The far-field body waves generated by a slip dislocation with an elliptically expanding rupture are analysed in the time domain. It is assumed that the ratio of the lengths of the axes of an expanding ellipse is an arbitrary constant α. The radiated body waves are described by the product of two factors. The first one due to the double couple without moment is excluded from the consideration. The second factor T_j (j stands for the P- and S- motions), which includes the time dependence of the seismic impulse and which reflects the character of the rupture propagation, is analysed for three models with different values of the parameter α. The graphic representation of the T_j pattern consists of three components: 1) the spatial distribution of the slope of the initial part of the impulse T_j, 2) the graphs of the impulse T_j as a function of time for the chosen directions, 3) the spatial distribution of the maximum amplitude of the impulse T_j. The slope of the initial part of the displacement T_j is the greatest in the rupture plane and the smallest in the direction perpendicular to the fault. If the angle between the rupture plane and the observer is kept constant, then the slope is the greatest for the direction whose projection on the rupture plane lies along the direction of maximum velocity of the rupture propagation. If the boundary of the faulting area is rectilinear or concave, then some impulses can exhibit two displacement maxima, at the times of the first and the second stopping phases, respectively. The maximum amplitude of the displacement T_j depends to a high degree on the ultimate boundary of faulting in relation to the initial point of rupture, as well as on the form of the rupture propagation. It is found that if the fault surface is not elongated and the starting point of the rupture is approximately in the center of the fault, then the maximum amplitude of the displacement T_j should be the greatest, in general, for the directions whose projection on the rupture plane lies along the direction of minimum and not of maximum velocity of the rupture propagation.

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The geometry of the slab as well as the stress inside the slab near the junction of the Kurile and the northern Honshu arcs, that is, the Hokkaido corner, are studied based on the seismicity and the focal mechanism solutions of mantle earthquakes. Focal mechanism solutions vary depending on the focal depth and the local strike of the slab. The distribution of mantle earthquakes and the variation of the mechanism solutions reveal slab contortion on the Kurile side of the Hokkaido corner. The relative motion on the fault plane is estimated based on the analysis of source processes of mantle earthquakes. The sense of the earthquake slip motion is consistent with the sense of the slab contortion. This may indicate that the slab contortion, suggesting a plastic deformation, results partly from the earthquake slip motion.

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A theory was developed on the free vibration of a crystal of rectangular parallelepiped and of general symmetry by extending Demarest's theory of cube resonance. All vibrational modes were classified and described in detail for the case of orthorhombic symmetry. The theory is applied to determine elastic constants of crystals from the resonance frequencies of its free vibrations. The method of numerical analysis of resonance frequency data was studied to derive a practical way of elastic constant determination. As an example, the elastic constants of two specimens of single crystal olivine (Mg_1.8Fe_0.2SiO₄) were determined. The applicability of the resonance method is largely extended by the present theory to the precise determination of elastic constants of single crystals.

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The Antarctic Continent and the surrounding ocean, which is called the Antarctic plate, enclosed by marginal seismic belts is one of the large aseismic areas on the earth, though there are active volcanoes in West Antarctica and the Ross-Weddell Graben. More than ten seismological stations have been established in Antarctica since International Geophysical Year (IGY) of 1957. However no earthquakes have been located in the Antarctic area by the World Wide Seismological Station Network (WWSSN), with the exception of volcanic eruptions of Deception Island.
"The Antarctic Seismological Bulletin" has been published on the basis of phase readings from the Antarctic Seismological Stations. The events for which the phase readings of P wave arrival time were reported from more than four stations, but for which the hypocenter determination was not made, were found in the bulletin.
Seismograms at Japanese Antarctic Station, Syowa, in Lutzow-Holm Bay, East Antarctica, seem to indicate the occurrence of some micro-earthquakes. This fact suggests the possibility of the occurrence of small/micro-earthquakes in other part of the Antarctica.
The present paper attempts to confirm the existence of earthquakes in Antarctica on the basis of the data from WWSSN and of temporary seismological observations at some stations in Antarctica.
The main results are summarized as follows:
1) Small earthquakes occur at least in West Antarctica and in the Ross-Weddell Graben, though the activity is very low. But the earthquakes are not generally detectable by the insufficient seismological network in Antarctica.
2) The seismicity around Syowa Station in East Antarctica is less than one micro-earthquake per month. However earthquakes occur in the marginal zone of East Antarctic Shield area.
3) The seismicity around the Dry Valleys in Victoria Land is one micro-or ultra micro-earthquake every two days and that around McMurdo Station on Ross Island is one earthquake per day.
4) The seismic activity in the volcanic region in the Antarctic is relatively higher than that in the surrounding region.
5) The seismicity in West Antarctica and in the Ross-Weddell Graben is some ten times higher than that in East Antarctica.

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In the present tsunami warning system, the predominance of the approaching tsunami is estimated, taking account of the earthquake magnitude and focal depth. However the predominance of tsunami also depends on other focal parameters, e.g. the rise time of the source time function, fault length etc. Accordingly it is quite natural that great tsunamis due to earthquakes with relatively small magnitudes have been sometimes observed. For the improvement of the tsunami warning system, it is necessary to develop the method to find the focal parameters before the tsunami wave arrivals and to make clear the dependence of the generation of tsunami on the above parameters. Effects of the focal parameters on the generation of tsunami and Rayleigh waves are investigated in a previous and in the present paper respectively. If the focal parameters are pre-estimated by the use of early arrival Rayleigh waves, the predominance of tsunami can be predicted. Although some of the focal parameters have fairly complex effects on both waves, it is shown that there is some possibility of the improvement of the present warning system by the use of tectonic features and body waves in addition to sub-oceanic Rayleigh wave observation.

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An equation which represents the crack propagation is obtained by approximating the wave equation and the boundary conditions in the neighborhood of the dislocation surface. The problem of crack propagation with an unsteady finite rupture velocity is solved with the aid of this model and the computation is carried out by using the finite difference method. The proposed model takes the rupture propagation as the diffusive phenomena of the inhomogeneous initial stress field. It is clarified in this paper that the most important focal parameters for the dynamical process of fault motion are the effective stress (defined as the static frictional stress minus the sliding frictional stress) and the fracture strength (defined as the static frictional stress minus the initial stress). The former accelerates the fault motion and the latter decelerates it. All the rupture phenomena can be interpreted by the relative magnitude between these stresses. The importance of both stresses is not ascertained until the inhomogeneous initial stress field is introduced.

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