An inverse method to find optimum fault parameters from geodetic data with random errors is extended so as to be applicable to a case of the data including a systematic error caused by movements of reference points in triangulation. Application of the new inverse method to static displacement data associated with the Kanto earthquake of 1923 yields a dislocation source model which adequately explains both the seismological and the geodetic data.
From the geodetic data, it is found that the fault motion of the Kanto earthquake is a reverse, right-lateral slip of 4.8m with a slip-angle of 140° on a plane which dips 25° towards N24°E, where the slip-angle is measured counterclockwise from a strike on the fault plane. The fault length, width, and the depth to the upper fault margin are determined as 95km, 54km, and 1.5km respectively. The seismic moment and stress drop of this earthquake are estimated to be 8.4×10²⁷ dyne·cm and 45 bars, respectively.
Taking the static fault solution as the basic model, the dynamic process of the fracture is investigated on the basis of the long-period seismograms recorded at Hongo, Tokyo. The result shows that the rupture starts from a relocated hypocenter, 35.41°N, 139.22°E and 13.5km (depth), and extends outwards on the fault plane with a propagating velocity of the rupture front of 2.0km/sec. The rise time of the source time function is assumed to be 5.0sec. The maximum amplitude of acceleration for a frequency range of 0.0-3.3Hz at Tokyo is estimated to be about 280gal for the horizontal component and to be 60gal for the vertical component, by applying an empirical formula to the calculated ground displacements.

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A new method to obtain theoretical seismograms for a layered medium is presented, where an appropriate path of integration for the integral with respect to wave-number is chosen. In this method, upper limit of the integral can be taken as a finite value depending on the time interval in the time domain for which seismograms are computed and pole contributions are implicitly included without consideration of residues at the poles.
Comparison of the present method with those in previous investigations is made and problems of the generation of seismic surface waves are numerically evaluated.

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The causes leading to slow earthquakes and multiple earthquakes are theoretically investigated. The unsteady propagation of longitudinal shear cracks are analysed as a mathematical model. The inhomogeneous distributions of initial stress, sliding frictional stress and specific fracture energy are introduced. The specific fracture energy is the amount of energy needed to creat a unit area of new crack surface. The energy rate balance is considered as the fracture criterion. The inhomogeneously distributed initial stress is regarded as an internal stress.
If the rate of decrease of initial stress minus sliding frictional stress, with respect to the distance from the rupture initiation point is low and if the nondimensional specific fracture energy that represents the material strength relative to the degree of stress concentration is high, then slow earthquakes will easily occur. In this case, even slight irregularities of initial stress and/or sliding frictional stress may contribute to rupture motions.
Multiple earthquakes will be caused by the discontinuous distributions of the specific fracture energy and/or the stress difference given by the initial stress minus the sliding frictional stress.

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The Coulomb criterion for shear failure is extended to predict fracture angles under general triaxial stresses, where the cohesive strength and the coefficient of internal friction are no longer considered constants and are functions of the intermediate and the minimum principal stresses.
Fracture angles calculated on the basis of the new criterion developed here agree with those obtained experimentally by other researchers within experimental errors.

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Formal solutions for the ocean bottom disturbances due to an underwater explosion are derived by using the Haskell matrix formulation. Numerical evaluation of the solutions is very difficult and takes a long computation time using present computers. We present a method in which the solution is decomposed into 'rays' by expanding it into an infinite series, where lower order terms correspond to early arrivals, and thus the method enables us to obtain correct wave forms of early arrivals by taking the first few terms. The reflectivity method by FUCHS and MULLER (1971), which takes only the first term in the expansion, corresponds to the first approximation of our method. Effect of free surface which is neglected in their reflectivity method can be taken into consideration by taking a few terms in the expansion. The method is a powerful one, although it is applicable only to compute the wave forms of early arrivals, because the expansion does not converge at the poles.
The method is used to calculate the theoretical synthetic seismograms for five different structures which satisfy the travel time of the P wave arrival. The results are compared with the observation which was taken on the continental-side of the Japan trench. In order to explain the amplitude behavior of the first few seconds, provided that the sediment can be represented by one homogeneous layer, a P wave velocity of about 3km/s and an S wave velocity of about 1km/s in the sediment, must be taken which results in large V_P/V_S ratio.

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