分散性表面波の減衰の定数 (Q)

抄録

Recently, measurements of the specific dissipation factor, Q, have been made not only for body waves, but also for surface waves, according to developments of observationall techniques. For instance, Y. SATÔ (1958) studied G-waves by means of Fourier analysis and found that Q for G-waves depends on frequency. The velocity of surface waves generally depends upon frequency and structures of the medium under consideration. Therefore, even if Q for body waves is independent of frequency, it is natural to consider that Q for surface waves depends not only on frequency and velocity distribution but also on distribution of Q for body waves in the medium.
In this paper, assuming that Q for body waves is independent of frequency and using the equation of motion in low loss medium proposed by L. KNOPOFF (1956), the apparent frequency dependence of Q for surface waves is investigated in the following two cases.
First, the frequency dependence of Q for Love waves (Q_L) in a layered medium, in which Q's for shear waves are Q₁ in the layer and Q₂ in the substratum, respectively, is investigated. In this case, it is, as was expected, found that Q_L varies with period even when Q for body waves is constant throughout the medium (Q₁=Q₂). Q_L generally tends to Q₁ and Q₂ as the period of Love waves tend to zero and infinity, respectively, as well as the velocity of Love waves tends to shear velocities in the layer and the substratum for both limits of periods. When Q₂ is larger than Q₁, and even when Q₂ is, strictly speaking, a little smaller than Q₁, Q_L has a minimum value for a certain period which tends to zero as the ratio of Q₂ to Q₁ becomes very large.
Second, the frequency dependence of Q_L or Q_R (for Rayleigh waves) in a semi-infinite medium, in which the velocity of body waves and Q for body waves vary linearly withh depth, is studied by using the variational methods. It is shown that the longer the period is, the smaller Q_L or Q_R is even when Q for body waves does not vary with depth.