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 (
QL) 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
QL varies with period even when
Q for body waves is constant throughout the medium (
Q1=
Q2).
QL 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,
QL 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
QL or
QR (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
QL or
QR is even when
Q for body waves does not vary with depth.
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