In the present paper, the s u rface spherical harmonic representations have been derived for the system of equations of motion, equation of continuity, thermodynamic equation and others, which may provide the study of the atmosphere with the first steps towards the management of a complete system of those equations, including the method of solving “ balance equation ”, simplified ω-equation, and further equations of kinetic and potential energies.
In some earthquakes, a prominent wave group of long period accompanied by the T-phase of seismic waves was observed on the records taken by the Wiechert seismographs at the coastal stations, Shionomisaki, Shimizu, Wajima etc. The period of the long wa v es is 7.5-15 sec., while that of the T-phase is 0.2-1.4sec. The T-phase of seismic waves may be the free waves whose pressure amplitudes are concentrated in the sound channel, so that it may be dispersive. The long waves seem to be the oceanic Rayleigh waves, corresponding probably to the rider waves of Pekeris. The wave train of long period under consideration is so prominent that it seems the T-phase and the long waves should be connected with each other in a certain way. The present writer show e d that a kind of coupling between the dispersive short waves and the dispersive long waves was possible, if the group velocities of the two waves were the same and the condition cT/c-U = c'T'/vc'-U'' where U'= U', was satisfied. For an example, it is shown that the T-phase with a period 0.5 sec. and the oceanic Rayleigh waves with a period 10 sec. may be connected with each other, almost satisfying the condition cited above. In the case of the Sanriku earthquake of 1933, only the long waves, which may be the rider waves, were observed at Choshi and Kakioka.
The seismicity of shallow e a rthquakes has been investigated to a considerable extent; on the other hand little is known as to the seismicity of intermediate and deep-focus earthquakes. This is mainly because of the low sensitivity of the present network of seismological observation in Japan, which happens to be most suitable for the zones of intermediate and deep-focus earthquakes. In the seismograms recorded at Matsushiro by a sensitive electromagnetic seismometer, however, many shocks which are small and probably deep have been found, and an example is presented in Chapter II. In order to detect those small deep shocks, a new method of estimating focal depth and epicentral distance by means of S-P time and apparent velocity, which can be observed by a multi-point observation of comparatively small dimensions, is proposed and discussed also in Chapter II, since the highly sensitive observation cannot he allowed in most of the present recording stations owing to high background noise. Thus, a continuous tripartite observation to find the apparent velocity and direction of seismic propagation was started at Matsushiro in June,1959. Chapter III deals with the instruments employed in this observation. Particularly, the improved film recorder, on which the observational accuracy largely depends, is explained rather in detail. The observation results and the seismicity of small but d eep shocks will be published in the next paper under the same title. Chapter I. Introduction