The ratios of the spectral amplitude at 10cps to that at 20cps of the compressional waves obtained from the explosions in the Matsushiro earthquake swarm area are used to study the latera1 variation of specific attenuation factor Q in this area. The head waves through the 6 km/sec-1ayer observed at the observation sites on Profiles A and B are analyzed for this purpose. This analysis showed that the location of the low Q region coincided with the seismically most active region, and the Q value in this region was extremely low, 30 to 50, which is 1/20 to 1/50 of the surrounding region.

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Gravity anomalies due to the upper mantle heterogeneity around north-eastern Japan are investigated. The anomaly based on UTSU'S model is characterized by a positive anomaly around the Japan Trench and a negative anomaly in the Sea of Japan. The latter reflects the peculiar feature of the upper mantle beneath the marginal sea. The residual anomaly computed from a detailed crustal section and the observed gravity anomaly also indicate the same pattern.
A new crust-mantle model around northeastern Japan is proposed. This model explains well the various geophysical observations.

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A chain-reaction-type fracture formation at the seismic source is hypothesized to interpret the magnitude frequency relation of earthquakes. Comparison of the results with actual data gives general agreement. The implication is that the magnitude of a particular earthquake cannot be predicted before the occurrence of the event but is defined only when all disturbances of chain-reaction-type fracture formation at the source are brought to complete termination.

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Explosion seismic data in two regions are studied by utilizing the time-term method. The results of two profiles in the Matsushiro earthquake swarm area agree very well with the previous models by ASANO et al. In one profile, the travel-time residuals plotted in the ordinate to distances in the abscissa show a convex tendency which strongly suggests vertical velocity gradient in the basement layer. The distance-dependent velocity is determined accurately with the modified time-term method.
Some defects in the model by HASHIZUME et al. for the Kesennuma-Oga profile are removed by the model obtained with the time-term method in the present study. It is particularly remarkable that the possibility of the lateral change in the P_n velocity near the Honshu-Japan Sea boundary is pointed out.

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The melting of albite has been investigated in the presence of water in the pressure range up to 30 kb. Fixed amounts of water have been contained in the melts so as to satisfy the condition that the melt is saturated with water or P_H2O=P_t up to a certain value of pressure, but at higher pressures the melt is undersaturated or P_H2O<P_t. The results show that the melting relation is largely influenced by the presence of only a very small amount of water and strongly support the partial melting hypothesis for the cause of the low-velocity layer. It is suggested that the temperature in the earth's mantle is quite near the melting curve of the mantle when the melting gradient based on the theory of the lattice defects is adopted.

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The normal mode solution for Love waves from a shear fault in a stratified layer over the half-space is investigated with special attention to the azimuthal behavior of amplitude compared with the radiation pattern of SH waves. It is found that Love waves are denoted by the sum of two terms associated with a particular set of rays of physical significance. For the torsional oscillation of a homogeneous elastic sphere due to the shear fault, a similar relation is recognized between higher radial modes and rays. The mode-ray relations obtained in the above two cases coincide with the ones derived in other literature from quite different considerations that interpret the normal modes by interference phenomena.
The radiation patterns of SH waves and of normal modes are found to be related through the apparent equivalent take-off angle lh, which is defined so that the radiation pattern of square amplitude for a normal mode may be equal to the pattern of the sum of the square amplitudes for SH waves emitted in the two directions specified by the take-off angles lh and π-lh. Provided that the apparent equivalent take-off angles are known beforehand as a function of the eigen-frequency and the focal depth, it is easy to obtain the azimuthal dependence of amplitude of the normal modes excited by a shear fault of arbitrary dip and slip, because the azimuthal behavior is the same as the radiation pattern of SH waves associated with the apparent equivalent take-off angles. Numerical experiments are shown for the fundamental torsional oscillation of a Gutenberg-Bullen A' spherical earth excited by a pure dip slip and a pure strike slip fault at depth 5.35km.

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This paper deals with the torsional vibration of radial higher modes of a spherical earth consisting of a homogeneous elastic mantle and a liquid core with special reference to the correspondence relation between normal modes and body waves.
The normal modes and the rays assigned by the mode-ray correspondence relation originally derived by Ben-Menahem are related very closely in several aspects even for the normal modes of the low radial modes having small colatitudinal order numbers. This relation connects modes and rays through the identity of the phase velocity of normal modes and the apparent velocity of body waves. Group velocities of the normal modes associated with a certain ray show nearly constant values independent of radial mode numbers, constants being a function of ray parameter. The travel time of surface waves specified by this constant group velocity gives almost the same value as that of the corresponding body wave. In addition, there are close correlations between the two radii, one to the lowermost maximum or zero point of the radial distribution of azimuthal displacement of the normal modes and the other to the deepest point of the ray.
The criterion is established which assigns normal modes of minimum numbers required for the construction of respective body wave phases. Direct, reflected and diffracted SH pulses produced by a point source at zero depth are synthesized by summing up contributions from a limited number of normal modes assigned by this criterion, which reveal almost identical patterns to those obtained by the summation of contributions from a large number of modes.
It is found that the separation of body wave phases is possible even from the standpoint of the normal mode theory except for pulses having mutually close ray parameters and that normal modes with very large order numbers are needed for the precise construction of pulses traveling the shallow region and that pulses penetrating to the inner region require normal modes up to much higher radial modes with relatively small order numbers.

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In general, it is not adequate to analyze the form of body waves radiated by a shallow earthquake, because the initial P-wave group may be contaminated by various complicated phases. But in the cases of the Niigata earthquake (h=12 km by ISS) of 1964 and the Taiwan-oki earthquake (h=42 km) of 1966, the initial P-wave form on seismograms has two distinct phases. One of these phases can be thought to be the stopping phase and the other to be the break-out phase. It is possible to obtain the seismic parameters by analyzing these two phases and to determine the fault plane of the earthquake.

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