A new method of calculating theoretical seismograms at the ocean bottom due to underwater explosions has been developed. The formulation is based on a method using numerical integration in the complex wave-number domain proposed by SATO and HIRATA (1980). The ray expansion method for a liquid layer (TANIMOTO and SATO, 1980) is also adopted. A delta matrix, which consists of 2 x 2 subdeterminants of the propagator matrix divided into frequency-dependent and frequency-independent parts in each layer, is introduced to avoid numerical errors. The method is effective for the practical use in studying both high frequency initial phases and low frequency boundary waves at the ocean bottom.
By using the theoretical seismograms, characteristic phases expected for an oceanic crustal structure are investigated. P to S and/or S to P converted waves generated at the bottom of the sedimentary layer and two kinds of boundary waves at the liquid-solid boundary, pseudo-Rayleigh waves and Stoneley waves, can be well identified in the theoretical seismograms. The Stoneley waves with a period of 2-15 s show clear dispersion due to the soft sediment overlying the oceanic crust.
Though converted waves are often found in recorded ocean bottom seismograms, long period dispersive waves have not been reported as yet. This study suggests a good possibility of obtaining important information on the oceanic crust if long period waves are well observed.

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The relation between earthquake size (radiated energy or seismic moment) and duration of faulting (predominant period or corner frequency) was investigated from a waveform analysis of shallow earthquakes with a seismic moment between 10¹⁰ and 10²⁵ dyne•cm. The earthquakes analyzed were observed at relatively short focal distances where anelastic attenuation had no serious effect on their waveforms. The waveforms are characterized by their simplicity and relative lack of coda.
We found that the radiated energy of the P and S wave is proportional to the fifth power of the period of P and S wave velocity seismograms, respectively, and that the relation between the seismic moment (M₀) and the corner frequency of the P wave (∫₀) is given by M₀∝∫0^-4. The above two relations are consistent with each other. The relation M₀∝∫0^-3 which is generally accepted for large earthquakes (M₀>10²⁵ dyne•cm) does not hold true for smaller earthquakes (M₀>10²⁵ dyne•cm), possibly because, for smaller earthquakes, slip velocity does not exceed a critical level owing to small rupture velocity and because effective stress is not constant and independent of seismic. moment.
The relation between M₀ and the fault length (L) was estimated as M₀∝L^2.5-L^3.2 from aftershock distributions ranging from a microearthquake to moderate earthquakes. By combining this relation with the M₀-f₀ relation, we have come to the conclusion that average rupture velocity and slip velocity decrease with the decreasing seismic moment. We have also concluded that the deviations of data from the relation M₀∝f₀^-3 are not attributed to small stress drop but small rupture velocity and slip velocity.

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The results from recent east-west gravity and magnetotelluric traverse across the Fuji River, Central Japan, show that (i) extremely low Bouguer anomalies are distributed along the Fuji River and characterized with a strong horizontal gradient 4.5 mgal/km, and (ii) a low-resistivity zone appears along the Fuji River.
The profile of density distribution was computed. From the results, it is seen that the sedimentary basin in this section has a steep slope beginning from the eastern part of the surveyed area and continuing even under the Itoigawa-Shizuoka Tectonic Line. The high-conductivity and low-density zone, whose density is smaller than 2.3 g/cm³, has a width of 1.5-2.0 km. These zones are possibly caused by the fracturing of rocks due to fault activity.

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If we assume that magnitudes of earthquakes are distributed identically and independently according to a negative-exponential function, then the maximum likelihood estimate proposed by Utsu for the b-value is biased from the true value. We suggest an unbiased alternative estimate which is asymptotically equivalent to the maximum likelihood estimate. The relation between the unbiased estimate and the maximum likelihood estimate are presented from a Bayesian viewpoint. The two estimates are compared in order to show the superiority of the unbiased estimate over the maximum likelihood estimate, on the basis of the expected entropy maximization principle for the predictive distributions. From the same principle, the posterior with the noninformative improper prior is recommended for the inferential distribution of the b-value rather than the standardized likelihood.

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