Richard J. Howarth

Duplicate analysis in geochemical practice. Part I. Theoretical approach and estimation of analytical reproducibility

Duplicate analytical results can be used to give rapid and realistic estimates of precision in analytical systems. In particular the effects of varying concentration of analyte on the variance of the measurement can be taken into account. When only small numbers of duplicate observations are available, the precision can be rapidly tested against an empirical standard level by use of a special control chart. Some common data-recording practices, however, can lead to erroneous estimates of detection limit, irrespective of the estimation procedure employed.

The rapid estimation and control of precision by duplicate determinations

Studies on computer-simulated models have provided several new methods of estimating, studying or controlling analytical precision in real systems. The methods are based upon precision estimators derived from the difference between duplicate analyses, and take into account variations in the precision of a determination with the concentration of the substance being determined. The methods have been checked by applying them to simulated samples of many duplicate analyses drawn by Monte Carlo techniques from specified populations, that is, in effect, from analytical systems with known precision characteristics. Some examples show the application of the methods in practice.

Metals in the sediments of Ensenada de San Simon (inner Ria de Vigo), Galicia, NW Spain

Abstract The Ensenada de San Simon is the inner part of the Ria de Vigo, one of the major mesotidal rias of the Galician coast, NW Spain. The geochemistry of its surface sediments, and the river sediments which drain into it from a granitic and metamorphic hinterland, are described. Multivariate statistical analysis of the sediment compositions (using ridge regression and mixture-modelling) enabled the major- and trace-element distributions to be accounted for in terms of both natural and anthropogenic sources: Between 60 and 80% of the Cr, Cu, Ni, Pb and Zn concentrations of the bottom sediments of the Ensenada can be explained by sediment input from the combined R. Oitaben and R. Verdugo, the R. Redondela and faecal matter from mussel rafts, but there is additional enrichment towards the mouth of the Ensenada. This enrichment is attributed to marine water entering the Ensenada from the polluted industrial areas of the adjacent Ria de Vigo. It is suggested that these metals are carried landwards in solution by the tidal incursion of marine water (the volume of which, on an annual basis, greatly exceeds that contributed by the rivers). Although the incoming marine waters may also be important in supplying Pb to the outer Ensenada, this element may also be delivered by land run-off, or by windborne vehicular emissions to the Ensenada as a result of the surrounding network of roads and a road bridge over the Estrecho de Rande.

Duplicate analysis in geochemical practice. Part II. Examination of proposed method and examples of its use

Monte Carlo simulation has been applied to test the robustness of a method for estimating precision as a function of concentration. The effect of deviations from the basic assumptions underlying the method are shown to be generally fairly small. The causes of such departures can be identified when they occur with actual laboratory results. Methods of recording laboratory observations can cause an over-optimistic bias of precision estimates in some circumstances.

The frequency distribution of analytical error

The widely held view that the frequency distribution of analytical error is log-normal at concentrations of analyte near the detection limit is examined in detail. It is argued that (a) there is no theoretical reason why such distributions should be log-normal and there is abundant evidence that they are not; (b) quasi-log-normal distributions can be produced as artifacts by data recording practices; and (c) inordinately large numbers of analytical results would be needed to distinguish a log-normal distribution from a normal distribution.

Palaeohydrodynamics of fluids in the Brent Group (Oseberg Field, Norwegian North Sea) from chemical and isotopic compositions of formation waters

Generally, the history of past sub-surface fluid movements is difficult to reconstruct. However, the composition of oil-field waters characterizes the origins and mixing processes that allow such a reconstruction. We have investigated present-day formation waters from Brent Group sedimentary rocks of the Oseberg Field in order to assess both their geochemical variations, and their origin(s). Water samples (sampled at the separator) produced from immediately above the oil-water contact and from the aquifer (water-saturated zone below the oil-water contact) were taken from 11 wells across the field. In addition, 3 trace water samples were extracted from oil produced from higher up in the oil column. The water samples were analysed for their chemical components and isotopic compositions. Conservative tracers such as Cl, Br, deltaD, and delta O-18 were used to evaluate the origin of the waters. All formation waters can be characterised as Na-Cl-brines. The separator samples are of aquifer origin, indicating that aquifer water, drawn up by the pressure reduction near the well, is produced from the lower few tens of metres of the oil-zone. By defining plausible endmembers, the waters can be described as mixtures of seawater (60-90%), meteoric water (10-30%), evaporated seawater (primary brines) (3-5%), and possibly waters which have dissolved evaporites (secondary brines). Alternatively, using multidimensional scaling, the waters can be described as mixtures of only 3 endmembers without presupposing their compositions. In fact, they are seawater, very dilute brine, and a secondary brine (confirming the power of this approach). Meteoric water was introduced into the reservoir during the end-Brent and early-Cretaceous periods of emergence and erosion, and partially replaced the marine pore fluids. Lateral chemical Variations across the Oseberg Field are extremely small. The waters from closer to the erosion surfaces show slightly stronger meteoric water isotopic signatures. The primary and secondary brines are believed to come from Permian and Triassic evaporitic rocks in the deeply buried Viking Graben to the west, and to have been modified by water-rock interactions along their migration path. These primary basinal brines have not been detected in the oil-zone waters, suggesting that the brines entered the reservoir after the main phase of oil-migration. There are indications that these external fluids were introduced into the reservoir along faults. Present-day aquifer waters are mixtures of waters from different origins and hardly vary at a field-scale. They are different in composition to the water trapped in the present oil-zone. One of the oil-zone samples is a very dilute brine. It is thought to represent a simple mixture of seawater and meteoric water. Due to oil-emplacement, this geochemical signature was preserved in the waters trapped within the oil-zone. Another oil-zone water shows a very similar chemical signature to the aquifer waters, but the chlorine isotopic signature is similar to that of the dilute oil-zone water. This water is interpreted to represent a palaeo-aquifer water. That is, it was within the aquifer zone in the past, but was trapped by subsequent emplacement of more oil. These Vertical differences can be explained by two features: (i) emergence of the Brent Group sedimentary rocks in the Early Cretaceous allowed ingress of meteoric water; (ii) subsequent rapid burial of Viking Graben rocks caused migration of petroleum and aqueous fluids into the adjacent, less deeply buried Oseberg Field

Rapid prediction of Building Research Establishment limestone durability class from porosity and saturation

Abstract The development of a rapid, non-parametric, and slightly conservative predictor for the estimation of probable weight loss in the standard Building Research Establishment sodium sulphate crystallisation test, and hence of estimated limestone durability class, based on [PorositySaturation]0.5 is described. The time saving offered by application of the look-up tables provided here reduces the 3–4 weeks required for the Building Research Establishment crystallization weight loss test to a matter of hours and offers considerable practical advantage for rapid assessment of the suitability of limestone building stones quarried abroad (e.g. in Jordan) for use in the salt weathering conditions of the UK. However, there is a relatively large variance associated with this estimator (particularly when the microporosity coefficient exceeds 0.65) and in critical cases it should be followed up by confirmatory use of the standard crystallization weight loss test.

A history of regression and related model-fitting in the Earth Sciences (1636?-2000)

The (statistical) modeling of the behavior of a dependent variate as a function of one or more predictors provides examples of model-fitting which span the development of the earth sciences from the 17th Century to the present. The historical development of these methods and their subsequent application is reviewed. Bonds predictions (c. 1636 and 1668) of change in the magnetic declination at London may be the earliest attempt to fit such models to geophysical data. Following publication of Newtons theory of gravitation in 1726, analysis of data on the length of a 1° meridian arc, and the length of a pendulum beating seconds, as a function of sin2(latitude), was used to determine the ellipticity of the oblate spheroid defining the Figure of the Earth. The pioneering computational methods of Mayer in 1750, Boscovich in 1755, and Lambert in 1765, and the subsequent independent discoveries of the principle of least squares by Gauss in 1799, Legendre in 1805, and Adrain in 1808, and its later substantiation on the basis of probability theory by Gauss in 1809 were all applied to the analysis of such geodetic and geophysical data. Notable later applications include: the geomagnetic survey of Ireland by Lloyd, Sabine, and Ross in 1836, Gausss model of the terrestrial magnetic field in 1838, and Airys 1845 analysis of the residuals from a fit to pendulum lengths, from which he recognized the anomalous character of measurements of gravitational force which had been made on islands. In the early 20th Century applications to geological topics proliferated, but the computational burden effectively held back applications of multivariate analysis. Following World War II, the arrival of digital computers in universities in the 1950s facilitated computation, and fitting linear or polynomial models as a function of geographic coordinates, trend surface analysis, became popular during the 1950–60s. The inception of geostatistics in France at this time by Matheron had its roots in meeting the evident need for improved estimators in spatial interpolation. Technical advances in regression analysis during the 1970s embraced the development of regression diagnostics and consequent attention to outliers; the recognition of problems caused by correlated predictors, and the subsequent introduction of ridge regression to overcome them; and techniques for fitting errors-in-variables and mixture models. Improvements in computational power have enabled ever more computer-intensive methods to be applied. These include algorithms which are robust in the presence of outliers, for example Rousseeuws 1984 Least Median Squares; nonparametric smoothing methods, such as kernel-functions, splines and Clevelands 1979 LOcally WEighted Scatterplot Smoother (LOWESS); and the Classification and Regression Tree (CART) technique of Breiman and others in 1984. Despite a continuing improvement in the rate of technology-transfer from the statistical to the earth-science community, despite an abrupt drop to a time-lag of about 10 years following the introduction of digital computers, these more recent developments are only just beginning to penetrate beyond the research community of earth scientists. Examples of applications to problem-solving in the earth sciences are given.

Sources for a history of the ternary diagram

Anyone reading the literature on the history of graphs will soon realize that the use of graphie displays of any type was really quite unusual until the mid-ninetenth century and that those scientists who did make use of them are often familiar to us as creative thinkers in their own fields of endeavour. A ternary diagram (also known as a triangular diagram ) is a particular type of graph which consists of an equilateral triangle in which a given plotted point represents the relative proportions ( a, b, c ) of three end-members (A, B and C), generally expressed as percentages and constrained by a + b + c = 100%. It has long been used to portray sample composition in terms of three constituents, or an observed colour in terms of three primary colours, because it is a convenient means of representing a three-component System in a planar projection, rather than as an isometric, or similar, view of a three-dimensional space. Recent papers suggest that its use is not as familiar to some statisticians as are other commonly used forms of graph. For example, although it was cited by Peddle in 1910 and more recently by Dickinson, it is not discussed in modern texts on statistical graphies nor in the key papers on the history of graphs. However, beginning with studies of colour-mixing in the eighteenth century, it has subsequently become widely used, particularly in geology, physical chemistry and metallurgy. In this paper, I attempt to document its gradual uptake as a standard method of data display and some of the scientific advances which its use has facilitated.

A COMPUTER SIMULATION APPROACH TO THE HIGH PRESSURE THERMOELASTICITY OF MGSIO3 PEROVSKITE

Abstract We have used a combination of molecular dynamics and lattice dynamics simulation techniques to calculate the thermoelastic properties of MgSiO3 perovskite over a wide range in P-T space. Our calculated values for the parameters which are of use in equation of state modelling are: Θ (K) = 1039, K0 (GPa) = 250, K′0 = 4.0, V0 (cm3 mol−1 K−1) = 24.44, γ0 = 1.97 and δT0 = 7.0. There is excellent agreement between our predicted values and the X-ray diffraction diamond anvil cell (XRD-DAC) experiments of Mao et al. (1991, J. Geophys. Res., 96: 8069–8079) but disagreement on the values of δT0 and γ when compared with the high pressure multi-anvil experiments of Wang et al. (1994, Phys. Earth Planet. Inter., 83: 13–41) and the fitted values of Anderson et al. (1995a, Phys. Earth Planet. Inter., 89: 35–49). In addition, the second Gruneisen parameter, q, was found to decrease with pressure, where q drops from 3.0 (0 GPa) to 1.7 at 100 GPa.