The seismic body waves at large distances from a propagating fault near a free surface in an elastic half-space are investigated both in the frequency domain and in the time domain. The results are presented in an analytical form. The fault is simulated by a distribution of double couples of body forces on the fault plane with an appropriate time shift in accordance with the velocity and the direction of the rupture. Two representative cases are considered for the geometry of the fault. The first is a strike-slip fault propagating horizontally along the free surface and the second is a dip-slip fault propagating vertically towards the free surface. It is shown that the effect of the fault finiteness in the horizontal direction on the spectra is characterized by vanishing amplitude and π phase change at particular frequencies. No such simple characteristics exist in the vertical direction. It is demonstrated for the second fault model that the reflected wave of the latest arrival is a very energetic event.

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P wave arrival times from the Long Shot underground nuclear explosion are used to systematically study its hypocenter and origin time. Azimuthal variations are shown to exist. If observations in the range 0°≤Δ≤30° are excluded in the analysis, the epicenter location is strongly biased. The adopted epicenter is 17km NW using 0°≤Δ≤105° observations. The solutions using observations in the ranges 0°≤Δ≤25° and 0°≤Δ≤35° are 11 and 9 km, respectively.

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Magnitude obtains its physical basis when it is converted to energy by a simple relation. Radiated energy is considered as the energy of earthquake. This energy is a function of the focal depth, the moment of a double couple force system and the time process at the source. Depth dependency of the energy is expressed by
1/ρ(1/V_P⁵+1.5/V_S⁵)
and is determined when a certain earth model is given. Such depenency, or the correction in energy determination, is calculated. The dip and slip angles and the direction of the strike do not affect the energy, but they give important effect to the amplitude of the wave from which the magnitude is calculated. Supposing that the energy and magnitude show one-to-one correspondence, the magnitude correction for the dip and slip angles and the direction of the strike as well as for the focal depth was introduced. By this correction, the magnitude obtains its physical meaning and expresses the moment of earthquakes. The two kinds of corrections mentioned above were obtained by using the theoretical seismograms of surface waves with poriods of 17-18 sec.

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The dynamical processes at the source of eleven deep-focus and intermediate-depth earthquakes that occurred around Japan have been investigated from the analysis of long-period P and S waveforms. The recorded P waveforms have been equalized at some distance around the focal region to get the source function, eliminating the combined effects of wave propagation in the earth and of the seismograph characteristics. It is found that the source process times derived from the source function, as well as from the recorded first half-periods, indicate some azimuthal dependence with respect to the orientation of one nodal plane and of the null vector, in most of the earthquakes. This dependence is interpreted as a result of shear faulting over a finite fault area, and used to determine the slip plane, slip direction, fault length and width. The seismic moment and the average dislocation over the plane are evaluated from P wave amplitudes together with the estimated fault dimension. A close agreement in general features between the recorded and synthesized waveforms including the absolute amplitudes of both P and S waves supports the above shear dislocation model. The overall distribution of the orientations of the slip planes and slip vectors of these earthquakes does not seem to be definitely related to the local dip or strike of seismic zones in this region. The calculated stress drops during these earthquakes, together with some available data, appear to show a gradual increase with focal depths down to 400 km. A tentative interpretation of this increase is that the stress drop might be related, at least qualitatively, to partial loss of the intrinsic (cohesive) shear strength of the material under increasing hydrostatic pressures, if these earthquakes are caused by brittle fractures in the lithosphere.

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Theoretical seismograms are successfully used for the study of phase velocity of Love type surface waves in a dipping layer overlying a rigid body. An exact solution in such a case was derived in a previous paper (IsHIS, 1970). It is found in the case of up-dip propagation that the period and duration become shorter with increasing distance, and the later phase arrives at a receiver from the opposite direction of a source, namely from the direction of an apex. It is also found by three facts presented in this paper that the phase velocity in the dipping structure is equal to that of a horizontal structure with a depth at an observation point.

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Seismic refraction and reflection measurements were made across the continental slope off the southeastern coast of Hokkaido and the Kuril-Kamchatka trench. The whole slope is covered by thick low-velocity sediments. Layers with velocities of 5.4 and 5.8 km/sec are found beneath the upper slope. Under the lower deep-sea terrace (1400-2000 m) an unconformity is observed by profiler technique which may show a presence of a large tectonic movement in this area in the past. A structural change is remarkable at water depth between about 4000 and 4500 m, and beneath the land-side slope of the trench a troughlike structure is buried by materials with velocities 4.2 and 2.0 km/sec. Beneath the oceanside slope of the Kuril-Kamchatka trench the crust of the oceanic type is obtained. Many clear faults are observed on this slope by seismic profiler measurements as same as in the Japan and the Izu-Ogasawara trenches.

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Based on the assumption that the double couple model is the most adequate representation of an earthquake, and with the aid of the dislocation theory and of the results in true triaxial experiments of rock fracture, it is pointed out that the directions of the maximum and minimum principal stresses released on the occurence of an earthquake make an angle of (45-θ)°, where θ is the fault angle, to those of tectonic principal maximum and minimum stresses, respectively. It is also pointed out that the released stress deduced from the analysis of a focal mechanism solution is the variation before and after the occurrence of an earthquake, and not the tectonic stress itself in a focal region. So that the discrepancy between both stresses is reasonably understood. Other related problems such as the difference between both focal mechanism solutions obtained from data of body waves and surface waves are briefly discussed.

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