In order to solvc the eigenvalue problem of an elastic body with complicated boundaries, a mass system of framework is employed, and the continuous medium is simulated thereby. For the mass system there is no difficulty in satisfying the boundary condition, which is a crucible for a continuous medium. In this way the disturbances caused by the initial excitation in a rectangular elastic body is calculated as a function of time using the finite difference formula, By the Fourier analysis of these propagating disturbances, which is a method with which the free oscillation of the earth is obtained, the eigenfrequencies and the eigenfunctions are calculated for a rectangular body. By this scheme the eigenvalue problem of a finite elastic material is solved. The problem with a crack inside is also solved and the features of spectra are compared with the case without a crack. This kind of technique might be of some use for the non-destructive testing of an elastic material.

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Love numbers are non-dimensional parameters that describe surface deformation of the earth due to external forces; tidal Love numbers (h_n>, l_n>, k_n>) represent earth's response to tidal force and load Love numbers (h'_n, l'_n, k'_n) represent the response to loading on the surface of the earth. The two sets of Love numbers have been considered as independent sets and numerical calculations have been performed as such. In this study we prove that there exists a simple relation, 1+1k_n-h_n=1+k'_n, valid for any non-rotating, spherically symmetric earth models. Previous calculations by several authors were examined and are found to be consistent with this relation. In addition to the two sets of Love numbers, we introduce a new set of "shear Love numbers" (h"_n, l"_n, k"_n), which describe the surface deformation caused by shear force applied to the surface of the earth. These three sets of Love numbers suffice to describe the earth's response of spheroidal type to any kind of external forces.

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The formulation derived in Part I of this paper, to obtain disturbances at a surface of a medium with superficial multi-layers due to a dimensional fault is revised by taking surface wave contributions approximately into consideration.
Surface accelerations due to a simple source model with source time function of ramp type are found to be too small, even if our interest in the present study is on rather long-period components. One possibility is shown that rather large accelerations are obtained by adopting different source time functions from the simple ramp type, keeping other focal factors the same as in the presently available fault model.
Accelerations thus obtained are of course only tentative and their absolute values cannot be discussed at the present stage of seismology. However, if surface structures at many places are clarified and detailed behaviors of short-period components in the source time function, especially for large earthquakes, are elucidated, then the present formulation may make it possible to discuss even absolute values of accelerations.

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The focal process of deep-focus earthquakes is modelled physically using a viscous frictional law. Numerical experiments are conducted in which the equation of crack propagation derived by YAMASHITA (1976) and the heat conduction equation are solved simultaneously. In this way, the interaction between fault motion and thermal conduction is taken into consideration. When the frictional characteristics of a deep-focus earthquake are described by a transient creep equation, the sliding frictional stress initially increases rapidly as the dislocation continues. However, when the temperature on the dislocation surface becomes significantly higher than the initial temperature or exceeds the solidus temperature, the sliding frictional stress begins to decrease. Efficient fault motion depends on this decrease in sliding frictional stress, and also requires a large effective stress in order to overcome the resistance caused by the initial increase of sliding frictional stress. Effective stress is defined as the static frictional stress minus the sliding frictional stress. This paper shows that a large stress drop is caused by a large effective stress and therefore the fact that deep-focus earthquakes have large stress drops is fully explained by the model proposed in this paper.

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Numerical experiments of tsunami generation and propagation are carried out for five earthquakes which occurred off the Pacific coast of the Tohoku and Hokkaido districts. The tsunami sources used in the experiments are the vertical displacement field of the sea bottom derived from the seismic fault model for each earthquake. Water surface disturbances are computed by a finite difference hydrodynamical method with finer grids in shallower water. The comparison of the computed tsunami behavior with available tsunami records along the coast shows that the distribution of observed tsunami heights can be explained in the first approximation by seismic fault models while the observed heights are 1.2 to 1.6 times larger than the computed heights. An example of a fault model inferred from seismic data (June 12, 1968) which is not suitable for a tsunami source is presented.

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This paper shows that five different families of spheroidal modes can be isolated, namely: 1) Inner Core and Stoneley modes ("K" modes); 2) "V" (vertical) modes, with mainly vertical displacement; 3) "C" (Colatitudinal) modes, with mainly horizontal displacement; 4) "R" (Rayleigh) modes, in which the horizontal and vertical displacements are totally coupled, and 5) "H" (Hybrid) modes, with intermediate coupling. V and C modes occur at high phase velocities, R modes at low phase velocities, and H modes at intermediate ones. Each of the families of modes has distinctly different properties, including group velocity, Q, and excitation functions.
Except for H modes, these families are arranged in "pseudo-overtone" branches, along which physical properties vary smoothly. A theoretical description of the properties of V, C and K modes is given, using the simplified model of a homogeneous, non-gravitating Earth. Two important observations are explained, using this model: i) The solution for C modes at low values of l are identical to the ones for corresponding T (Torsional) modes, and have, therefore, the same eigenperiods are relative excitation functions, and ii) the radial modes _nS₀ are the l=0 members of the V family, and their apparent scarcity results simply because only that family has modes with l=0. Furthermore, the group velocity of K, C, V and R modes is shown to be consistent with the physical concept of dispersion along a pseudo-overtone branch. An interpretation of the existence of the different families in terms of an increase in mode-coupling with angular order is presented.
A formal classification of the spheroidal modes into 5 families is made, and a new nomenclature is proposed, which is closely related to their physical properties.

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Ray theory is applied successfully to derive asymptotic frequency equations of the radial oscillations of a homogeneous elastic sphere and a sphere with one concentric surface of discontinuity in it, and of the spheroidal oscillation of a homogeneous sphere. The method is similar to the one used for getting frequency equations for plane stratified media, and is based on the idea that for steady vibration of a sphere to be possible some interference condition has to be satisfied by body waves traveling in it. It is shown that these equations are identical to those obtained by the normal mode theory.
It is found that the solotone effect has an immediate connection with multiple reflections of body waves at the discontinuity in the medium.
Decoupling of P- and S-waves at high frequencies is well illustrated for the spheroidal modes in terms of the distribution of eigenfrequencies and the radial dependence of eigenfunctions.

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