INTERPRETATION OF THE GRAVITY ANOMALY OVER A CAUSATIVE BODY WITH CIRCULAR SYMMETRY*

The interpretation of the gravity anomaly on a horizontal plane over a causative body having circular symmetry about a vertical axis is considered from a rather unconventional approach. As the analytical expression for the gravity effect of a circular body assumes a closed form only on the axis of symmetry, the interpretation in this approach is carried out with the anomaly profile along the axis—which leads to simpler and faster computation. A numerical method is developed for computation of the anomaly profile along the vertical axis from the horizontal radial profile of the symmetric anomaly by upward continuation. Provision is also made for an end correction when the radial profile has only a limited extension. Some simple geometrical shapes are assumed for the causative body. Its parameters are then determined from least squares fitting of its gravity effects to the observed (upward continued) vertical profile (i) by the steepest descent method and (ii) by the Newton-Raphson method. Some applications of these methods are demonstrated.     

THE START AND EARLY HISTORY OF CHEMOMETRICS:SELECTED INTERVIEWS.PART 1

This is a first foray into the historical start and early years of chemometrics from about 1972 onwards.We have gathered interviews with three originators(Kowalski,Wold and Massart)as well as with aselected group of six other well-known chemometricians who gradually became active in the 1970s(Christie,Clementi,Hopke,Martens,Brown and Deming).The interviews include amongst a host ofsubjective recollections a succinct record of the key historical literature as highlighted by the interviewees'own rankings of‘earliest’and‘best’.A discussion of the most general commonalities in these interviews together with other historicalmaterial is presented in the second part of the paper.     

RAINFALL AND TEMPERATURE ATTRIBUTES ON THE LESOTHO–DRAKENSBERG ESCARPMENT EDGE, SOUTHERN AFRICA

Located near the southeastern limit of Africa, the Lesotho‐Drakensberg and associated escarpment is the highest range of African mountains south of the massifs in Tanzania. At the escarpment summit and on the adjacent high peaks, the climate is generally interpreted as marginal periglacial yet few data, specifically rainfall and temperature, exist on record at these altitudes. Climatic data from two temporary field stations on the escarpment edge, one of which is the highest rainfall station yet on record in southern Africa, provide contemporary surface‐climate conditions. Mean annual rainfall recorded between 2001 and 2005 averages 767.8 mm at Sani Pass summit (three complete years), and 753.2 mm on Sentinel Peak (two complete years); these values are less than those recorded for the same period in the mountain foothills. Even though rainfall is slightly below long‐term rainfall averages for the area due to a marginally dry spell, the data show that earlier estimates of between 1000 mm and 2000 mm rainfall per annum on the escarpment are too high. A measured mean air temperature of 5.8°C at Sani Pass, however, falls within the range estimated for the escarpment summit. Frost cycles in air and at the soil surface are frequent in winter, but absent in soil for summer, and no long‐duration surface‐soil freeze was measured. Temperatures thus confirm the marginal periglacial nature as postulated for previously, but precipitation data indicate a dryer environment than anticipated. Palaeoenvironmental scenarios, notably arguments for former glaciation based on extrapolations from somewhat exaggerated contemporary precipitation values, thus require re‐consideration.     

ELIMINATING COMPLEX EIGENVECTORS AND EIGENVALUES IN MULTIWAY ANALYSES USING THE DIRECT TRILINEAR DECOMPOSITION METHOD

The direct trilinear decomposition method(DTDM)is an algorithm for performing quantitative curveresolution of three-dimensional data that follow the so-called trilinear model,e.g.chromatography-spectroscopy or emission-excitation fluorescence.Under certain conditions complexeigenvalues and eigenvectors emerge when the generalized eigenproblem is solved in DTDM.Previouspublications never treated those cases.In this paper we show how similarity transformations can be usedto eliminate the imaginary part of the complex eigenvalues and eigenvectors,thereby increasing theusefulness of DTDM in practical applications.The similarity transformation technique was first used byour laboratory to solve the similar problem in the generalized rank annihilation method(GRAM).Because unique elution profiles and spectra can be derived by using data matrices from three or moresamples simultaneously,DTDM with similarity transformations is more efficient than GRAM in the casewhere there are many samples to be investigated.     

Applications of grain-pivoting and sliding analyses to selective entrapment of gravel and to flow-competence evaluations

Models of sediment threshold by grain pivoting or sliding over underlying particles are examined in order to explore their application to evaluations of selective entrainment of gravel by flowing water. Of special interest is whether such process-based models provide satisfactory evaluations of flow competence and the movement of large clasts by floods. A detailed derivation is undertaken, focusing first on the fluid flow and forces at the particle level. The resulting threshold equation for the particle-level velocity is then modified to yield the mean entrainment stress for the flow as a whole. This approach is appropriate for considerations of selective entrainment of grains of varying sizes within a deposit, the sorting being due to their relative projection distances above the bed and the dependence of their pivoting angles on grain size and shape. The resulting threshold equations contain a number of coefficients (e.g. drag and lift) whose values are poorly known, but can be constrained by requiring agreement with the Shields curve for the threshold of grains in uniform deposits. If pivoting coefficients based on laboratory measurements with tetrahedral arrangements of particles are used in the models, smaller degrees of selective sorting are predicted than found in the field measurements of gravel entrainment. However, if reasonable modifications of those coefficients are made for expected field conditions, then the models yield good agreement with the data. Sliding models, where sorting is due entirely to projection distances of the grains above the bed, yield somewhat poorer agreement with the field data; however, the sliding models may have support from laboratory experiments on gravel entrainment in that the data and theoretical curves have similar concave trends. The existing measurements lack documentation of the mechanisms of grain movement, so it is not possible to conclusively determine the relative importance of grain pivoting versus sliding. In spite of such uncertainties, the results are encouraging and it is concluded that pivoting and sliding models for grain entrainment do have potential for field computations of selective entrainment and flow competence.     

Polybaric Evolution of Calc-alkaline Magmas from Nisyros, Southeastern Hellenic Arc, Greece

The lavas of Nisyros were erupted between about 0?2 m.y B.P.and 1422 A.D., and range in composition from basaltic andesiteto rhyodacite. Most were erupted prior to caldera collapse (exactdate unknown), and the post-caldera lavas are petrographically(presence of strongly resorbed phenocrysts) and chemically (lowerTiO₂ K₂O, P₂O₅, and LIL elements) distinct from the pre-calderalavas. The pre-caldera lavas do not form a continuous seriessince lavas with SiO₂ contents between 60 and 66 wt.% are absent.Nevertheless, major element variations demonstrate that fractionalcrystalliz ation (involving removal of olivine, dinopyroxene,plagioclase, and Fe-Ti oxide from the basaltic andesites andandesites and plagioclase, clinopyroxene, hypersthene, Ti-magnetite,ilmenite, apatite, and zircon from the dacites and rhyodacites)played a major role in the evolution of the pre-caldera lavas.Several lines of evidence indicate that other processes werealso important in magma evolution: (1) Quantitative modelingof major element data shows that phenocryst phases of unlikelycomposi tion or unrealistic assemblages of phenocryst phasesare required to relate the dacites and rhyodacites to the basalticandesites and andesites; (2) The proportions of olivine andclinopyroxene required in quantitative models for the initialstages of evolution differ from those observed petrographicallyand this is not likely to reflect either differential ratesof crystal settling or the curvature of cotectics along whichliquids of basaltic andesite to andesite composition lie; (3)The concentrations of Rb, Cs, Ba, La, Sm, Eu, and Th in therhyod.acites are too high for these lavas to be related to thedacites by fractional crystallization alone; and (4) ⁸⁷Sr/⁸⁶Srratios for the andesites and rhyodacites are higher than thosefor the basaltic andesites and dacites, respectively. It isshown that fractional crystallization was accompanied by assimilation,and that magma mixing played a minor role (if any) in the evolutionof the pre-caldera lavas. Trace element and isotopic data indicatethat the andesites evolved from the basaltic andesites by AFCinvolving average crust or upper crust, whereas the rhyodacitesevolved from the dacites by AFC involving lower crust. Additionalevidence for polybaric evolution is provided by the occurrenceof distinct Ab-rich cores of plagioclase phenocrysts in thedacites and rhyodacites, which record a period of high pressurecrystallization, and by the occurrence of both normal and reverse-zonedphenocrysts in the basaltic andesites and andesites. Furthermore,calculated pressures of crystallization are {small tilde}8 kbfor the dacites and rhyodacites and 3?5–4 kb for the basalticandesites and andesites. It is concluded that the dacites andrhyodacites evolved via AFC from basaltic andesites and andesiteslargely in chambers sited near the base of the crust whereasthe basaltic andesites and andesites mostly evolved in chamberssited at mid-crustal levels. Eruption from different chambersexplains the compositional gap in the chemistry of the pre-calderalavas since eruptive products represent a more or less randomsampling of residual liquids which separate (via filter pressing)from bodies of crystallizing magma at various depths. Magmamixing was important in the evolution of the post-caldera lavas,but geochemical data require that these magmas evolved fromparental magmas which were derived from a more refractory sourcethan the parental magmas to the pre-caldera lavas. ^*Present address: Netherlands Energy Research Foundation (ECN), P.O. Box 1, 1755 ZG Petten, The Netherlands     

Cenozoic Volcanism in Tibet: Evidence for a Transition from Oceanic to Continental Subduction

Geochronological (K–Ar or ⁴⁰Ar/³⁹Ar), major and traceelement, Sr–Nd–Pb isotopic and mineral chemicaldata are presented for newly discovered Cenozoic volcanic rocksin the western Qiangtang and central Lhasa terranes of Tibet.Alkali basalts of 65–45 Ma occur in the western Qiangtangterrane and represent primitive mantle melts as indicated byhigh mg-numbers [100 x Mg/(Mg + Fe)] (54–65), Cr (204–839ppm) and Ni (94–218 ppm) contents, and relatively lowratios of ⁸⁷Sr/⁸⁶Sr (0·7046–0·7061), ²⁰⁶Pb/²⁰⁴Pb(18·21–18·89), ²⁰⁷Pb/²⁰⁴Pb (15·49–15·61)and ²⁰⁸Pb/²⁰⁴Pb (38·42–38·89), and highratios of ¹⁴³Nd/¹⁴⁴Nd (0·5124–0·5127). Incontrast, younger volcanic rocks in the western Qiangtang terrane(