The transition mentioned in the title has not yet been studied theoretically, though this may be expected to occur physically. Many theoretical investigations are needed in order to elucidate the phenomenon; those on dispersion-curves, amplitudes of displacement for any period, orbits of particle and amplitude distributions in the vertical direction etc.
Here, however, the first alone is dealt with. The feature of transition is somewhat like those of waves in a plate (TAZIME, 1958b) and of waves in a layer overlying an absolutely rigid half space (TAZIME, 1959b). Therefore numerical calculations are executed only for σ
1=0.25 and 0.48 where σ, means POISSON's ratio in the superficial layer.
In the present case if υ
p2/υ
p1>1, a large number of higher order of
Mn modes must be reduced again to odd orders of liquid-liquid waves. Similarly, a large number of higher order of
Mn mode must be reduced again to even orders of liquid-liquid waves.
Dispersion curves obtained are shown in Figs. 2 to 7 by thick lines where chain lines indicate (1·2) and dotted lines indicate the second equation of (2·10). Elastic constants used here are tabulated in Table 2. On the dotted line, amplitudes of displacement potential must be zero.
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