçözümü ile depremlerin moment tansörleri kestirilmeğe çalışılmıştır. Aynı bilgisayar yazılımıyla moment tansörlere uygulanmış olan bir dizi ayrıştırma (decomposition) işlemleri sonucunda, incelenen Batı Anadolu depremlerinde daha çok çekme gerilmesinin ( tensile stress) baskın olduğu, Doğu Anadolu Fay Zonundaki depremlerde ise bir sıkıştırma bileşeniyle birlikte makaslama hareketinin de egemen olduğu ortaya çıkmıştır. Bu sonuç; Batı Anadolu'da bir açılma, Doğu Anadolu'da bir sıkışma rejiminin sürdüğü şeklindeki Türkiye'nin genç tektonik (neotektonik) yorumunu desteklemektedir. Ayrıca, Türkiye ve çevresinde olan ve moment tansörleri bilinen 38 adet depremin moment tansör analizleri yapılmış, benzer sonuçlar veren bazı çalışmalardan örnekler sunulmuştur. Bunların yanısıra, çeşitli kaynak modelleri için kompleks moment tansör tanımlan ve analizleri verilmiştir. Yapılan testlerle, elde edilen sonuçların bugünkü olanaklarla isabetli olduğu ortaya çıkmıştır.

One of the main goal in seismology is to describe the physics of the seismic source. A common approach is the approximation of seismic sources by a model of equivalent body forces if a seismic event involves no extend bodies, its source can be described phenomenological by a vector field or by any one of three kinds of symmetric second order tensor fields. The vector field is the equivalent force. The tensor fields are the stress-free strain, the stress glut and any other moment tensor density. In the conventional focal mechanism solution, usually, a double couple force system is assumed. On the other hand it is known that seismic source is not a double couple in most of the cases. It is shown theoretically that the seismic source can be represented perfectly by a seismic moment tensor, and in turn, the most generalized representation of the force system acting at the earthquake source can be obtained from the inversion of seismic moment tensor. Then seismic moment tensor is necessary and sufficient condition for the description of the physics of seismic sources. This is a quantity, and it characterizes all the information about the source. Knopoff and Gilbert (1960) investigated the seismic radiation for variety shear dislocation sources. The equivalent body forces are defined by Burridge and Knopoff (1964). Gilbert (1970), introduced the seismic moment tensor for calculating the excitation normal modes of free oscillation of the earth. The concept of a seismic moment tensor, has been defined as the volume integral of the stress drop. Knopoff and Randall (1970) represented the equivalent forces by a linear vector dipole. Randall (1971) showed that seismic moment of a generalized dislocation is a tensor. Gilbert (1973) gives the moment tensor elements for an isotropic source, a shear dislocation and a compensated linear vector dipole. Buland and Gilbert (1976) designed a matched filtering for seismic moment tensor. By using the representation theorem for seismic sources the observed displacement at an arbitrary position (x) at the time (t) due to a distribution of equivalent body forces (fj) in a source region is xxi .^ mmm^mmmı^m.p^m uk(x,t) = J|Gkj(x,t;r,t) f^rj^r dt -ooV where (Gy) are the components of the Green's function, and (r,t ) are coordinates of source point. The subscript k indicates the component of the displacement. Hence, the observed displacement is uk (x,t) = [Gkj)i *s(D] m, where * denotes the temporal convolution, and s(t ) is source rime function, my are constant representing the components of the second rank seismic moment tensor. Then, generally, the observed displacement in matrix form is u = Gm This is the seismogram is a linear combination of the seismic moment tensor and the Green's function. The linearity between the Green's function elements and the moment tensor was first used by Gilbert (1973) for moment tensor inversion. Green's function is the impulse response of the medium between source and receiver. Wang and Herrmann (1980), Herrmann and Wang (1985) presented expression for the 10 Green's functions required to describe the wave field due to an arbitrary point dislocation source and a point explosion buried in a plane layered elastic medium. (Bouchon, 1981) expressed the Green's function for an elastic layered medium as a double integral over frequency and horizontal wave number, who shows that for any time window, the wave number integral can be exactly represented by a discrete summation. The concept seismic moment tensor was further extended by Backus and Mulcahy (1976) and Backus (1977 a,b). Moment tensor can be determined from free oscillations of the earth (e.g.Gilbert and Dziewonski, 1975), long-period surface waves (e.g. McCowan, 1976; Mendiguren, 1977; Aid and Patton, 1978; Kanamori and Given 1981, 1982; Nakanishi and Kanamori, 1982, 1984), and long-period body waves (e.g. Stump and Johnson, 1977; Strelitz, 1978, 1980 a,b; Fitch et al., 1980, 1981; Langston, 1981; Dziewonksi et al., 1981; Dziewonski and Woodhouse, 1983 a, b; Jost and Herrmann, 1989; Kikuchi and Kanamori 1991). Fitch et al. (1981) compared moment tensors from surface waves and body waves. Thus, if the Green's function representing the medium is known, seismic moment tensor can be inverted from the seismogram. This kind of parameterization gives us a set of linear equations. Then, linear inverse theory can be applied to solve this problem. It can be performed either in time or xxii frequency domain. This is called "the linear moment tensor inversion". The linear moment tensor inversion is estimated by six independent moment tensor components. As the result of the decomposition each elementary moment tensor obtained from decomposition procedure represents corresponding force component. The equivalent forces can be determined from an analysis of the eigenvalues and eigenvectors of the moment tensor. The moment tensor can be decomposed into an isotropic and deviatoric component (Fitch et al., 1980; Jost and Herrmann, 1989), or a major and minor double couple (Ben- Menahem and Singh, 1981; Kanamori and Given, 1981; Jost and Herrmann, 1989), or an isotropic part (IP) and double couple (DC) and compensated linear vector dipole (CLVD) (Knopoff and Randall, 1970; Ben-Menahem and Singh, 1981; Jost and Herrmann, 1989). Besides a complete moment tensor can be the superposition of an isotropic component and three vector dipoles (or three CLVD's or three double couple, Ben-Menahem and Singh, 1981; Jost and Herrmann, 1989). The eigenvectors corresponding to each eigenvalues give the principal axes of source mechanism. Figure S.l The schematic view of a moment tensor source that it is decomposed into an isotropic part (IP), a double couple (DC) and compensated linear vector dipole (CLVD). The centroid moment tensor solution have been proposed by Dziewonski et al. (1981). This method is a nonlinear iterative method as different than the linear inversion method. Many application of the centroid moment tensor inversion have been performed for the regional and local scale studies by Dziewonski and Woodhouse (1983 a,b), Woodhouse and Dziewonski (1984), Ekström and Dziewonski (1985). Additional of the source xxm characteristics the lateral heterogeneity of the earth have been investigated by the Patton (1980), Romanowicz (1981), Nakanishi and Kanamori (1982), Dziewonski et al., (1984). In this study, second-rank time independent moment tensors are used. The higher order solution of the 2 moment tensor have been implimented by Backus and Mulcahy (1976), Backus (1977 a,b), Stump and Johnson (1982), Dziewonski and Woodhouse (1983 a). Also the time dependent moment tensor solution have been implemented by Dziewonski and Gilbert (1974), Gilbert and Dziewonski (1975), Backus and Mulcahy (1976), Backus (1977 a), Stump and Johnson (1977), Strelitz (1980), Sipkin (1982), Vasco and Johnson (1988). In the present study 6 earthquakes selected from Western Anatolian region and East Anatolian Fault have been analyzed by using linear moment tensor inversion method. The seismograms have been obtained from the 82 WWSSN type stations. Their epicentral distances range between about 30° and 90°. The seismograms have been digitized with the 0.5 and 1 sec sample rates. Dominant moment tensor elements of the teleseismic earthquakes have been investigated by linear moment tensor inversion method. The process of the calculation of moment tensor elements of the earthquakes have been performed in two steps. In the first step, the source parameters and source time function of the earthquake have been estimated using the waveform inversion method. In the second step, the best double couple solution of the moment tensor is estimated, and the moment tensor is decomposed. The dominant equivalent force of the moment tensor that represents the source, is determined by the decomposition process which gives the contribution rate of the equivalent body forces. The results obtained from the inverse solution show that two earthquakes from Eastern Anatolian Fault zone (14.06.1964, 22.05.1971) have a dominant double couple component. These two earthquakes have also isotropic components which represents an implosion type source. The four events from the west Anatolia region (25.03.1969, 28.03.1969, 06.04.1969, 28.03.1970) display tensile crack type source. The contribution rates of double couple are fairly low, with a rate of less than 30%. The source types in both two regions seems to be coherent with tectonic kinematics of the regions. As the yield of the compression regime in the Eastern Anatolia, this kinematic nature have been represented by thrust faults in the region. The isotropic components of the moment tensor solution indicate an implosive type volume change. The result may represent the thickening crust in the region. The tensile crack type sources are appropriated with the normal faults of the western Anatolia. These faults are the results of the extension in the region. xxiv In chapter 6, our analysing method was applied to 38 earthquakes which occurred in Turkish and surroundings for which moment tensor elements given by ISC bulletin. As an examples, one of the decomposition results is given in Appendix- J. This is a decomposition of the moment tensor estimated by HRVD for 13 March 1992 Erzincan earthquake. The results show that the 79% of the 38 earthquakes have a dominant double couple source, and remaining the 21% have a dominant CLVD component. The proportion of earthquakes that have a CLVD component of 20% or greater is 53%. Several specific source models have been examined to find the rate of distortion on the P waveforms in time domain and the amount of deflection from DC components. The examined source models are pull-a-part rupture and a listric fault respectively. The results for there models are given in Appendices D through F.