Recently, determinations of focal parameters have been widely investigated by comparing observed seismograms with synthesized ones. As a source model, the dislocation model has been accepted as a realistic one, since it was introduced in the field of seismology. For the medium, however, in almost all the studies a very simple model such as an infinite or a semiinfinite medium is assumed. In this case, one should recognize limitations in the appropriateness of the assumption.
In the present study, theoretical seismograms due to a moving fault in a layered medium are compared with those in an infinite and a semi-infinite medium. The results are summarized as follows:
Roughly speaking, if waves are incident on each interface of the layered medium with a small angle of incidence, then the seismograms in the simple medium differ little from those in the layered medium. But even for this case, if the infinite medium is assumed, one should take account of the development of the surface SP waves and Rayleigh waves, contributed from the upper part of the fault. If the angle of incidence is so large that almost total reflection takes place at the lower boundary beneath the source, the difference is significant. For this case, computations on only major phases are recommended to save computation time, referring to the reflection and transmission coefficients at each boundary due to the incidence of the plane wave. Waves which undergo P-S or S-P conversion at the boundary are in general not major phases.
It seems quite difficult and not practical to obtain synthesized seismograms of particle accelerations because of inadequate accuracy and long computation time. It is better to estimate the maximum acceleration using the rough relation (maximum acceleration)=(maximum velocity/rise time).

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An integral of a triple product of associated Legendre functions was analytically evaluated by GAUNT (1929). His formula for the evaluation of the integral can not readily be executed by a fortran computer program because of the mathematical complexity. A convenient method of evaluating the integral by means of recurrence relations of Legendre functions is obtained. The integral thus obtained is applied to the truncation error estimate for the Stokes integration extended over an arbitrarily-shaped area and to the Molodenskii correction for the geoidal-height estimation.

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Expressions for displacements due to a moving fault in an infinite medium are derived in the form of a single numerical integration. Accurate displacements, from which particle velocities and accelerations can be evaluated with sufficient accuracy, can be computed with less computation time than the conventional double integral method.

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The rate of crystallization of synthesized albite glass under pressures ranging up to 20 kb and temperatures ranging up to 850°C is investigated. A piston-cylinder device is used and the rate is estimated by measuring changes in electrical conductivity.
The results are complied assuming the Avrami's equation for the fraction transformed, X: 1-X=exp(-Atⁿ). It is shown that the value of n changes in the initial part of crystallization and also it is both pressure and temperature dependent.
It is also shown that the rate of crystallization depends on both pressure and temperature and further the applications of both pressure and temperature have a profound effect on increasing the rate of crystallization.

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The source mechanism of the Niigata earthquake of 1964 (M_s≈7.5) is re-studied in detail on the basis of the P wave first motion, S wave polarization angle, long-period surface wave, aftershock, precise levelling, tide gage, and tilt measurement data. The long-period surface wave data and geodetic data are interpreted consistently in terms of a thrust fault reaching the earth's surface and having a dip of 56° toward N81°W, a dimension of 80km (length)×30km (width), and an average dislocation of 3.3m. The seismic moment is 3.2×10²⁷ dyne·cm. The stress drop is estimated to be 70bars. This value is not very different from the stress drops obtained for moderate to large shallow earthquakes which occurred in the Japanese islands. The fault plane geometry obtained here is slightly different from that determined from the P wave first motions. Combining this result with the weak beginning of the initial P waves, we may interpret the entire faulting process in terms of a multiple faulting which consists of the two events: the initial localized rupture is followed, after about 4sec, by the major faulting, which is responsible for the excitation of long-period waves.

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The purpose of this study is to obtain an accurate pattern of the geographical distribution of travel-time residuals of P waves from deep earthquakes in and around Japan. The residuals were calculated on the basis of relocated hypocenters. The large-scale lateral heterogeneity of the upper mantle beneath the island arc was taken into account in the hypocenter determination, but the degree of heterogeneity was not assumed. Two kinds of residuals (I and II) were considered. The residual I is the observed travel-time minus the calculated travel-time corrected for the lateral heterogeneity. The residual II is the observed travel-time minus the calculated travel-time without such correction. The residual I is mainly controlled by the local structure of the crust and uppermost mantle beneath the station. It correlates with the gravity anomaly. The residual II is related to the large-scale anomalous upper mantle structure represented by a high-velocity oceanic lithosphere underthrusted beneath the island arc. The average P-velocity contrast between the underthrusted lithosphere and the upper mantle on the continental side of it was estimated to be at least 3%.

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Large earthquakes on the Pacific coast are characterized, on the average, by σ≈30 bars and L≈2w independently of the size, where σ is the stress drop, L is the fault length, and w is the fault width. It follows from these that the seismic moment is determined straightforwardly from the fault size alone. Such a convenient method of estimation of the seismic moment is also applicable to the major earthquakes in the Japanese islands which are characterized, on the average, by σ≈60 bars and L≈2w. These results can be used for reliable assignment of moment to future large earthquakes as well as historical large earthquakes for which detailed mechanism studies cannot be made. The uncertainty in the method presented here is much less than that in estimating moments from the earthquake magnitude.

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