Soğurulmanın dalga biçimi üzerindeki etkisi

Abstract

Gerek sismik yansına çalışmalarında, gerekse sismolojide soğrulmadan kaynaklanan okuma zamanlarındaki gecikmeyi gidermek gerekir. Sinyallerdeki ' bu gecikme giriş dalgacığının nefes genişliği ile ilişkilidir. Bundan dolayı giriş dalgacığının farklı nefes genişlikleri için çıkış dalgacığının gecikme zamanlarının değişimini incelemek gerekir. Bu çalışmada sabit bir Q değeri ile hızın sabit olması halinde kaynak dalgacığın in yol alması durumunda, dalgacığın nefes genişliğindeki ve yansırca zamanındaki gecikme değişimi irdelenmiştir. Sonuçta giriş ve çıkış sinyalin arasındaki nefes genişliği farkı ile gecikme zamanı farkı arasında doğru sal bir ilişki bulunmuştur. Daha sonra dalgacığın nefes genişliğine bağlı ola rak gecikme zamanı ile ilgili bir bağıntı geliştirilmiştir. Bu bağıntı aşağı da olduğu gibi tanımlanır: jt«(V/2-l/1) İnf l-*0.241-^jj 0.933 At : Gecikme zamanı(Soğrulma mekanizmasının neden olduğu gecik îtte. ) Vı : Dalgacığın başlangıçtaki nefes genişliği. ^ 2 : Dalgacığın soğrulmadan sonraki nefes genişliği, dt: Dalgacığın samandaki örnekleme aralığı Zaman ortamında dalgacığın nefes genişliğine bağlı kalarak Q hesaplaması ile ilgili bir bağıntı geliştirilmiştir. Bu bağıntı aşağıdaki gibi tanımlanabilir: ' Q._4lBiLLrIn(I+o.2£Y| -0.2« dt Dalgacığın başlangıçtaki seyahat süresi. Dalgacığın soğrulmadan sonraki seyahat süresi. Dalgacığın başlangıçtaki nefes genişliği. Dalgacığın soğrulmadan sonraki nefes genişliği. Dalgacığın zamandaki örnekleme aralığı. Uygulamada ölçülen efektif Q değeri aslında ortamın Q katsayısı ile saçılmadan (scattering) kaynaklanan Q değerlerin terslerinin toplamıdır. Ya ni 1/Q, = 1/CL + 1/Qe şeklindedir.

The most commonly used measures of attenuation in rocks are the attenuation coefficient, <»(/), the quality factor, Q, its inverse 1/Q (dissipation factor), and the logarithmic decrement, 6 Generally speaking, except for unconsolidated, water-satured sediments, the specific dissipation constant.or quality factor, Q, is believed to be assentially independent of frequency and is related to the rate at which the mechanical energy of vibration Is converted irreversibly into heat. The definition of Q does not depend on the detailed mechanism by which the energy is dissipated (Waters, 1987). These quantities are related as follows: 1 m*U)v^ 6 q" nf =/7 where v is velocity and f is frequncy in hertz. Absorption is frequency dependent and may be computed from, Then, -nm where the knowns are the travel distance a and Ai(f) and A2(f) the input-output amplitude spectra, respectively. For most rocks, a plot of a(/) versus f appears to be linear with frequency (Knopoff and Mac Donald, 1958; Gutenberg, 1959; Gardner et al, 1964; Gordon and Davis, 1968; Pandit and Savage, 1973; Toksoz et al, 1979; Waters, 1987). The attenuation coefficient, <="" (db="" (nepers="" length).="" also,="" a(db="" a.)«="" 8.686^="" absorption="" must="" accompanied="" body="" wave="" dispersion="" so="" that="" causality="" can="" satisfied.="" if="" b="" slope="" of="" a="" least-="" squares="" fit="" straight="" line="" data="" computed="" from="" equation="" (1)="" then,="" ct(="" )a-bu="" (2)="" equation,="" gives="" coefficient="" and="" quality="" factor="" q.="" here="" v="" stands="" for="" phase="" velocity.="" (3),="" ax-b="" where, n <5> Qv The desired unknown x, is in fact the product of two other unknowns, £e, the quality factor, Q, and the wave phase velocity, v. VI! The main problem in the determination of the Q lies in the fact that the true loss mechanism is difficult to separate out from other and often stronger damping mechanisms, such as geometric spreading, reflections transmissions, and scattering. Time delays are introduced by highly attenuating rocks (Q = 20, say). These delays affect estimates of velocity and can influence a geologic interpretation (Angelerl and Loinger, 1984). Attenuation can also result from layering by a combination of transmission losses and intrabed multiples (O'Doherty and Anstey, 1971). Schoenberger and Levin (1974) reported that attenuation due to layering accounted for 30 - 50% of the total frequency dependent attenuation estimated from field seismograms at two well locations. Sherwood and Trorey (1965) showed the complete response of Shoenberger and Levin's isolated reflection has minumum phase property. It is generally believed that rocks to possess some measurable intrinsic attenuation which degrades both the amplitude and frequency content of propagating wave, body wave dispersion has been the subject of greater contention. Velocity dispersion associated with attenuation can have a larger effect, causing delay of the seismic traveltimes. Using the attenuation coefficient model which is a linear function of frequency, and assuming the quality factor Q and the body wave velocity are constant. In the present work, we have calculated the waveforms of different attenuated signals. It has been observed that the breadth width of the attenuated output wavelet is increased due to the attenuation. The other fact observed is that some delay in the reflection traveltimes appear due to distorsion in the waveform. The amount of traveltime delay can be calculated from: VffS At -(l/a-l/i)[ln^l +0.241 -^JJ (6) Where tf\ is input wavelet breadth width, V1 is output wavelet breadth width and dt is the sampling interval. The quality factor Q can be calculated in the time domain (Ecevitoğlu, 1987) give the following equation for the body waves : IT nAW (7) Where, T is the total (two-way) traveltime and AW is the amount of wavelet breadth increase during the time T. Essentially this equation is applicable to frequency rich wavelets. However, in calculating the quality factor Q, for frequency poor wavelets equation (7) can be rearranged as: V /7(l/2-l/,)L V <*wJ where, T'T2-Tl i IX is the totaKtwo-way) traveltime and is the amount of wavelet breadth increase during the tijne T and dt Is the sampling Interval