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The detailed three-dimensional P and S wave velocity structure in the focal region of the 1984 Western Nagano Prefecture Earthquake occurring close to an active volcano, Mt. Ontake, central Japan, is derived from a tomographic inversion of travel time data obtained by the 1986 Joint Seismological Research in Western Nagano Prefecture. The data set includes 7,693 P-wave and 6,070 S-wave arrival times observed at 49 stations from 212 local earthquakes and 2 explosions. The velocities in the shallow portion of upper crust are determined at each grid point with its spacing of 1-2 km and good resolutions are obtained from the Earth's surface to a depth of 4 km. There exist strong lateral heterogeneities especially from the surface to a depth of 1 km. The seismic velocity map obtained in the height of 1 km above sea level well corresponds to the maps of surface geology and Bouguer gravity anomaly. This correspondence, however, is not so clear in the deeper layers. And, the greater the depth, the less heterogeneous the velocity structure. The velocity distribution on the fault seems to correspond to the distribution of dislocation and rupture front estimated from an analysis of strong motion and geodetic data: the low velocity region has the large amount of dislocation and the retarded rupture front.

SUMMARYThe problem of harmonic waves in layered and fibre-reinforced composites is solved by a method of finite elements. Piecewise linear approximating functions are used for the displacement and stress fields in a mixed variational formulation, recently proposed by one of the writers in the form of a new quotient. Numerical computations are made for approximate phase-velocities of harmonic waves in layered composites, where asymmetric and symmetric triangular meshes, and square meshes with interior nodes, are used. To illustrate the accuracy and effectiveness of the method, these approximate solutions are compared with those given by means of exponential test functions, and the exact ones by Rytov, etc. Calculations are also performed for harmonic waves in fibre-reinforced composites. Dispersion curves for these waves are obtained and displayed graphically.

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