Using Sequential Self-Calibration Method to Identify Conductivity Distribution: Conditioning on Tracer Test data

An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases.     

The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application

Many decision-making processes in the Earth sciences require the combination of multiple data originating from diverse sources. These data are often indirect and uncertain, and their combination would call for a probabilistic approach. These data are also partially redundant with each other or with all others taken jointly. This overlap in information arises due to a variety of reasons—because the data arises from the same geology, because they originate from the same location or the same measurement device, etc. The proposed tau model combines partially redundant data, each taking the form of a prior probability for the event being assessed to occur given that single datum. The parameters of that tau model measure the additional contribution brought by any single datum over that of all previously considered data; they are data sequence-dependent and also data value-dependent. Data redundancy depends on the sequence in which the data is considered and also on the data values themselves. However, for a given sequence, averaging the tau model parameters over all possible data values leads to exact analytical expressions and corresponding approximations and inference avenues. Information on multiple-point connectivity of permeability arrives from core data, well-test data and seismic data which are defined over varying supports with complex redundancy between these information sources. In order to compute these tau weights for determining connectivity, one needs a model of data redundancy, here expressed as a vectorial training image (Ti) constructed using a prior conceptual knowledge of geology and the physics of data measurement. From such a vectorial Ti, the tau weights can be computed exactly. Neglecting data redundancy leads to an over-compounding of individual data information and the possible risk of making extreme decisions.     

Group Time Delay in the Reflection of P-Polarized Electromagnetic Plane Waves at a Stratigraphic Interface

The group time delay (GTD) formulae of quasi-total reflection of inhomogeneous P-polarized electromagnetic waves (P-PEW, whose electric field parallels to the plane of incidence), caused by the Goos–Hänchen effect, is derived by the phase shift of the wave. A numerical example where the frequency equals to 1 GHz is given. The curves of calculating results show that there are three discontinuous points at the critical angle of phase shift vector, the critical angle of attenuation vector and 90^○. When the angle of incidence is equal to one of these three angles, the GTD will become infinite, and the electromagnetic wave will propagate along the interface. The GTD will be very large, when the angle of incidence is close to one of these three angles. The results indicate that there is an important relationship between the two critical angles and the conductivity and permittivity of the two strata, and that the GTD has an important relationship with the angle of incidence. These results can be used to determine the lithology of the strata and to delimit the interfaces of strata more effectively. It is suggested that this research may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.     

Stability Analysis and Numerical Simulation of Differential Frost Heave

Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analysis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution occurs at shallow freezing depths and near-zero surface loads when positive perturbations in the ice content at the freezing front lead to a concomitant increase in thermomolecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface patterns will evolve with a length scale in the order of 2–4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Revised chemical models of ζ Oph based on HST data

Hubble Space Telescope observations by Savage, Cardelli and Sofia (1992) and Cardelliet al. (1993) have led to improved gas phase abundances for many elements in the diffuse cloud towards the star Oph. Most remarkably, it was found that oxygen is much more strongly depleted than previousCopernicus observations indicated. As a consequence, chemical models of the Oph cloud are severely affected by the drop in the observed oxygen abundance by almost a factor of two; some previous model calculations for the Oph cloud failed to reproduce-even approximately-the observed high CO column density. The model calculations for the Oph cloud developed by Wagenblast (1992) in which the abundance of all observed neutral molecules could be reproduced have been revised and it is found that oxygen and nitrogen hydrides are required to be formed efficiently on the surface of grains; further, there are indications for a high cosmic ray ionization rate of the order 10^–16 s^–1.     

Secular changes in the short-term preventive,positive, and temperature checks to population growth in Europe, 1460 to 1909

Annual variations in births, marriages, deaths, grain prices, and quarterly temperature series in England, France, Prussia, and Sweden are analyzed using a distributed lag model. The results provide support for the existence of the shortterm preventive, positive and temperature checks to population growth. Decreases in fertility and nuptiality are generally associated with increases in grain prices. Increases in mortality appear to be associated with high grain prices, cold winters and hot summers. Changes in these responses over time are examined within the context of economic development.The causes of a high mortality are various; but the greater number of known causes may be referred to five heads: 1) excessive cold or heat; 2) privation of food; 3) effluvial poisons generated in marshes, foul prisons, camps, cities; and epidemic diseases, such as typhus, plague, small pox, and other zymotic diseases; 4) mechanical and chemical injuries; 5) spontaneous disorders to which the structure of the human organization renders it liable. - Farr (1846, p. 164)....a foresight of the difficulties attending the rearing of a family acts as a preventive check, and the actual distresses of some of the lower classes, by which they are disabled from giving the proper food and attention to their children, acts as a positive check to the natural increase of population. - Malthus (1798, Chapter 4).The research on which this paper is based has been funded by grants R01-HD18107 and T32-HD07275 from the U.S. National Institute of Child Health and Human Development. This paper is associated with the author's Basic Patterns in Annual Variations in Fertility, Nuptiality, Mortality, and Prices in Preindustrial Europe,Population Studies 42, 2, 1988, 275-303. I thank Ronald Lee, Ulla Larsen, and Jan de Vries for helpful comments and suggestions.     

Definition and measurement of salinity in salt lakes

Salinity is the most important chemical attribute of athalassic salt lakes. Even so, some confusion persists of what salinity means and how to measure it. For sal lakes, salinity is best defined as the sum total of all ion concentrations, or total ion concentration. Ideally, it is recommended that salinities be expressed on a mass per mass basis and as ppt (parts per thousand). Direct measurements of salinity can only be derived from full ionic analyses. Indirect measurements can be derived by determinations of density, conductivity, freezing point depression and total dissolved solids or matter.     

Particulate content of savanna fire emissions

As part of the FOS-DECAFE experiment at Lamto (Ivory Coast) in January 1991, various aerosol samples were collected at ground level near prescribed fires or under local background conditions, to characterize the emissions of particulate matter from the burning of savanna vegetation. This paper deals with total aerosol (TPM) and carbon measurements. Detailed trace element and polycyclic hydrocarbon data are discussed in other papers presented in this issue.Near the fire plumes, the aerosols from biomass burning are primarily of a carbonaceous nature (C%70% of the aerosol mass) and consist predominantly of submicron particles (more than 90% in mass.) They are characterized by their organic nature (black to total carbon ratio Cb/Ct in the range 3–20%) and their high potassium content (K/Cb0.6). These aerosols undergo aging during their first minutes in the atmosphere causing slight alterations in their size distribution and chemical composition. However, they remain enriched in potassium (K/Cb=0.21) and pyrene, a polycyclic aromatic hydrocarbon, such that both of these species may be used as tracers of savanna burning aerosols. We show that during this period of the year, the background atmosphere experiences severe pollution from both terrigenous sources and regional biomass burning (44% of the aerosol). Daynight variations of the background carbon concentrations suggest that fire ignition and spreading occur primarily during the day. Simultaneous TPM and CO₂ real-time measurements point to a temporal and spatial heterogeneity of the burning so that the ratio of the above background concentrations (TPM/CO₂) varies from 2 to 400 g/kg C. Smoldering processes are intense sources of particles but particulate emissions may also be important during the rapidly spreading heading fires in connection with the generation of heavy brown smoke. We propose emission factor values (EF) for aerosols from the savanna biomass burning aerosols: EF (TPM)=11.4±4.6 and 69±25 g/kg C_{dry plant} and EF(Ct)=7.4±3.4 and 56±16 g C/kg C_{dry plant} for flaming and smoldering processes respectively. In these estimates, the range of uncertainty is mostly due to the intra-fire variability. These values are significantly lower than those reported in the literature for the combustion of other types of vegetation. But due to the large amounts of vegetation biomass being burnt in African savannas, the annual flux of particulate carbon into the atmosphere is estimated to be of the order of 8 Tg C, which rivals particulate carbon emissions from anthropogenic activities in temperate regions.