Diagrammatic solutions for hydraulic head moments in 1-D and 2-D bounded domains

We present a diagrammatic method for solving stochastic 1-D and 2-D steady-state flow equations in bounded domains. The diagrammatic method results in explicit solutions for the moments of the hydraulic head. This avoids certain numerical constraints encountered in realization-based methods. The diagrammatic technique also allows for the consideration of finite domains or large fluctuations, and is not restricted by distributional assumptions. The results of the method for 1-D and 2-D finite domains are compared with those obtained through a realization-based approach. Mean and variance of head are well reproduced for all log-conductivity variances inputted, including those larger than one. The diagrammatic results also compare favorably to hydraulic head moments derived by standard analytic methods requiring a linearized form of the flow equation.     

Petrology, geochemistry and uranium mineralisation of post-collisional magmatism around Goanikontes, southern Central Zone, Damaran Orogen, Namibia

The Goanikontes area lies within the southern Central Zone of the northeast trending branch of the Damara Orogen. The cover succession around Goanikontes, which comprises Etusis to Chuos Formation metasediments, is in tectonic contact with older pre-Damaran basement rocks. The area can be divided into three structural domains with basement in the east, a northeast-plunging anticline of Damaran metasediments to the west and a high strain zone up to 1 km wide that separates them and truncates the anticline. The high strain zone has provided an important focus for the emplacement of sheeted granites adjacent to the basement-cover contact. Goanikontes is also one of several significant uranium anomalies within the Damaran Orogen, and the excellent 3D exposure of the Swakop river has provided evidence for an interpretation of the tectono-metamorphic setting of magmatism and mineralisation. The granitoids have been divided into equigranular granites and sheeted leucogranites. The sequence of emplacement of the equigranular granites is from red syenogranite (534±7 Ma) to later grey monzogranite (517±7 Ma) with foliated basement-hosted granite of probable time equivalence to the syenogranites. Each type can be distinguished on major- and trace-element geochemistry. The later sheeted leucogranites, which are volumetrically the most important, intrude both basement and cover rocks. These have been divided into six distinct types based on field characteristics and structural setting backed by geochemical data and fluid extraction analyses. The earliest type A are irregular in form, boudinaged and folded by D₃, and geochemically distinct with notably low HFSE; type B's are white, weakly foliated, folded by D₃, garnetiferous and highly peraluminous; type C are tourmaline-bearing, occasionally boudinaged and exhibit the typical sheet-form within the cover rocks. Of the post-D₃ sheets, type D, which is restricted to the high strain zone is characterised by smoky quartz, high radioactivity and often by visible betafite or beta-uranophane; type E, the dominant type within the high strain zone contains prominent oxidation haloes and type F is red in colour, coarsely pegmatitic and has the highest concentration of alkalis. The uranium-mineralised type D sheets have consistently higher fluid and CO₂ content than other sheeted leucogranites. The close correlation between sheet type and uranium abundance, supported by linear trends on LIL plots suggests that the distribution of radiogenic elements is primarily magmatic with more recent meteoric re-distribution, rather than due to substantial hydrothermal modification     

Efficient reservoir history matching using subspace vectors

In this paper, we describe a method of history matching in which changes to the reservoir model are constructed from a limited set of basis vectors. The purpose of this reparameterization is to reduce the cost of a Newton iteration, without altering the final estimate of model parameters and without substantially slowing the rate of convergence. The utility of a subspace method depends on several factors, including the choice and number of the subspace vectors to be used. Computational gains in efficiency result partly from a reduction in the size of the matrix system that must be solved in a Newton iteration. More important contributions, however, result from a reduction in the number of sensitivity coefficients that must be computed, reduction in the dimensions of the matrices that must be multiplied, and elimination of matrix products involving the inverse of the prior model covariance matrix. These factors affect the efficiency of each Newton iteration. Although computation of the optimal set of subspace vectors may be expensive, we show that the rate of convergence and the final results are somewhat insensitive to the choice of subspace vectors. We also show that it is desirable to start with a small number of subspace vectors and gradually increase the number at each Newton iteration until an acceptable level of data mismatch is obtained.     

Fractal velocity models in refraction seismology

The introduction of noise components to a simple crustal velocity model is shown to markedly affect the appearance of synthetic seismograms calculated according to ray theory applied to refraction experiments. Here we simulate noise by a self-similar process with a power spectral density which falls off as inverse wavenumber to a simple power (0–2). The major effect is to destroy the coherency of the arrival branches normally expected from deterministic velocity models; the arrival amplitudes also show large trace-to-trace variations and considerable sensitivity to shot position. Some of these differences can be ascribed to the variety of noise model chosen (i.e., white noise, flicker noise and brown noise). It is argued that there is no clear distinction between coherent noise and geological structure.     

Internal control of fluid compositions in amphibolite-facies scapolitic calc-silicates,Mary Kathleen,Australia

Unaltered metasediments of the Mary Kathleen Fold Belt are composed predominantly of layered amphibolite-facies scapolitic calc-silicate rocks in which minimal infiltration of externally derived fluids occurred during regional metamorphism. There were substantial differences in volatile activities between different layers in the layered sequences, in particular: a _CO2/a _{H 2 O} inferred from reaction progress estimates and analysis of biotite-clinopyroxene-fluid phase relations; a _NaCl/a _{H 2 O} inferred from scapolite compositions; and a _HCl/a _{H 2 O} inferred from biotite compositions. In one outcrop in which a clinopyroxene-producing reaction dominated, differences in approximate X _{CO 2}of up to 0.25 occurred between several samples collected over 50 metres. Variations in a _{H 2 O}/a _HCl of up to one order of magnitude are inferred at 1 to 50 m scales from biotite-Cl contents, and variations in NaCl contents of scapolite from 0.0 to up to 0.6 Cl atoms in the Cl–CO₃–SO₄ site reflect a large variation of a _NaCl in the coexisting fluid at similar scales. Most calcsilicate layers internally buffered fluid compositions in the H₂O–CO₂–NaCl–HCl system. Local occurrences of NaCl-rich scapolite suggest that some layers may have been in equilibrium with halite during early prograde metamorphism. At peak metamorphic temperatures, disolution of halite was complete but layers containing high-NaCl scapolite continued to buffer fluid at high values of a _NaCl. Fluid immiscibility does not appear to have affected the progress of the devolatilization reactions. Although fluid was predominantly internally buffered, moderate quantities of fluid were released by prograde mineral reactions in many layers, up to 30 cm³ fluid per 100 cm³ rock. Numerous episodes of fluid escape were required, probably via microfractures, such that the released fluid did not obviously influence reaction progress in the layers through which it passed. The anomaly of beautifully preserved internal buffering signatures and the requirement for produced fluid locally to pass across layers in a deforming rock sequence suggest that the escaping fluid did not leave any readily observable tracks. This is explained by rapid rates of fracture propogation and fluid migration therein. This internally buffered system contrasts strongly with adjacent calc-silicate rocks that show evidence for infiltration of externally derived fluids at high fluid/rock ratios, and highlights the broad range of fluid behaviour that can be expected in deforming, heterogeneous rock sequences.     

The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology

This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.     

Seasonal and daily variation of mercury evasion at coastal and off shore sites from the Mediterranean Sea

Dissolved gaseous mercury (DGM) was measured continuously using two newly developed techniques and a manual technique. The continuous techniques were based on the equilibrium between the aqueous and gaseous phase (DGM = Hg_extr / H', Hg_extr is the measured mercury concentration in the gas phase, H' is the Henry's Law coefficient at the desired temperature). In order to calculate the annual mercury evasion from the Mediterranean Sea, diurnal and seasonal measurements of DGM, total gaseous mercury in air (TGM), water temperature and wind speed were performed. During August 2003, March–April 2004 and October–November 2004 measurements of these parameters were conducted on board the RV Urania. The continuous measurements of DGM showed a diurnal variation in concentration, at both coastal and off shore sites, with higher concentrations during daytime than nighttime. The concentration difference could be as large as 130 fM between day and night. The degree of saturation was calculated directly from the measurements, S = Hg_extr / TGM and was found to vary between the different seasons. The highest average degree of saturation (850%) and the largest variation in saturation (600–1150%) was observed during the summer. The spring showed the lowest variation (260–360%) and the lowest average degree of saturation (320%). The autumn also showed a large variation in saturation (500–1070%) but a lower average (740%) compared to the summer cruise. This might be explained by the temperature difference between the different seasons, since that parameter varied the most. The flux from the sea surface was calculated using the gas exchange model developed by Nightingale et al. [Nightingale, P.D., Malin, G., Law, C.S., Watson, A.J., Liss, P.S., Liddicoat, M.I., Boutin, J., Upstill-Goddard, R. C., 2000. In situ evaluation of air–sea gas exchange parameterization using novel conservative and volatile tracers. Global Biogeochemical Cycles, 14(1):373–387]. The evasion varied between the different seasons with the highest evasion during the autumn, 24.6 pmol m^− 2 h^− 1. The summer value was estimated to 22.3 pmol m^− 2 h^− 1 and the spring to 7.6 pmol m^− 2 h^− 1. Using this data the yearly evasion from the Mediterranean Sea surface was estimated to 77 tons.     

Crustal structure between the Knipovich Ridge and the Van Mijenfjorden (Svalbard)

Marine Geophysical Research - The Alfred Wegener Institute of Polar and Marine Research, the University of Bergen and Hokkaido University acquired new seismic refraction data along a transect from...