It is shown that the frequency distributions of earthquakes with respect to energy and magnitude are derived from a deformation-fracture relation. When the spectrum W(k) of the plastic deformation of the medium is represented by a power function of structural wave number k, the frequency distribution with respect to wave energy, n(E) dE, is also represented by a power function. The coefficient b of the frequency distribution with respect to magnitude, logN(M)=a-bM, depends upon the exponent of the power function of W(k), the coefficient a depends upon the source area, spectrum strength of the deformation, energy density of seismic wave radiation.
The relationship between the elastic and the optical anisotropy was studied for silicates and other few minerals. It was found for silicates that in the direction of the large refractive index, the longitudinal wave velocity is larger and the linear compressibility is smaller, and in the direction of the small refractive index, the longitudinal wave velocity is smaller and the linear compressibility is larger. This relation is represented by the empirical formula that ΔV=67ΔNkm/s and (1/β) Δβ=12.5ΔN, where ΔN is double refraction, ΔV is the value of the anisotropy on the longitudinal wave velocity and (1/β)Δβ is the value of the anisotropy on the linear compressibility. However the relationship of ΔV-ΔN is greatly different from the relationship between the mean longitudinal wave velocity andthe mean optical refractive index; dV/dN=19.5km/s. The value of the anisotropy on the longitudinal wave velocity in Stishovite, the high pressure polymorph of SiO2, was estimated to be 1.81km/s from the refractive index by Stishov and Popova, and 3.02km/s from the refractive index by CHAD et al..
Comparison between strictly rectangular filters and approximate ones are discussed in the time domain using theoretical seismograms calculated for a Gutenberg-Bullen A′ earth model. Filtering is accomplished by a process of convolution. Main results are as follows. Digital filtering is, on the whole, carried out successfully even in dealing with complicated disturbances consisting of many spectral components of varying strength. The deviation of output from approximate filters from ideally filtered output depends largely on relative spectral amplitude of input data near the cut-off frequencies of a designed filter and little on the band width. It is possible to estimate the deviation without knowledge of ideally filtered output when some conditions are satisfied, that is, (fn)min·(t2-t1)>>1, (fi-fj)min·(t2-t1)>>1, where fn is the eigen-frequency, t2-t1 the time interval employed in filtering and fi>fj. Concerning a problem of aliasing, Fourier amplitude spectrum and filtered results of inadequately digitized data are given.
When a crystal structure of ammonium fluoride, NH4F, reversibly transforms from Wurtzite structure to NaCl structure at ca. 4kb, a number of small elastic shocks are accompanied with the volume change by the rapid phase transition for polycrystalline specimen. These shocks are also generated during the lowering pressure run, where NaCl structure transforms to Wurtzite structure. If we assume that each of the shocks corresponds to a phase transition in a small volume in the specimen, the amount of the reactant is given by the accumulated number of shocks. Fitting the bulk rate of the phase transition by the equation of the rate theory; dX/dt=K(1-X)p, where X is the mole fraction of the reactant at the time t, we obtain p≈1 and K≈10-1sec-1. The present result shows that the phase transition is the first order reaction and the bulk rate of the phase transition is in the order of 10-1sec-1, although the process of the phase transition is not continuous but is the superposition of very rapid ones with elastic wave radiation.
An instrument was deviced, which determines the earthquake intensity mechanically, and put into a trial observation in the Matsushiro Seismological Observatory from July, 1967 for the Matsushiro swarm earthquakes. The instrument employs a 3cps vertical transducer of moving coil type, and its output, corresponding to the relation between intensity scale and ground acceleration proposed by the Japan Meteorological Agency. The present paper reports the comparison between two intensities obtained by the conventional method and by the instrument, considering parameters such as epicentral distance, depth, azimuth and magnitude. The results are summarized in the following. 1) Coincidence was found between two intensities for 48% of perceptible earthquakes. Whether two intensities coincide or not has no corelation to S-P time, depth/epicentral distance, azimuth or magnitude. 2) A coincidence coefficient of 59% was obtained for earthquakes of intensity I, II and III, which were the majority of the observed earthquakes. 3) 69% of earthquakes of discrepant intensities gave 0 for instrumental intensity and 1 for empirical intensity. Combinations of 0-I and 1-I have no definite correlation to the earthquake magnitude. 4) Vertical ground accelerations of less than 0.8gal are still perceptible to human bodies. By making the lower limit of the perceptible acceleration smaller, most of the discrepant cases can be eliminated. 5) Earthquakes of intensity I give sometimes considerably high ground acceleration; however, its period is very short. We hope a more comprehensive instrument is developed, which determines the earthquake intensity, by introducing horizontal components and improving the criterion between intensity and acceleration.
The precision and accuracy of locations of hypocenters of the earthquake off Tokachi of 16 May 1968 and its aftershocks are discussed mainly based on the comparison between both data determined by JMA and USCGS. USCGS epicenters are generally on the continental side of JMA epicenters. The average distance of both JMA and USCGS epicenters of each shock is 26.4km. However there are systematic differences between the JMA-USCGS epicenter deviation of aftershocks north of the mainshock and those of aftershocks south of the mainshock. The USCGS epicenters of northern aftershocks are deviated to north-west direction from the JMA epicenter while USCGS epicenters of southern aftershocks are deviated to west direction from the JMA epicenter. Focal depths of USCGS hypocenters are a little deeper than those of JMA hypocenters. 40% of JMA hypocenters and 80% of USCGS hypocenters are located in the depth of 30-40km which correspond to the top layer of the mantle. Slight differences of b-values in the magnitude-frequency relations are observed among aftershockes in the northern area (around the epicenter of the greatest aftershock), those in the middle area (around the epicenter of the main shock) and those in the southern area (around the epicenter of the second greatest aftershock). The geophysical significance of the above results is briefly discussed.
Some surface waves propagating in the high velocity layer model were analyzed. Dispersion curves for the surface wave of this type have already been disccussed by the present author. Two dimensional models used are Aluminum-Lamiverre and Aluminum-Plastics models. Observed phase and group velocities of leaking modes well fit the dispersion curves obtained by OLIVER and MAJOR'S and SU and DORMAN'S methods. The attenuation coefficients of the leaking mode were calculated from the spectral analysis and were compared with the imaginary part of the complex root of the characteristic equation. The agreement was good. The coupling of the body wave with the leaking mode was also investigated. Thus, OLIVER'S hypothesis for the coupling could be confirmed.