Fitting the Linear Model of Coregionalization by Generalized Least Squares

In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS₁), (ii) calculated using the fourth-order moments with the theoretical sills (GLS₂), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS₃). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS₁ and theoretical GLS₂ are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS₁ can be recommended for future studies using the LMC.     

Biotite weathering and nutrient uptake by ectomycorrhizal fungus, Suillus tomentosus, in liquid-culture experiments

Ectomycorrhiza-forming fungi (EMF) alter the nutrient-acquisition capabilities of vascular plants, and may play an important role in mineral weathering and the partitioning of products of weathering in soils under nutrient-limited conditions. In this study, we isolated the weathering function of Suillus tomentosus in liquid-cultures with biotite micas incubated at room temperature. We hypothesized that the fungus would accelerate weathering by hyphal attachment to biotite surfaces and transmission of nutrient cations via direct exchange into the fungal biomass. We combined a mass-balance approach with scanning electron microscopy (SEM) and atomic force microscopy (AFM) to estimate weathering rates and study dissolution features on biotite surfaces. Weathering of biotite flakes was about 2-3 orders of magnitude faster in shaken liquid-cultures with fungus compared to shaken controls without fungus, but with added inorganic acids. Adding fungus in nonshaken cultures caused a higher dissolution rate than in inorganic pH controls without fungus, but it was not significantly faster than organic pH controls without fungus. The K⁺, Mg²⁺ and Fe²⁺ from biotite were preferentially partitioned into fungal biomass in the shaken cultures, while in the nonshaken cultures, K⁺ and Mg²⁺ was lost from biomass and Fe²⁺ bioaccumulated much less. Fungal hyphae attached to biotite surfaces, but no significant surface changes were detected by SEM. When cultures were shaken, the AFM images of basal planes appeared to be rougher and had abundant dissolution channels, but such channel development was minor in nonshaken conditions. Even under shaken conditions the channels only accounted for only 1/100 of the total dissolution rate of 2.7 × 10⁻¹⁰ mol of biotite m⁻² s⁻¹. The results suggest that fungal weathering predominantly occurred not by attachment and direct transfer of nutrients via hyphae, but because of the acidification of the bulk liquid by organic acids, fungal respiration (CO₂), and complexation of cations which accelerated dissolution of biotite. Results further suggest that both carbohydrate source (abundant here) and a host with which nutrients are exchanged (missing here) may be required for EMF to exert an important weathering effect in soils. Unsaturated conditions and physical dispersal of nutrient-rich minerals in soils may also confer a benefit for hyphal growth and attachment, and promote the attachment-mediated weathering which has been observed elsewhere on soil mineral surfaces.     

Applicability of the theory of hollow inclusions for overcoring stress measurements in rock

Summary Whenever solid or hollow inclusions are used as instrumented probes in overcoring techniques, residual stresses remain in the overcored rock sample and in the probes. When using such devices for computing the in-situ stress field components from measured strains or displacements, it is common practice to assume that the overcoring diameter is infinite and that there is a perfect bonding between the rock and the probes. The validity of these assumptions depends on the magnitude of the residual stresses at the rock-probe contact as compared to the tensile and shear strengths of the rock-probe bond material. It also depends on the distribution of residual stresses in the overcored sample.In comparison to previous work, new expressions are proposed in this paper for the residual stresses associated with solid or hollow inclusion type stress probes in anisotropic ground. These expressions are presented in dimensionless form and are used to show that the distribution and magnitude of residual stresses depend on the isotropic-anisotropic rock character, the degree and type of rock anisotropy, the orientation of the rock anisotropy with respect to the hole in which the probes are located and the relative deformability of the rock with respect to the deformability of the material comprising the probes. The conditions that are required for neglecting the overcored sample diameter are also discussed. This is shown for rocks that can be described as isotropic, transversely isotropic and orthotropic materials.     

Low-pressure adsorption of Ar, Kr, and Xe on carbonaceous materials (kerogen and carbon blacks), ferrihydrite, and montmorillonite: Implications for the trapping of noble gases onto meteoritic matter

Noble gases trapped in meteorites are tightly bound in a carbonaceous carrier labeled “phase Q.” Mechanisms having led to their retention in this phase or in its precursors are poorly understood. To test physical adsorption as a way of retaining noble gases into precursors of meteoritic materials, we have performed adsorption experiments for Ar, Kr, and Xe at low pressures (10⁻⁴ mbar to 500 mbar) encompassing pressures proposed for the evolving solar nebula. Low-pressure adsorption isotherms were obtained for ferrihydrite and montmorillonite, both phases being present in Orgueil (CI), for terrestrial type III kerogen, the best chemical analog of phase Q studied so far, and for carbon blacks, which are present in phase Q and can be considered as possible precursors.Based on adsorption data obtained at low pressures relevant to the protosolar nebula, we propose that the amount of noble gases that can be adsorbed onto primitive materials is much higher than previously inferred from experiments carried out at higher pressures. The adsorption capacity increases from kerogen, carbon blacks, montmorillonite to ferrihydrite. Because of its low specific surface area, kerogen can hardly account for the noble gas inventory of Q. Carbon blacks in the temperature range 75 K-100 K can adsorb up to two orders of magnitude more noble gases than those found in Q. Irreversible trapping of a few percent of noble gases adsorbed on such materials could represent a viable process for incorporating noble gases in phase Q precursors. This temperature range cannot be ruled out for the zone of accretion of the meteorite precursors according to recent astrophysical models and observations, although it is near the lower end of the temperatures proposed for the evolving solar nebula.     

The red bed controversy revisited: shape analysis of Colorado Plateau units suggests long magnetization times

Several Triassic and earliest Jurassic sedimentary units from the Colorado Plateau region have distributions of virtual geomagnetic poles (VGPs) that are highly elongate along the path of apparent polar wander (APW). This suggests that the remanent magnetizations measured in these units were acquired over an extended period of time, possibly approaching 35 m.y., and are not precisely coeval with the stratigraphic age of the rock. Comparison with other paleomagnetic studies shows that the observed elongation is not a general attribute of the age of the rock, nor is it related to paleolatitude. The rocks that yield elongate VGP distributions are dominantly red to brown mudstones, and it is possible that their remanence is dominated by a slowly acquired chemical remanent magnetization, as suggested by Larson et al. [J. Geophys. Res. 87 (1982) 1081] and other authors. However, several superficially similar units from the Colorado Plateau have nearly circular VGP distributions. The process by which remanence is acquired in clastic sedimentary rocks merits further study.     

Establishing constraints on groundwater ages with Cl,C, H,and noble gases: A case study in the eastern Paris basin,France

Groundwaters from the Tithonian/Kimmeridgian, Oxfordian and Upper Dogger aquifers, within the eastern part of the Paris basin (France), were characterised using ³H, ¹⁴C and ³⁶Cl, and noble gases tracers, to evaluate their residence times and determine their recharge period. This information is an important prerequisite to evaluating the confinement properties of the Callovo-Oxfordian clay formation sandwiched between the Oxfordian aquifer and the Dogger aquifer, currently being investigated by the French nuclear waste management agency (Andra) for radioactive waste disposal. Data presented in this paper are used to test 4 hypotheses.     

Contribution of geophysical surveys to groundwater modelling of a porous aquifer in semiarid Niger: An overview

Subsurface geophysical surveys were carried out using a large range of methods in an unconfined sandstone aquifer in semiarid south-western Niger for improving both the conceptual model of water flow through the unsaturated zone and the parameterization of numerical a groundwater model of the aquifer. Methods included: electromagnetic mapping, electrical resistivity tomography (ERT), resistivity logging, time domain electromagnetic sounding (TDEM), and magnetic resonance sounding (MRS). Analyses of electrical conductivities, complemented by geochemical measurements, allowed us to identify preferential pathways for infiltration and drainage beneath gullies and alluvial fans. The mean water content estimated by MRS (13%) was used for computing the regional groundwater recharge from long-term change in the water table. The ranges in permeability and water content obtained with MRS allowed a reduction of the degree of freedom of aquifer parameters used in groundwater modelling.