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     

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).     

Paleomagnetism of Cretaceous units of the Mametchinskiy Peninsula, Kuyul Region, Northeastern Russia: implications for development and evolution of the Northwest Pacific Basin

The northernmost part of the Kamchatka Peninsula of northeastern Russia, located along the northwestern margin of the Bering Sea, consists of zones of complexly deformed accreted terranes. Progressing from the northwestern Bering Sea inland are the Olyutorskiy, Ukelayat, and Koryak superterranes, which were accreted to the Okhotsk–Chukotsk volcanic–plutonic belt (OChVB) during the Campanian–Maastrichtian (Koryak) to Middle Eocene (Olyutorskiy), respectively. To constrain the accretion paleolatitude of the Koryak superterrane, we paleomagnetically sampled a sedimentary series on the Mametchinskiy Peninsula. At the Mametchinskiy Peninsula, in the northeastern Penzhinskaya Guba (61.45° N, 163.75° E), a gently deformed, well-bedded section of fine-grained Lower to lower Upper Cretaceous turbidites, the Mametchinskaya and Tylakrylskaya Formations are exposed. These strata, which represent the lower part of the sedimentary cover of the terranes in this region and the forearc of OChVB, were sampled at 39 sites (three to seven samples per site). Within the Ainyn terrane, more than 1000 m of section of Cenomanian–Turonian age was sampled at a basal locality (sample groups I and II, sites 1–18, 19–29) and at an upper locality of Valanginian–Barremian age (sample group III, sites 30–39) along the western shore of the Peninsula. Thermal demagnetization and principal component analysis of the demagnetization data show lower-temperature (A) and higher-temperature (B) magnetic components. Although group III samples did not display a coherent A component, the A component of group I and II samples was observed as a single-polarity lower-unblocking temperature component generally removed by 100–400 °C. This component failed the fold test at the 95% confidence level. With respect to direction, the A component is similar to both the present-day field and axial–geocentric dipole directions expected at this site. The B component was observed during thermal demagnetization steps up to 580 °C and was always of downward-directed inclination. Coherence of bedding corrections within each section do not allow statistically meaningful fold tests within groups I, II or III. Assuming the B component represents a Cretaceous magnetization, two overall models are proposed. In the first model (preferred), with the highest clustering of directions (k-value=36.7, N (sites)=36), indicates significant poleward motion of the Ainyn terrane (observed paleolatitude λ_M1=61.0±6.5°; expected North America plate reference site paleolatitude λ_E=74.0±3.5°). In the second model, no significant poleward displacement is implied (λ_M2=72.0±9.6).     

Nano-mechanical Properties and Pore-Scale Characterization of Different Rank Coals

Characterization of coal micro-structure and the associated rock mechanical properties are of key importance for coal seam exploration, coal bed methane development, enhanced coal bed methane production and CO₂ storage in deep coal seams. Considerable knowledge exists about coal chemical properties, but less is known about the nanoscale to the micro-scale structure of coals and how they change with coal strength across coal ranks. Thus, in this study, 3D X-ray micro-computed tomography (with a voxel size of 3.43 µm) and nano-indentation tests were conducted on coal samples of different ranks from peat to anthracite. The micro-structure of peats showed a well-developed pore system with meso- and micro-pores. The meso-pores essentially disappear with increasing rank, whereas the micro-pores persist and then increase past the bituminous rank. The micro-fracture system develops past the peat stage and by sub-bituminous ranks and changes into larger and mature fracture systems at higher ranks. The nano-indentation modulus showed the increasing trend from low- to high-rank coal with a perfect linear relationship with vitrinite reflectance and is highly correlated with carbon content as expected.

     

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.     

Synthetic fluid inclusions. XV. TEM investigation of plastic flow associated with reequilibration of fluid inclusions in natural quartz

The nature and abundance of dislocations in quartz surrounding fluid inclusions were studied to obtain a better understanding of processes associated with fluid inclusion reequilibration. Synthetic fluid inclusions containing 10 wt% NaCl aqueous solution were formed in three samples at 700 °C and 5 kbar. One of the samples was quenched along an isochore to serve as a reference sample. The other two samples were quenched along a P-T path that generated internal pressures in excess of the confining pressure. The two samples were held at the final reequilibration P-T conditions of 625 °C and 2 kbar for 30 and 180 days, respectively. Following the experiments, microstructures associated with fluid inclusions were examined with the TEM. Quartz in healed fractures in the reference sample that was quenched isochorically shows a moderate dislocation activity. Quartz adjacent to reequilibrated fluid inclusions in the other two samples, however, showed a marked increase in dislocation activity compared to the un-reequilibrated sample. Deformation of the inclusion walls occurred anisotropically by expansion of mobile dislocations in their slip systems. Dislocation expansion was controlled by glide in the rhombohedral planes {1 0 1 1} that was restricted to narrow zones (≤3 μm) in the immediate vicinity of the fluid inclusion walls outside of the healed fracture plane. These plastic zones were observed after both short term (30 days) and long term (180 days) experiments and are attributed to hydrolytic weakening of quartz around fluid inclusions owing to diffusion of water into the quartz matrix during the experiment. The close spatial association of submicroscopic water bubbles with dislocations, and the rarity of water bubbles in the reference sample, show clearly that in both the 30 and 180 day experiments reequilibration involves water loss from the fluid inclusions. Our results indicate that synthetic fluid inclusions in this study recover (chemically and volumetrically), even at relatively fast experimental loading rates, such that internal stresses never reach the point of brittle failure. The driving force for fluid inclusion deformation involves two related mechanisms: plastic deformation of hydrolytically weakened wet quartz in the healed fracture, and water leakage associated with preexisting and strain-induced dislocations. Received: 5 May 1998 / Accepted: 10 February 2000     

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.     

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.