Arc Magmas from Slab to Eruption: The Case of Kliuchevskoy Volcano

Arc magmas are generated by a number of mantle and crustal processes. Our multidisciplinary, long-term research is aimed at deciphering these processes for a single arc volcano, Kliuchevskoy volcano in Kamchatka. Some key results of the study follow: 1) Modeling of trace element and H2O contents in melt inclusions suggests that the primary magmas originate via hydrous flux-melting of the mantle wedge at temperatures close to the dry peridotite solidus. The role of decompression melting is minor or absent at Kliuchevskoy and other arc volcanoes built on relatively thick crust. 2) Geochemistry of high-Mg olivine suggests that primary Kliuchevskoy magmas have substantial contribution from olivine-free pyroxenite (up to 30 %), which could be formed by reaction of slab melts (or supercritical fluids) with mantle wedge peridotite. 3) Parental Kliuchevskoy melts start to crystallize as deep as the Moho boundary, and the erupted magmas reflect multistage and complex processes of crystallization, magma mixing and crustal assimilation. None of the Kliuchevskoy rocks analyzed thus far represent true primary melt compositions. 4) The Kliuchevskoy Holocene eruptive history is not steady-state in terms of eruption rate and geochemistry. There are two millenial cycles with major and trace element and OSr- Nd-Pb and U-series isotope compositions of the magmas changing gradually from more to less affected by crustal (?) assimilation. The onset of the cycles correlates with periods of enhanced volcanic activity in Kamchatka, suggesting that the extent of magma-crust interaction is inversely related to magma production rate and thus magma flux from the mantle

Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

Determination of electromagnetic medium from the Fresnel surface

We study Maxwell's equations on a 4-manifold where the electromagnetic medium is described by an antisymmetric $2\choose 2$-tensor $\kappa$. In this setting, the Tamm-Rubilar tensor density determines a polynomial surface of fourth order in each cotangent space. This surface is called the Fresnel surface and acts as a generalisation of the light-cone determined by a Lorentz metric; the Fresnel surface parameterises electromagnetic wave-speed as a function of direction. Favaro and Bergamin have recently proven that if $\kappa$ has only a principal part and if the Fresnel surface of $\kappa$ coincides with the light cone for a Lorentz metric $g$, then $\kappa$ is proportional to the Hodge star operator of $g$. That is, under additional assumptions, the Fresnel surface of $\kappa$ determines the conformal class of $\kappa$. The purpose of this paper is twofold. First, we provide a new proof of this result using Gr\"obner bases. Second, we describe a number of cases where the Fresnel surface does not determine the conformal class of the original $2\choose 2$-tensor $\kappa$. For example, if $\kappa$ is invertible we show that $\kappa$ and $\kappa^{-1}$ have the same Fresnel surfaces.Comment: 23 pages, 1 figur

Silver and copper fractionation in MORB

Ag and Cu are strongly chalcophile elements, and their behavior in magmatic systems is highly dependent on the presence of solid or liquid sulfide phase in magmas and their sources..

Wave propagation in linear electrodynamics

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.Comment: 13 pages. Phys. Rev. D, to appea

Mathematical Conception of "Phenomenological" Equilibrium Thermodynamics

In the paper, the principal aspects of the mathematical theory of equilibrium thermodynamics are distinguished. It is proved that the points of degeneration of a Bose gas of fractal dimension in the momentum space coincide with critical points or real gases, whereas the jumps of critical indices and the Maxwell rule are related to the tunnel generalization of thermodynamics. Semiclassical methods are considered for the tunnel generalization of thermodynamics and also for the second and ultrasecond quantization (operators of creation and annihilation of pairs). To every pure gas there corresponds a new critical point of the limit negative pressure below which the liquid passes to a dispersed state (a foam). Relations for critical points of a homogeneous mixture of pure gases are given in dependence on the concentration of gases.Comment: 37 pages, 9 figure, more precise explanations, more references. arXiv admin note: substantial text overlap with arXiv:1202.525

Belingwe komatiites (2.7 Ga) originate from a plume with moderate water content, as inferred from inclusions in olivine

Major and trace elements, and volatile components have been measured in melt inclusions in olivine from fresh 2.7 Ga old komatiites from the Reliance Formation of the Belingwe Greenstone Belt, Zimbabwe. Reconstructed compositions of melt inclusions contain 20–23.5 wt% MgO and up to 0.3 wt% H2O; these compositions probably represent those of the erupted lava. In inclusions in relatively evolved (low Fo) olivines, an excess of Na2O, CaO, Li, La, Cu, Rb, Y, Sc as well as volatile components (H2O, F, Cl and S) relative to other highly incompatible elements is attributed to assimilation of seawater altered mafic material. No assimilation signature is observed for the most primitive melt inclusions hosted in the magnesium rich olivines. The primary melt composition, estimated using melt inclusions in the most magnesian olivine (Fo 93.5), contains up to 27.5 wt% MgO and ca. 0.2 wt% H2O. The presence of H2O slightly depressed the liquidus temperature to ca. 1513 °C. Our results suggest formation of the Belingwe komatiite magma at ca. 7 GPa pressure and ca. 1790 °C temperature in a mantle plume. The plume picked up water and probably chlorine through interaction with a hydrous transition mantle zone in the way similar to that previously proposed by Sobolev et al. (2016) for komatiites in Canada

Evidence for Archean hydrous deep-mantle reservoir provided by Abitibi komatiites

Archean komatiites result from melting under extreme conditions of the Earth’s mantle. Their chemical compositions evoke very high eruption temperatures, up to 1600°C, providing clues to still higher temperatures in their mantle source [1]. This message is clouded, however, by uncertainty about the water content in komatiite magmas. One school holds that komatiites were essentially dry and originated in mantle plumes [2] while the other argues that these magmas contained several percent of water, which drastically reduced their eruption temperature and links them to subduction processes [3]

Building the Record of late Miocene to Pleistocene Explosive Activity in the Kurile-Kamchatka Volcanic Arc: Initial Results and Challenges

Large explosive eruptions are among the most extreme natural events and can produce hemispheric or even global catastrophic effects. One of the prerequisites of predicting future giant eruptions is the understanding of sizes and recurrence times of past similar events. Volcanism of the North Pacific arcs is highly explosive, which is attested by large nested calderas and numerous tephra layers in marine and terrestrial sediments..