Rastgele ortamlarda dalga yayılımının modellenmesi
Başlık çevirisi mevcut değil.
- Tez No: 39458
- Danışmanlar: PROF.DR. NEZİHİ CANITEZ
- Tez Türü: Doktora
- Konular: Jeofizik Mühendisliği, Geophysics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 158
Özet
ÖZET İnhomojen ortamlardaki dalga yayılımı rastgele ortam tanımı kullanarak incelenebilir. Uzaysal hızların ve yoğunlukların dağılımının stokastik süreçler ile incelenebildiği, istatistiksel momentler ile tanımlanan rastgele ortam kullanımı ile oluşturulan sismogramlar, gerçek bir sismogramda olduğu gibi, yayılma zamanlarındaki ve genlikteki sapmaları, soğrulmayı, ikincil dalgalan ve koda dalgalarının oluşumunu içermektedir. Sismogramlardaki bu tür etkileri kullanarak, ortamdaki inhomojenliklerin büyüklüklerinin kestirilmesi tezin ana fikrini oluşturmaktadır. Rastgele ortam olarak Gaussian, von Karman ve genelleştirilmiş Gaussian ortamlar ile çalışılmıştır. Gaussian ortam belirli ölçekten değişimlere izin verdiğinden, ancak yavaş değişim içeren ortamların modellenmesinde kullanılmıştır, von Karman ortam ise, her türlü ölçekten değişim içeren ortamların modellenmesi amacıyla kullanılmıştır. Sürekli ortamlar için tanımlı olan bu yaklaşım ile sonlu ve ayrık değerli gözlem uzayında çalışmak mümkün değildir. Bundan dolayı, fiziksel problemlerin incelenebilmesi amacıyla bu tezde, genelleştirilmiş Gaussian adını verdiğimiz yeni bir ortam tanımlaması oluşturulmuştur. Rastgele ortamlardaki dalga yayılımı, yeni bir yöntem olan ve bu tezde tanımlanan Hartley yöntemi ile modellenmiştir. Oluşturulan sismogramlara ait kodalarm spektrumları modellenerek, rastgele ortamı tanımlayan istatistiksel büyüklüklerin kestirimi yapılmaya çalışılmıştır. Modellemede kullanılan bağıntılar, Born yaklaşımı kullanılarak elde edilmiştir. Gaussian ortam için bulunan sonuçlar ile ortamı tanımlayan istatistiksel büyüklüklerin kestirimi tam doğrulukla yapılmıştır. Sürekli ortamlar için tanımlı olan von Karman ortam için elde edilen sonuçların kestirimi ise yetersiz duyarlıkta elde edilmiştir. Bu tezde tanımlanan ve fraktal özellik gösteren von Karman ortama yaklaşım sağlayan genelleştirilmiş Gaussian ortamı tanımlayan büyüklüklerin kestirimi tam olarak yapılabilmiştir. Oluşturulan bu yaklaşım TUBITAK-Gebze sayısal deprem istasyonunun kaydettiği patlatma verilerinden seçilen bir veri setine uygulanmıştır. Aynı kaynak-alıcı konumu için bulunan koda spektrumları benzer özelliklere sahip olarak elde edilmiş ve teori ile uyumlu sonuçlar bulunmuştur. Sonuç olarak, farklı ölçekten değişim içeren İnhomojen ortamlardaki istatistiksel büyüklüklerin eldesi için yeni bir yöntem tanımlanmıştır. Oluşturulan bu yöntem, benzeşimler ve gerçek veri ile uyumlu sonuçlar vermiştir. Ek olarak, iki yeni yaklaşım tanımlanmıştır. İlk yaklaşım, her türlü ortamdaki dalga yayılımınm modellenmesini sağlayan Hartley yönteminden oluşmaktadır, ikinci yaklaşım ise, farklı ölçekten değişimleri içeren rastgele ortamı tanımlayan genelleştirilmiş Gaussian ortam tanımını içermektedir. vi
Özet (Çeviri)
asymmetric form. The lower limit approximately equals the sampling distance and agrees with our theoretical results. Also, the correlation function of het erogeneous medium is derived. The agreement between the simulated and theoretical correlations is excellent. In the last part of this thesis, we apply these concepts on a real data set. This data set was from quarry blast records of the TUBITAK-Gebze digital seismic station. All of the records have the same source-receiver path. Each coda power spectrum shows a band limited form approximately in the [1-21^2] interval. Using the backscattering coefficient which is defined for generalized Gaussian media, the lower and upper limit of the correlation function is es timated. The lower limit is found to be 910m and the upper limit 1200m. This results have confidence in this interval according to the source-receiver distance and the spatial sampling. However, we can not correlated with other data sets which has different source-receiver path; because, thus far we are not be able to collect additional data suitable for this purpose. In conclusion, a method for the determination of statistical parameters of a multi-scale heterogenous medium has been developed. This method appears to give very satisfactory results for the simulated and real data sets. Also, this method does not need any special tools such as spectral estimation techniques. In addition, two new ideas are demonstrated. First, the Hartley method is introduced for modeling wave propagation in general media. Next, generalized Gaussian random media, for defining multi-scale random media, is defined and demonstrated. xivrandom media. They simulated wave propagation with the 2- D finite difference method. Their results showed that the backscattering coefficient can be suc cessfully predicted by the codas power spectrum for Gaussian random media. However, they could not invert the backscattering coefficient for exponential random media, successfully. Roth and Korn (1993) investigated the validity of single scattering theory in weakly inhomogeneous 2-D random media using the finite difference approximation. They used different autocorrelation functions from Frankel and Clayton (1986). Their results showed that single scattering theory can be used to determine the energy loss of a plane wave due to scat tering in both 1-D and 2-D random media and agree with a analytical result of Sato (1984). Finite difference modeling has also been applied to the elastic wave equation; both to study the relationship between the medium and the ob served scattered field (Frankel and Clayton, 1986; Mclaughlin and Anderson, 1987; Dougherty and Stephens, 1988; Charrette, 1990; Coates and Charrette, 1993) and to study the response of typical seismic processing streams used on data collected in highly heterogeneous regions (Gibson and Levander, 1988; 1990). In the scattering literature, highly heterogenous media are often approx imated by random fields. The advantage of this approach is that a complex, multi-dimensional velocity function can be expressed in terms of a few simple statistical parameters. In Chapter 2, the conditions for statistical characteri zation is described. One statistical parameter which can be used to describe the variability of a velocity field is the autocorrelation function. The prop erties of three commonly used autocorrelation functions, the Gaussian, expo nential, and von Karman are investigated, and their applicability to earth is discussed. All three spectra are nearly flat at low wavenumbers, but at higher wavenumbers the Gaussian falls off exponentially, while the exponential and von Karman fall off with a power law dependence. The fall off rate controls the roughness of the medium. Those characterized by the Gaussian autocorre lation are smoothly varying, while the exponential and von Karman functions are more highly textured. These functions are isotropic and inhomogeneities do not have any preferred orientation. It is probably realistic to consider, for the entire crust, that small scale inhomogeneities do not have a preferred orientation. However, in seismic exploration, we are interested in inhomo geneities in a particular rock or in small region of the crust where anisotropy gains importance. One example might be the deposition of overlapping lenses with different lithologies. The lens shape suggests that the correlation length of these features might be different in the horizontal and vertical direction. Although each lens may have isotropic elastic moduli, the composite medium may display an effective or apparent anisotropy. The preferred orientation of the fluctuations should be reflected in the autocorrelation function. For sim plicity, it will be assumed that all azimuthal variation in the autocorrelation function can be explained through the dimensionless ellipsoidal norm. The interesting aspect of ellipsoidal autocorrelation functions is that they allow us to describe media in which the inhomogeneities are isotropic, elongated in a particular direction, or even flattened.random media. They simulated wave propagation with the 2- D finite difference method. Their results showed that the backscattering coefficient can be suc cessfully predicted by the codas power spectrum for Gaussian random media. However, they could not invert the backscattering coefficient for exponential random media, successfully. Roth and Korn (1993) investigated the validity of single scattering theory in weakly inhomogeneous 2-D random media using the finite difference approximation. They used different autocorrelation functions from Frankel and Clayton (1986). Their results showed that single scattering theory can be used to determine the energy loss of a plane wave due to scat tering in both 1-D and 2-D random media and agree with a analytical result of Sato (1984). Finite difference modeling has also been applied to the elastic wave equation; both to study the relationship between the medium and the ob served scattered field (Frankel and Clayton, 1986; Mclaughlin and Anderson, 1987; Dougherty and Stephens, 1988; Charrette, 1990; Coates and Charrette, 1993) and to study the response of typical seismic processing streams used on data collected in highly heterogeneous regions (Gibson and Levander, 1988; 1990). In the scattering literature, highly heterogenous media are often approx imated by random fields. The advantage of this approach is that a complex, multi-dimensional velocity function can be expressed in terms of a few simple statistical parameters. In Chapter 2, the conditions for statistical characteri zation is described. One statistical parameter which can be used to describe the variability of a velocity field is the autocorrelation function. The prop erties of three commonly used autocorrelation functions, the Gaussian, expo nential, and von Karman are investigated, and their applicability to earth is discussed. All three spectra are nearly flat at low wavenumbers, but at higher wavenumbers the Gaussian falls off exponentially, while the exponential and von Karman fall off with a power law dependence. The fall off rate controls the roughness of the medium. Those characterized by the Gaussian autocorre lation are smoothly varying, while the exponential and von Karman functions are more highly textured. These functions are isotropic and inhomogeneities do not have any preferred orientation. It is probably realistic to consider, for the entire crust, that small scale inhomogeneities do not have a preferred orientation. However, in seismic exploration, we are interested in inhomo geneities in a particular rock or in small region of the crust where anisotropy gains importance. One example might be the deposition of overlapping lenses with different lithologies. The lens shape suggests that the correlation length of these features might be different in the horizontal and vertical direction. Although each lens may have isotropic elastic moduli, the composite medium may display an effective or apparent anisotropy. The preferred orientation of the fluctuations should be reflected in the autocorrelation function. For sim plicity, it will be assumed that all azimuthal variation in the autocorrelation function can be explained through the dimensionless ellipsoidal norm. The interesting aspect of ellipsoidal autocorrelation functions is that they allow us to describe media in which the inhomogeneities are isotropic, elongated in a particular direction, or even flattened.a background part and perturbative part (Born approximation or first Born approximation). Chernov (1960) investigated the applicability of the Born ap proximation for scattering in random acoustic media. The generality of his analysis lead to an overly strict validity criterion which is only valid when the scattered field depends linearly on the incident field. This condition is verified if kD
Benzer Tezler
- İlk varış zamanlarından sismik ortama ait istatistiksel parametrelerin kestirilmesi
Estimating medium statistical parameters using first arrival travel times
DENİZ VARILSÜHA
Yüksek Lisans
Türkçe
2015
Jeofizik Mühendisliğiİstanbul Teknik ÜniversitesiJeofizik Mühendisliği Ana Bilim Dalı
PROF. DR. AYŞE KAŞLILAR ŞİŞMAN
- Use of hydrodynamic stability approach for the calculations of inflow boundary conditions and spread of an axisymmetric turbulent swirling jet
Hidrodinamik kararlılık analizi ile oluşturulan giriş koşulları kullanılarak çalkantılı sarmal jet akışı benzetiminin yapılması
AMIR HOSSEIN MEHRABI KERMAN
Yüksek Lisans
İngilizce
2020
Makine Mühendisliğiİstanbul Teknik ÜniversitesiMakine Mühendisliği Ana Bilim Dalı
PROF. DR. İLYAS BEDİİ ÖZDEMİR
- Mikrodalga soğurucu tasarımı
Microwave absorber design
İBRAHİM ÇATALKAYA
Doktora
Türkçe
2017
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik Üniversitesiİletişim Sistemleri Ana Bilim Dalı
PROF. DR. SEDEF KENT PINAR
- Marmara Bölgesi'nde soğurulma yapısının incelenmesi
Investigation of attenuation structure in the Marmara region
AYŞE KAŞLILAR ÖZCAN
- Application of time-domain technique to study the ray movement inside bounded anisotropic medium
Sınırlı anisotropik ortamlarda dalga ilerleyişinin incelenmesi için zaman-alanı tekniğinin uygulanması
ALPER BİBER
Doktora
İngilizce
2003
Fizik ve Fizik MühendisliğiOrta Doğu Teknik ÜniversitesiFizik Ana Bilim Dalı
PROF. DR. MEHMET TOMAK