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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク The Kolsky basic model and modified model for attenuation and dispersion ： ウィキペディア英語版 The Kolsky basic model and modified model for attenuation and dispersion The Kolsky basic model and modified model for attenuation and dispersion is the mathematical Q models that is most used in seismic applications. The basic Kolsky model is used for its simplicity in seismic data processing, however it does not rigorously satisfy the Minimum phase criterion and cannot satisfy the Kramers–Kronig relations. But then the Kolsky's modified model comes to our rescue, producing an accurate representation of the velocity dispersion within the seismic frequency band. The basic Kolsky model is presented in Kolsky's book "Stress waves in solids" that are available as a Google book.("Stress waves in Solids".(1963 edition) ) Kolsky's modified model is presented in Wang's book Seismic inverse Q filtering. This book is also available as a Google book:(Seismic inverse Q filtering (2008), ) == Basic == The theoretical background for mathematical Q models can be found in the Wikipedia article: Mathematical Q models. Here we found a function K(w) we can call a propagation constant in line with Futterman.〔Futterman (1962) p.5280〕 :$K(iw)\; =k(w)+\; i\; a(w)\; \backslash quad\; (1.3)$ k(w) can be linked to the phase velocity of the seismic wave with the formula: :$c(w)=\backslash frac\; \backslash quad\; (1.4)$ To obtain a solution that can be applied to seismic k(w) must be connected to a function that represent the way the seismic wave propagates in the seismic media. This functions can be regarded as a Q-model. In his outline Wang calls the Kolsky-Futterman model the Kolsky model. The model assumes the attenuation α(w) to be strictly linear with frequency over the range of measurement:〔Wang 2008, p. 18, sec. 2.1: Kolsky's attenuation-dispersion model〕 :$\backslash alpha=\backslash frac\; \backslash quad\; (1.5)$ And defines the phase velocity as: :$\backslash frac\; =\backslash frac\; (1-\backslash frac\; ln\; |\backslash frac|)\; \backslash quad\; (1.6)$ Where cr and Qr are the phase velocity and the Q value at a reference frequency wr. For a large value of Qr >>1 the solution (1.6) can be approximated to :$\backslash frac\; =\backslash frac\; |\backslash frac|^\; \backslash quad\; (1.7)$ where :$\backslash gamma\; =(\backslash pi\; Q\_r)^$ Kolsky’s model was derived from and fitted well with experimental observations. A requirement in the theory for materials satisfying the linear attenuation assumption is that the reference frequency wr is a finite (arbitrarily small but nonzero) cut-off on the absorption. According to Kolsky, we are free to choose wr following the phenomenological criterion that it be small compared with the lowest measured frequency w in the frequency band.〔Wang 2008, p.19〕 Those who want a deeper insight into this concept can go to Futterman (1962)〔Futterman W.I. 1962. Dispersive body waves. Journal of Geophysical Research 67. p.5279-91〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「The Kolsky basic model and modified model for attenuation and dispersion」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.