In order that any wave group may predominate, several conditions must be satisfied. The subject is considered on sharpness of spectrum in each factor contained in the integral expression of waves. The wave group seems to be most important which satisfies condition dω/dξ=x/t, if spectrum of the source is flat. The lower limit of the epicentral distance x is investigated numerically which permits generation of LOVE-waves. The present result of calculation is compared with the result obtained by experiment. Many experiences in experiments of RAYLEIGH waves suggests that the lower limit of x calculated here is rather severe than that observed. However, different types of waves are compared with each other and present assumptions in spectrum may be simpler than spectrum in practice. The authors think that the present consideration tells some substantial aspects of surface waves.

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Observations and analyses were elaborately carried out to make a more precise interpretation of the seismic waves generated by explosions than before. Among the wave groups which were recorded, the first one is the initial motion of direct or refracted P-waves; the second one is most likely the bodily waves unlike the views hitherto accepted, so it is considered a group of waves including reflected and refracted P-waves and later direct phases which succeeded the first wave group. As for the third and the fourth wave groups by comparative study of the theoretical and observed characteristics of their phase and amplitude, a satisfactory conclusion, both qualitatively and quantitatively, has been reached by regarding the third group as M₂₁ waves and the fourth group as M₁₁ waves. It has been clarified also that the most superficial layer contributed to the generation of these M-waves.
The reciprocity was also discussed. In order to make a precise examination of reciprocity, various kinds of conditions, especially explosion condition and horizontally layered structure, etc., should be unified beforehand.

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Active volcanoes of an island arc are situated in a specific belt, which is called a volcanic belt and parallels to an oceanic trench associated with the island arc. The trenchside border of a volcanic belt is named a volcanic front, as volcanoes are clustered rather near the border on the trench side than at the axis of the belt (Figs. 1 and 2).
Mantle earthquakes of an island arc show a systematic distribution of the foci on a plane dipping away from an oceanic trench, the plane being called a seismic plane.
Mantle earthquakes are closely related in space to volcanoes of the island arc. The depths of the seismic plane underneath the volcanic belt are limited to a range from 150 to 250km. On the other hand, basic differences in chemical composition among the basaltic primary magmas reflect differences in the depth at which the magmas were generated, instead of successive stages in the differentiation of magma. The depths of the seismic plane appear to be responsible for the magma-generation depths, as the systematic regional variation in chemical composition of the primary magmas shows a close correlation to the regional variation in depth of the seismic plane. Therefore, the generation of mantle earthquakes and the generation of primary magmas would have a common origin (Fig. 3).
Complementary relationships in distribution between hypocenters of mantle earthquakes and the magma-generation zone are stressed on in this paper and are summarized as follows:
1. The hypocenters of mantle earthquakes are abundant in the frontal area of the volcanic front, where no volcanoes are present. To the contrary, they are rare underneath the volcanic belt. The relationship is clearly given in a map of Japan (Figs. 4 and 5).
2. Ratio of total numbers of mantle earthquakes at depths from 175 to 275km to total numbers of those from 75 to 125km is distinctly lower in island arcs than in non-islandarc regions. The relationship is given in a histogram and a table. Under the island arcs the hypocenters are relatively scarce at depths from 175 to 275km, where magmas would be generated (Fig. 7 and Table 1).
3. Along the belt at the back of a volcanic front, either the bulk of the belt is occupied by many of volcanoes as is the case in Japan, or some sections of the belt are occupied by a series of volcanoes as is the case in the Pacific coast region of South America. In the latter case, nonvolcanic sections of the belt at the back of an extension of the volcanic front display higher seismicity in the mantle.
Thus the greater part of epicenters of mantle earthquakes shows a complementary distribution to loci of volcanoes in island arcs. It would imply an exclusive relation between the generation of mantle earthquakes and the generation of primary magmas. Therefore, it seems very likely that the source of energy is common with the each other and the difference of generating whether shocks or magmas is attributed to a condition of circumstance, for instance, the temperature of the particular place.

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About two tons of explosives were fired twice in Endani, Kurayosi, Tottori Prefecture on November 16, 1963 and on November 21, 1964, and once at Hanabusa Mine, Gifu Prefecture on November 18, 1964. A shaft of an abandoned mine was used as a shot hole for each explosion. There were about twenty temporary stations in each explosion and good seismograms were obtained. These experiments are described and the results of observation are presented in this paper.

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By using data of the first and second Kurayosi and the Hanabusa explosions presented in Part 1, the crustal structure in the western part of Japan was derived. The velocity structure of the second layer with velocity 6.1km/s was considered and the existence of the layer with velocity 6.4-6.6km/s was ascertained. On the travel time graph of the Kurayosi explosions, the phase with velocity 6.4-6.6km/s gives clear first arrivals. Neglecting fluctuation of travel times due to inhomogeneity of the surface or within the crust, the trial was made to obtain the range of depth of boundaries as well as that of velocity whenever possible. From the interpretation of travel time graphs, two possibilities for the deeper part of crust, Model I and Model II, are given in Figs. 3 and 4. In Model I there is a gap of the Mohorovicic discontinuity west of Biwa Lake by about 4km and in Model II there is another layer with pretty high velocity 7.4-7.5km/s above the layer with velocity 8.0-8.2km/s. The thickness of crust is quite different between the two models. The apparent velocity of 8.0km/s was obtained pretty clearly.

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Mathematically, M (ω, ξ)=0 means a mapping of one variable on the plane of the other complex variable. In this stage, no physical condition is involved. At first, a technique of calculating complex variables is described. Using supplemental parameters Θ_j′s, wave numbers η_j′s in vertical direction can be easily investigated. Multi-valueness of η_j is attributed to arbitrary selection of m_j even or odd. Next, explicit expressions of ω and ξ are obtained which contain only another complex variable γ. Some arbitrariness of m₂-m₁ has been related to orders of modes due to multi-valueness of trigonometric functions. Preferable RIEMANN sheet of mappings should be chosen in future by considerations on physical conditions.

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