Local stability and estimation of uncertainty for solutions to inverse problems

 We present a method for studying local stability of a solution to an inverse problem and evaluate the uncertainty in determining true values of particular observables. The investigation is done under the assumption that only the Gaussian part of fluctuations about the local minimum of the cost (likelihood) function is essential. Our approach is based on the spectral analysis of the Hessian operator associated with the cost function at its extremal point, and we put forward an effective iterative algorithm suitable for numerical implementation in the case of a computationally large problem. Received: 16 May 2001 / Accepted: 22 October 2001     

An experimental study of solid matrix weakening in water‐saturated Savonnières limestone

Petrophysical properties of carbonate reservoirs are less predictable than that of siliciclastic reservoirs. One of the main reasons for this is the physical and chemical interactions of carbonate rocks with pore fluids. Such interactions can significantly change the elastic properties of the rock matrix and grains, making the applicability of Gassmann's fluid substitution procedure debatable. This study is an attempt to understand the mechanisms of fluid‐rock interactions and the influence of these interactions on elastic parameters of carbonates. We performed precise indentation tests on Savonnières limestone at a microscale level under dry, distilled water, and n‐Decane saturated conditions. Our experiments display softening of the rock matrix after water saturation. We have found that mainly the ooid cortices, peloid nuclei and prismatic intergranular cement are affected by water flooding. We also observed a shear modulus reduction in Savonnières limestone in an experiment performed at ultrasonic frequencies. One of the most important results obtained in our experimental study is that the Gassmann fluid substitution theory might not always be applicable to predict the elastic moduli of fluid‐saturated limestones.     

New Olivine Reference Material for In Situ Microanalysis

A new olivine reference material – MongOL Sh11‐2 – for in situ analysis has been prepared from the central portion of a large (20 × 20 × 10 cm) mantle peridotite xenolith from a ~ 0.5 My old basaltic breccia at Shavaryn‐Tsaram, Tariat region, central Mongolia. The xenolith is a fertile mantle lherzolite with minimal signs of alteration. Approximately 10 g of 0.5–2 mm gem quality olivine fragments were separated under binocular microscope and analysed by EPMA, LA‐ICP‐MS, SIMS and bulk analytical methods (ID‐ICP‐MS for Mg and Fe, XRF, ICP‐MS) for major, minor and trace elements at six institutions world‐wide. The results show that the olivine fragments are sufficiently homogeneous with respect to major (Mg, Fe, Si), minor and trace elements. Significant inhomogeneity was revealed only for phosphorus (homogeneity index of 12.4), whereas Li, Na, Al, Sc, Ti and Cr show minor inhomogeneity (homogeneity index of 1–2). The presence of some mineral and fluid‐melt micro‐inclusions may be responsible for the inconsistency in mass fractions obtained by in situ and bulk analytical methods for Al, Cu, Sr, Zr, Ga, Dy and Ho. Here we report reference and information values for twenty‐seven major, minor and trace elements.     

Control Volume Method for the Dynamo Problem in the Sphere with the Free Rotating Inner Core

A model of thermally driven dynamo in the Boussinesq approximation in the spherical shell with the free rotating inner core is considered. To solve equations we use a new in dynamo modeling control volume technique (for details of this method for hydrodynamics see Patankar, 1980). The main advantage of this method over previous attempts to solve magnetohydrodynamics equations in the spherical grids is that no filtering of high harmonics in the pole regions is needed. We present the results of simulations for the self-consistent dynamo system evolution over the diffusion time and longer periods. Different ways of stabilizations of magnetohydrodynamics equations, when convective terms are of the same order (or larger) as conductive ones, are considered.     

Gamma-ray bursts from unstable Poynting-dominated outflows

Poynting-flux driven outflows from magnetized rotators are a plausible explanation for gamma-ray burst engines. We suggest a new possibility for how such outflows might transfer energy into radiating particles. We argue that, in a region near the rotation axis, the Poynting flux drives non-linearly unstable large-amplitude electromagnetic waves (LAEMW) that 'break' at radii     where the MHD approximation becomes inapplicable. In the 'foaming' (relativistically reconnecting) regions formed during the wave breaks, the random electric fields stochastically accelerate particles to ultrarelativistic energies which then radiate in turbulent electromagnetic fields. The typical energy of the emitted photons is a fraction of the fundamental Compton energy     with     plus additional boosting due to the bulk motion of the medium. The emission properties are similar to synchrotron radiation, with a typical cooling time ∼10⁻³ s. During the wave break, the plasma is also bulk accelerated in the outward radial direction and at larger radii can produce afterglows due to interactions with the external medium. The near equipartition fields required by afterglow models may be due to magnetic field regeneration in the outflowing plasma (similar to field generation by LAEMW in laser–plasma interactions) and mixing with the upstream plasma.     

Early Holocene M~6 explosive eruption from Plosky volcanic massif (Kamchatka) and its tephra as a link between terrestrial and marine paleoenvironmental records

We report tephrochronological and geochemical data on early Holocene activity from Plosky volcanic massif in the Kliuchevskoi volcanic group, Kamchatka Peninsula. Explosive activity of this volcano lasted for ~1.5 kyr, produced a series of widely dispersed tephra layers, and was followed by profuse low-viscosity lava flows. This eruptive episode started a major reorganization of the volcanic structures in the western part of the Kliuchevskoi volcanic group. An explosive eruption from Plosky (M~6), previously unstudied, produced tephra (coded PL2) of a volume of 10–12 km³ (11–13 Gt), being one of the largest Holocene explosive eruptions in Kamchatka. Characteristic diagnostic features of the PL2 tephra are predominantly vitric sponge-shaped fragments with rare phenocrysts and microlites of plagioclase, olivine and pyroxenes, medium- to high-K basaltic andesitic bulk composition, high-K, high-Al and high-P trachyandesitic glass composition with SiO₂ = 57.5–59.5 wt%, K₂O = 2.3–2.7 wt%, Al₂O₃ = 15.8–16.5 wt%, and P₂O₅ = 0.5–0.7 wt%. Other diagnostic features include a typical subduction-related pattern of incompatible elements, high concentrations of all REE (>10× mantle values), moderate enrichment in LREE (La/Yb ~ 5.3), and non-fractionated mantle-like pattern of LILE. Geochemical fingerprinting of the PL2 tephra with the help of EMP and LA-ICP-MS analyses allowed us to map its occurrence in terrestrial sections across Kamchatka and to identify this layer in Bering Sea sediment cores at a distance of >600 km from the source. New high-precision ¹⁴C dates suggest that the PL2 eruption occurred ~10,200 cal BP, which makes it a valuable isochrone for early Holocene climate fluctuations and permits direct links between terrestrial and marine paleoenvironmental records. The terrestrial and marine ¹⁴C dates related to the PL2 tephra have allowed us to estimate an early Holocene reservoir age for the western Bering Sea at 1,410 ± 64 ¹⁴C years. Another important tephra from the early Holocene eruptive episode of Plosky volcano, coded PL1, was dated at 11,650 cal BP. This marker is the oldest geochemically characterized and dated tephra marker layer in Kamchatka to date and is an important local marker for the Younger Dryas—early Holocene transition. One more tephra from Plosky, coded PL3, can be used as a marker northeast of the source at a distance of ~110 km.     

Adsorption of Fe(II) and U(VI) to carboxyl-functionalized microspheres: The influence of speciation on uranyl reduction studied by titration and XAFS

The chemical reduction of U(VI) by Fe(II) is a potentially important pathway for immobilization of uranium in subsurface environments. Although the presence of surfaces has been shown to catalyze the reaction between Fe(II) and U(VI) aqueous species, the mechanism(s) responsible for the enhanced reactivity remain ambiguous. To gain further insight into the U-Fe redox process at a complexing, non-conducting surface that is relevant to common organic phases in the environment, we studied suspensions containing combinations of 0.1 mM U(VI), 1.0 mM Fe(II), and 4.2 g/L carboxyl-functionalized polystyrene microspheres. Acid-base titrations were used to monitor protolytic reactions, and Fe K-edge and U L-edge X-ray absorption fine structure spectroscopy was used to determine the valence and atomic environment of the adsorbed Fe and U species. In the Fe + surface carboxyl system, a transition from monomeric to oligomeric Fe(II) surface species was observed between pH 7.5 and pH 8.4. In the U + surface carboxyl system, the U(VI) cation was adsorbed as a mononuclear uranyl-carboxyl complex at both pH 7.5 and 8.4. In the ternary U + Fe + surface carboxyl system, U(VI) was not reduced by the solvated or adsorbed Fe(II) at pH 7.5 over a 4-month period, whereas complete and rapid reduction to U(IV) nanoparticles occurred at pH 8.4. The U(IV) product reoxidized rapidly upon exposure to air, but it was stable over a 4-month period under anoxic conditions. Fe atoms were found in the local environment of the reduced U(IV) atoms at a distance of 3.56 Å. The U(IV)-Fe coordination is consistent with an inner-sphere electron transfer mechanism between the redox centers and involvement of Fe(II) atoms in both steps of the reduction from U(VI) to U(IV). The inability of Fe(II) to reduce U(VI) in solution and at pH 7.5 in the U + Fe + carboxyl system is explained by the formation of a transient, “dead-end” U(V)-Fe(III) complex that blocks the U(V) disproportionation pathway after the first electron transfer. The increased reactivity at pH 8.4 relative to pH 7.5 is explained by the reaction of U(VI) with an Fe(II) oligomer, whereby the bonds between Fe atoms facilitate the transfer of a second electron to the hypothetical U(V)-Fe(III) intermediate. We discuss how this mechanism may explain the commonly observed higher efficiency of uranyl reduction by adsorbed or structural Fe(II) relative to aqueous Fe(II).