21. Propagation and Apparent Attenuation of Elastic Waves in a Heterogeneous Medium with Certain Periodic Structures
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概要
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The attenuation of seismic waves propagated in a heterogeneous medium is investigated. Heterogeneity of the medium is represented by the velocity distribution alone and the structure under consideration is expressed in Fourier cosine series. In this proplem the differential equation is of Hill's type, and conditions of instabilityare discussed. Since the unstable solutions obtained are of the standing waves, some modification and reformation for discussing the stability of the progressive waves are made. It is concluded that the wave amplitude with wave length λn isaffected by the structural component with wave length Ln=λn/2 and is independent, of the other components, and that the function of the apparent attenuation for the specified wave amplitude is of hyperbolic secant but not of exponential. On the other hand, the phase of this specific wave is shifted by every component of the structure. In addition, the phase shift of waves passing through the medium is negligibly small; the phase velocity is apparently fixed for all frequencies. A similar problem will arise in that of surface wave propagation along a rough surface. In the appendix, Hill's equation is solved in forms convenient in discussing the stability of its solution.速度の分布がc0(1+Σr0r=1εrcos2rγx)で表わされる不均質媒質を伝わる波動の伝搬を調べた.伝搬径路の不均質性をフーリエ解析するとこのような速度分布に置きかえることが可能であろう.また,同様な問題は平らでない地形を横切る表面波の伝搬と結びつけて考えることもできる.このような媒質における波動方程式はヒルの方程式で書かれ,その解の安定性を議論するためにWhittakerやInceらによつて与えられた解を少し一般化して用いた.
- 1964-12-25
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