Ultrasonic wave velocity and stress-strain relation for three types of marbles with different grain sizes are measured under tri-axial compression. The range of axial differential stress and strain is up to 3Kb and 7% respectively. It is found that the strength of the marbles decreases as the grain size increases like the metallic polycrystals. In the plastic region, ultrasonic wave velocity of marbles decreases as the strain increases. A phenomenological model is proposed to explain qualitatively the behavior observed.

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Expressions for displacement potentials due to a dip-slip fault and a strike-slip fault model with arbitrary dip angle are presented in Cartesian coordinates, cylindrical coordinates and spherical coordinates. From these results, displacements and stresses when the time variation of the source is a step function type are also derived.
It is shown that the solutions obtained above can easily be expanded to those for moving dislocation models.
In the last part of this paper, the solutions in polar coordinates are expressed in another polar coordinates with different origin. The expressions can immediately be applied to the problems of generation of seismic waves and excitation of the free oscillations of the earth due to a dislocation in a spherical earth.

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The torsional free oscillation due to a dip-slip fault or a strike-slip fault is studied in an earth model with homogeneous mantle and homogeneous liquid core. Because of the simple earth model assumption, only the fundamental mode of order number two, ₀T₂, is investigated.
It is found that the ₀T₂ is effectively excited by a vertical strike-slip fault. The surface amplitude of the free oscillation due to a horizontal or a vertical dip-slip fault is about three percent of that due to a vertical strike-slip fault. Radiation patterns, except for a horizontal or a vertical dip-slip fault, are governed by P₂² (cos θ) (cos 2ψ sin 2ψ).
If a step function time variation fault is assumed, then the maximum surface amplitude of 6×10^-2cm is estimated when the area of the fault is 10⁴km² and the mean offset over the fault-plane is 5m.

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A relation between predominant period and magnitude is investigated both experimentally and theoretically. If we disregard the difference in the predominant periods of P and S waves, the results for earthquakes with magnitude less than about 5 are consistent with those derived from the velocity spectra of two theoretical source models given by HASKELL and AKI. For earthquakes with magnitude larger than about 6, the periods theoretically derived deviate largely from the observed ones. This is caused by the definition of magnitude which is based on the amplitudes of surface waves with period of 20 seconds.
Assuming a linear relation between magnitude and logarithm of seismic energy, we find logT=-A-B log σ+CM, where σ is the stress drop and A, B and C are constant. Corresponding to various relations between the stress drop and magnitude, the curves relating log T with M can be drawn in various forms. Only when the stress drop is constant through all the magnitudes, log T is a linear function of magnitude.
The above-mentioned tneoretical models give the same source spectra for P and S waves. Therefore the difference in the predominant periods for P and S waves must be explained by other factors, for example, by the difference in the attenuation of seismic waves. When the attenuation factor Q for S waves is appreciably smaller than that for P waves, the difference in the predominant periods may be explained for microearthquakes, but for large earthquakes, because of their long periods, the difference in the values of Q is not effective.

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Various approaches have been explored to elucidate the nature of the core-mantle boundary, such as its position, physical shape, and the distribution of physical constants. In this study these investigations are reviewed and the possibility is examined to study the unknown factors of the core-mantle boundary characteristics when more abundant seismic data become available in the future.
In order to determine the physical constants of the lower mantle close to the core-mantle boundary, it is quite important to investigate the effect of diffraction due to the core. An attempt to obtain Q distributions in the mantle by taking spectral ratio of direct waves at different stations has been made. If the effect of diffraction is unknown, however, it is impossible to make correction for observed spectral amplitudes to find correct Q values in the lower mantle. To elucidate the nature of the core-mantle boundary, other method for obtaining the attenuation function along the boundary by taking spectral ratio of the core-diffracted waves has been developed. For this case, it is necessary to know the attenuation function for a wide variety of the core-mantle boundary structures which are suggested from other evidences.
To eliminate the effect of diffraction, it is promising to analyze the spectra of waves reflected at the core boundary. But even for this case, it would be required to solve the problems of determining the reflection coefficients when spherical waves are incident onto spherical boundary having the gradual change of physical constants.
In the present paper, the model studies of these bottlenecks are planned. First, the precise diffraction pattern by an impenetrable sphere is obtained from sonic wave experiments. Second, the difference between the diffraction patterns due to the various structures of the core-mantle boundary is studied by use of two-dimensional models which have core-mantle boundary structures with continuous velocity change, as well as irregular boundary structures. The difference between the diffraction patterns is found to be too large to make the diffraction compensation to the spectral ratio of the direct waves possible with an aim of getting Q values in the lower mantle.
The attenuation functions of the diffracted waves in the shadow zone are also obtained by ultrasonic model experiments and compared with seismic data. The results show that a kind of irregular core-mantle boundary structure having a thickness of 30 to 100km accounts for the seismic data.
PcP spectra are generally insensitive to the structure with continuously changing velocities and other physical constants, while they are sensitive to the layered structure having discontinuous boundaries. This result suggests the possibility to discriminate whether or not there is a layered structure at the core-mantle boundary by use of the spectra of PcP.

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Long-period P waveforms have been analyzed to interpret the source mechanism of four intermediate earthquakes with magnitudes of 6.0-6.5 and focal depths between 100 and 200km.
The synthetic seismograms appropriate to each recording station have been constructed, to compare with observed records, on the basis of moving dislocation models with various parameters, including the fault length and width, the amount of dislocation, its time dependence and the fracture velocity, taking into account the combined effects of wave propagation in the earth and of a recording instrument. General features of the observed waveforms do not differ greatly from those for a double-couple point source, but the comparison with synthesized waveforms at a number of stations indicated seismic moment of order of 5-9×10²⁶ dyne·cm, and also probable ranges for some other source parameters on tne assumed source. The bounds of the stress-strain drop, the released strain energy, and of efficiency of seismic wave radiation at the source were also discussed.

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The present article lists the results of studying the group-velocity dispersion of Love and Rayleigh surface waves in connection with the crustal structure of the Sea of Okhotsk and the Bering Sea. The dispersion of group velocities was determined for earthquakes of the Aleutian, the Kuril and the Japanes Islands and of Kamchatka. Records of surface waves at the station of Yakutsk, Tixi, Petropavlovsk, Magadan, Okha, Uglegorsk, South-Sakhalinsk, North-Kurilsk were used.
The crustal structure in a number of places of this area was determined by various geophysical methods, ^{1), 2)} but the propagation of surface waves on this territory is practically not yet investigated.

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