Geometry of stress function surfaces for an asymmetric continuum

A two-dimensional stress field of dislocation or fault is geometrically studied for an asymmetric continuum. For geometric surfaces of the stress and couple-stress functions, the mean and Gaussian curvatures are derived. The mean curvature of couple-stress function surface is connected with the asymmetric of stress tensor. Moreover, the Gaussian curvature of stress function surface is characterized by both the stress and couple-stress. On the other hand, the mean curvature of stress function surface is not affected by the asymmetry of stress. Based on these geometric expressions, the Coulomb’s failure criterion and the friction coefficient are expressed by the curvatures of couple-stress function surface. Moreover, geometric structures of stress and couple stress function surfaces are shown for edge and wedge dislocations as faults. The curvatures of these surfaces show that the effect of couple-stress is constrained around the dislocations only.     

Forecast of volcanic eruptions by chemical methods

From the magmatic emanations differentiation point of view it is possible to calculate some ratios such as F/CO₂, Cl/CO₂, SO₂/CO₂, SO₂/H₂S, H₂S/CO₂ and CO₂/N₂ in the tumarolic gases for the forecasting of volcanic activity. In order to predict the cruptions of a volcano it is needed to select several fumaroles or hot springs having different regimes of variation of the above ratios. The study of some fumaroles composition at the Asama. Mihara, Kirishima and other volcanoes in Japan showed a close connection between volcanic gas compositions and state of the volcanoes.     

Differentation of magmatic emanation

Chemical properties of magmatic emanation can be estimated roughly by i) volatiles from rocks by heating at various temperatures, ii) volcanic emanations, iii) residual magmatic emanations, iv) calculation from chemical equilibrium between volatile matters and magmas. Magmatic emanation is assumed to consist all of the volatile matters in magmas such asH ₂ O, HCl, HF, SO ₂ H ₂ S, H ₂,CO 2,N ₂ and others (halides, etc.) at about 1200°C, although various kinds of magmatic emanations can be formed at different conditions. Magmatic emanation separated from magmas will change their chemical properties by many factors such as changes of temperature and pressure (displacement of chemical equilibrium), and reactions with other substances and it will differentiate into volcanic gases, volcanic waters, volcanic sublimates, and hydrothermal deposits (hot spring deposits). At temperatures above the critical point of water, separation of solid phase (sublimates), liquid phase, and displacement of chemical equilibrium may take place, and gaseous phase will gradually change their chemical properties as will be seen at many fumaroles. Chloride, hydrogen, andSO ₂ contents will gradually decrease along with lowering temperature. Once aqueous liquid phase appears below the critical point of water, all the soluble materials may dissolve into this hydrothermal solution. Consequently, the gaseous phase at this stage must have usually a little hydrogen chloride as is observed at many fumaroles. Aqueous solutions must be of acidic nature by dissolution of acid forming components, and by hydrolysis (Chloride type). When a self-reduction-oxidation reaction of sulfurous acid takes place, an aqueous solution of sulfate type will be formed. At this stage, solid phases consist of the remained sublimates which are difficultly soluble in aqueous solution, and deposits formed by reaction in the hydrothermal solutions. The gaseous phases below the boiling point of water, have usually a little water, and consist mainly ofCO ₂ type,H ₂ S type,N ₂ type, and mixed type owing to elimination or addition of components by reactions with waters or wall rocks according to their geological conditions. Aqueous solutions which was of acidic nature must be changed into alkaline solutions by reaction with wall rocks for a long time. When the oxidation of sulfur compounds takes place, an aqueous solution of sulfate type will be formed. Hydrogen sulfide type of water will be formed by reaction of sulfides with acid waters or absorption of hydrogen sulfide. Carbonate type of water will be formed whenCO ₂ is absorbed. Solid phases at this stage consist usually of hydrothermal deposits except for that at solfatara or mofette. The course of differentiation of magmatic emanation could take place in more complicated ways than that of magmatic differentiation.     

Differential geometric approach to the stress aspect of a fault: Airy stress function surface and curvatures

We considered the two-dimensional stress aspect of a fault from the viewpoint of differential geometry. For this analysis, we concentrated on the curvatures of the Airy stress function surface. We found the following: (i) Because the principal stresses are the principal curvatures of the stress function surface, the first and the second invariant quantities in the elasticity correspond to invariant quantities in differential geometry; specifically, the mean and Gaussian curvatures, respectively; (ii) Coulomb’s failure criterion shows that the coefficient of friction is the physical expression of the geometric energy of the stress function surface; (iii) The differential geometric expression of the Goursat formula shows that the fault (dislocation) type (strike-slip or dip-slip) corresponds to the stress function surface type (elliptic or hyperbolic). Finally, we discuss the need to use non-biharmonic stress tensor theory to describe the stress aspect of multi-faults or an earthquake source zone.     

Boron isotopic composition of fumarolic condensates from some volcanoes in Japanese island arcs

Boron samples from 40 fumarolic condensates from volcanoes in the Ryukyu arc (Satsuma Iwo-jima and Shiratori Iwo-yama) and the North-east Japan arc (Usu-shinzan, Showa-shinzan, Esan and Issaikyo-yama) all have ${}^{11}\text{B}{}^{10}\text{B}$ ratios close to 4.07. Higher values, from 4.09 to 4.13, were only observed in condensates from volcanoes in the southernmost end of the North-east Japan arc (Nasu-dake), the northern part of the Izu-Bonin arc (Hakone), and the North Mariana arc (Ogasawara Iwo-jima). These higher values suggest geological interaction of the magmas with sea-water enriched in ¹¹B.     

Petrography of Yamato 984028 lherzolitic shergottite and its melt vein: Implications for its shock metamorphism and origin of the vein

Yamato 984028 (Y984028) is a newly identified lherzolitic shergottite, recovered from the Yamato Mountains, Antarctica, in 1999. As part of a consortium study, we conducted petrographic observations of Y984028 and its melt vein in order to investigate its shock metamorphism. The rock displays the typical non-poikilitic texture of lherzolitic shergottite, characterized by a framework of olivine, minor pyroxene (pigeonite and augite), and interstitial maskelynite. Shock metamorphic features include irregular fractures in olivine and pyroxene, shock-induced twin-lamellae in pyroxene, and the complete conversion of plagioclase to maskelynite, features consistent with those found in other lherzolitic shergottites. The melt vein is composed of coarse mineral fragments (mainly olivine) entrained in a matrix of fine-grained euhedral olivine (with several modes of compositional zoning) and interstitial glassy material. Some coarse olivine fragments consist of an assemblage of fine-grained euhedral to subhedral olivine crystals, suggesting shock-induced fragmentation, recrystallization, and/or a process of sintering. The implication is that the fine-grained olivine crystals in the matrix of the melt vein represent complicated crystallization environments and histories.     

Experimental study of reaction between perovskite and molten iron to 146 GPa and implications for chemically distinct buoyant layer at the top of the core

Partitioning of oxygen and silicon between molten iron and (Mg,Fe)SiO₃ perovskite was investigated by a combination of laser-heated diamond-anvil cell (LHDAC) and analytical transmission electron microscope (TEM) to 146 GPa and 3,500 K. The chemical compositions of co-existing quenched molten iron and perovskite were determined quantitatively with energy-dispersive X-ray spectrometry (EDS) and electron energy loss spectroscopy (EELS). The results demonstrate that the quenched liquid iron in contact with perovskite contained substantial amounts of oxygen and silicon at such high pressure and temperature (P–T). The chemical equilibrium between perovskite, ferropericlase, and molten iron at the P–T conditions of the core–mantle boundary (CMB) was calculated in Mg–Fe–Si–O system from these experimental results and previous data on partitioning of oxygen between molten iron and ferropericlase. We found that molten iron should include oxygen and silicon more than required to account for the core density deficit (<10%) when co-existing with both perovskite and ferropericlase at the CMB. This suggests that the very bottom of the mantle may consist of either one of perovskite or ferropericlase. Alternatively, it is also possible that the bulk outer core liquid is not in direct contact with the mantle. Seismological observations of a small P-wave velocity reduction in the topmost core suggest the presence of chemically-distinct buoyant liquid layer. Such layer physically separates the mantle from the bulk outer core liquid, hindering the chemical reaction between them.