Yoshiaki Ida

Interionic repulsive force and compressibility of ions

Abstract The compressibility of an individual ion is examined, in comparison with a known set of data for the alkali halides. A simple extrapolation of ionic radius to high pressure is not acceptable, because the pressure derivative of ionic radius changes for different salts. According to the classical concept of an elastic ion, the repulsive potential energy between the ions i and j is specified by the nature of each ion as: (ρ i + ρ j ) exp[ (ρ i + ρ j − r) (ρ i + ρ j ) ] as a function of the interionic distance r. In this expression, qi and ρi are the ionic radius and ionic compressibility, respectively, in a suitably modified meaning. Such a form of the repulsive potential fits well to the data of lattice constants and bulk moduli. The parameters qi and ρi are evaluated for alkali and halogen ions, and an anion turns out to be much more compressible than a cation. The present treatment may be usefully applied to the minerals in the Earths mantle, which contain only a few major ions.

Effect of hydrostatic pressure on the lattice parameters of Fe2SiO4 olivine up to 70 kbar

The pressure dependence of the three lattice parameters and unit cell volume of fayalite (Fe2SiO4 olivine) was determined by X-ray diffraction under hydrostatic pressures up to 70 kbar. In order to eliminate stress inhomogeneity within a composite material consisting of a specimen mixed with an internal-pressure standard, a liquid (1 : 1 mixture of ethanol and methanol) was used as a pressure-transmitting medium. The isothermal bulk modulus calculated on the basis of the second-order Birch-Murnaghan equation of state gives the values K0 = 1.19 ± 0.10 Mbar and K0′ = 7 ± 4, and if we assume K0′ = 5: K0 = 1.24 ± 0.02 Mbar. Three axes of fayalite were found to be compressible in the following order, b >c >a. Comparisons with the results obtained under non-hydrostatic compression are made.

Eigen oscillation of a fluid sphere and source mechanism of harmonic volcanic tremor

Abstract The eigen oscillation of a fluid sphere embedded in an infinite elastic medium is analyzed to understand the source mechanism of volcanic tremor that vibrates nearly monotonically and attenuates slowly. The dimensionless eigen frequencies of the sinusoidal oscillation are calculated in a complex form with the attenuation factor in its imaginary part for various combinations of the three parameters: the contrasts of P-wave velocity, density and rigidity between the fluid and the country rock. Eigen oscillations consist of a high attenuation mode with a rapidly decaying pulsive wave at a low frequency and infinite number of regular modes with slowly decaying vibrations. For regular modes, the frequency of oscillation obtained from the real part of an eigen value is distributed in approximately regular intervals while the attenuation factor from the imaginary part is almost constant independent of the mode. Each eigen frequency of regular and high attenuation modes is degenerated with two independent eigen functions describing different distributions of displacement, velocity and stress. The theory is applied to harmonic volcanic tremor observed at Kusatsu-Shirane Volcano, central Japan. Observed spectral peaks of the tremor are explained by the eigen frequencies and attenuation factors of several lowest regular modes if the spherical fluid oscillator has a radius of dozens of meters and a P-wave velocity of about several hundred meters per second.

Low frequency electrical impedance of partially molten gabbro: The effect of melt geometry on electrical properties

Abstract Electrical impedance of partially molten gabbro was measured as a function of the frequency of the applied electric field. The impedance of the partially molten gabbro was mainly controlled by the volume and geometry of partial melt, which were observed with an optical microscope study of the quenched sample. The experimental results are interpreted by a theory that formulates the electrical property of rocks containing partial melt, taking ionic diffusion in the melt into account. The theory evaluates the contributions from two types of melt-geometry distributed in the rock matrix, namely: 1. (a) nearly isolated melt pockets, and 2. (b) connected melt along grain boundaries. According to the theory, connected melt mainly contributes to the increase of net conductivity, while melt pockets increase displacement current and cause the frequency dependence of impedance. The characteristic ionic diffusivity in melt pockets was determined from the peak frequency of the imaginary part of impedance. The magnitude of diffusion coefficient is estimated to be of the order of 10 −7 to 10 −6 cm 2 /sec. This suggests that sodium, iron, magnesium and/or calcium ions mainly carry the electric charge in partial melt. The observed frequency dependence of impedance is considered to reflect ionic polarization in melt pockets due to the migration of these alkali ions toward solid-melt interfaces. The present experimental and theoretical work suggests that electrical properties of the earths upper mantle may involve an intrinsic frequency dependence associated with ionic diffusion in the frequency range of geomagnetic observation, if a partial melt zone exists. The analysis of the earths conductivity structure may be inadequate if such intrinsic frequency dependence of mantle media is neglected.

Slow-moving deformation pulses along tectonic faults

Abstract A model of slow-moving disturbances of deformation is proposed to interpret the observed propagations of earthquake foci and nonseismic creep. The analysis is based on the assumption that thin fault gouge participates in the viscous slip. Nonuniform deformation diffusses at the rate of ν = μ w/2 η for the gouge of viscosity η and thickness w that is enclosed by the elastic rocks of rigidity μ. A crack-like solution propagates uniformly, involving the discontinuity that bounds the faulted area by an unfractured part, or by another gouge with different viscosity. The unit of the propagation velocity of such cracks is also given by the above-defined ν. Comparing the expression of ν with the various field observations, most of which yield the propagation speeds of 10–10 4 km/year, the effective viscosity of the gouge is estimated as 10 11 –10 14 poises. The nonseismic fault creep in central California is analysed, and a little higher value of acting stress is obtained than the result of Nason and Weertman (1973).

Cyclic fluid effusion accompanied by pressure change: Implication for volcanic eruptions and tremor

Magma effusion and tremor sometimes occur in quite regular intervals with periodic pressure changes, as observed in volcanic eruptions at Kilauea Volcano, lava dome growth at Unzen Volcano, and tremor episodes at Izu-Oshima Volcano. These events have more or less asymmetric pressure change of quasi-sinusoidal to saw-toothed shape with longer time elapsing in build-up of the fluid pressure than in its relaxation. Such cyclic fluid effusion can be explained systematically by a simple model in which fluid is supplied at a constant rate, accumulates in an elastic chamber, and flows out in a cylindrical vent that may widen or narrow due to viscous deformation of the surrounding country rock.

Geometrical effects and low-attenuation resonance of volcanic fluid inclusions for the source mechanism of long-period earthquakes

[1]xa0We formulate the resonances of three simple geometrical inclusions (a plane, a cylinder and a sphere) and find several clues to distinguishing the shape of volcanic fluid systems and their relevance to the observation of long-period earthquakes. The series of eigenfrequencies for a cylindrical and a spherical inclusion have shifts of π/4 and π/2, respectively, in their higher modes from the eigenfrequencies of a planar inclusion. The ratios between the higher and fundamental characteristic frequencies can be indicators of the geometry of volcanic fluid inclusions. Furthermore, the eigenattenuation factor of a planar inclusion is a constant value that is determined uniquely by the impedance contrast between the fluid and the surrounding elastic medium, and is independent of mode. In marked contrast, cylindrical and spherical inclusions have smaller or greater eigenattenuation factors, particularly in lower modes. Under certain conditions of P wave velocity contrast, and Poissons ratio of the surrounding elastic medium, lower modes have less than 0.1 times the attenuation factor of higher modes. We name these “low-attenuation modes” (LAMs). LAMs are physically related to the conversion of volumetric changes to shear deformation of the surrounding elastic medium and the radiation of shear waves from the curved boundaries. Some monotonic waveforms of long-period earthquakes can be interpreted by the excitation of these LAMs. Crack modes are also simply formulated by the resonance of a rectangular inclusion and also become LAMs whose attenuation factors are related to the aspect ratio of the crack.

An isotropic source of volcanic tremor-observation with a dense seismic network at Izu-Oshima volcano, Japan

Abstract Volcanic tremor is frequently observed associated with activities of volcanoes. In order to study the nature of the volcanic tremor in detail we installed a dense seismic network covering the area of the summit crater of Izu-Oshima volcano. We succeeded in observing volcanic tremors preceding a small explosive eruption on November 16, 1987. The explosion was followed by a significant draining back of lava which had filled the summit crater of the 1986 eruption. We analyzed the low-frequency components of the tremor (near 0.7 Hz) and found that it was generated by an isotropic (volumetric) source located 350 m above sea level. Assuming a cyclic pressure change at the source the amplitude of the seismic moment is 3.4 × 10 10 Nm. This corresponds to a pressure fluctuation of 3 × 10 3 Pa (0.03 bar) in the system containing the cavity of 10 7 m 3 , which is comparable to the volume of subsidence at the 1987 eruption.

Earthquakes series preceding very long period seismic signals, observed during the 2000 Miyakejima volcanic activity

[1]xa0Unusual earthquakes series were observed one to two hours before a very long-period (VLP) seismic pulse that happened once or twice a day, during the 2000 activity of Miyakejima volcano, Japan. The series on July 11 and 12 have particularly a clear feature. The time intervals of the earthquakes in the series decrease at a constant rate in the manner of geometric progression. The maximum amplitude of each earthquake is initially almost constant, but linearly decreases with time from few minutes before the occurrence of a VLP pulse. Hypocenters of these earthquakes are below the south-western region of the crater, and near the sea level in depth. We interpret these earthquakes series as repetition of a gradual stress accumulation, and release under the variable critical stress level. The critical stress level is first constant, but linearly decreases later.

Ground deformation associated with volcanic tremor at Izu-Oshima Volcano

Izu-Oshima volcano had summit and fissure eruptions in November, 1986 after 12 years of dormancy, and three small eruptions followed these events within one year. Episodic and continuous volcanic tremors were observed for the period containing these eruptions. It is a remarkable discovery that the episodic volcanic tremor was accompanied by a small but sharp ground deformation, the polarity of which was variable. The distribution of tilt vectors reveals that the source of ground deformation was always located beneath the northwestern flank of the volcano, where a magma reservoir was predicted by other studies. On the other hand, the seismologically detected tremor source was determined to be at a shallow depth below the central pit crater, a few kilometers away from the predicted magma reservoir. It is thus inferred that the tremor source near the crater generated pressure increases or decreases that were simultaneously transmitted through the vent to the magma reservoir and lead to its expansion or contraction.