Consider a sequence of, say, 10 to 20 vector observations in threedimensional space. It is suspected that a few subsets of consecutive observations are made up of collinear points. The purpose of this paper is to construct a statistically based algorithm to find such linear segments and to assess their accuracy. A similar assessment is made for coplanar sets of points.This algorithm is applied here to palaeomagnetic data and is claimed to be superior to previous methods of palaeomagnetic analysis in terms of completeness and balance of analysis, treatment of measurement errors and other sources of scatter, criteria for identification of linear and planar sets of points, and statistical rigour. Stability spectra, with statistically based confidence limits, are obtained as a by-product.linear components of different ages will generally have stability ranges which partially overlap. During progressive demagnetization the remanence vector moves in a path in threedimensional space, R 3 (Fig. 1). This path is sampled at a sequence of n points in R3 determined by the n progressive demagnetization steps; the origin may be added as a precisely determined (n + I)th data point. This paper is concerned with analysing the geometry of this problem first tackled by Kirschvink (1980), namely:(1) to identify the linear segments of the trajectory, which should be defined by consecutive, nearly collinear, experimentally determined points, and which should define the directions of the underlying discrete NFW vector components;( 2 ) to identify planar segments of the trajectory which would often correspond to overlapping parts of the stability ranges of two vector components;(3) having modelled the whole trajectory in terms of a small number of vector components, to determine the vector composition of the regions of overlap (the stability spectrum, see Section 11).In this paper we construct an appropriate statistical model for this problem and present a new algorithm which has a number of important features. J. T. Kent, J. C Briden and K. V. Mardia A statistical modelAt each stage of the demagnetization treatment we measure the remanent magnetization as a vector in three-dimensional space. Thus our observations can be represented as a sequence
A punctuated 103.3 m thick succession of upper Palaeogene to Quaternary sediments has been recovered in a borehole from the upper Hebrides Slope, west of Britain. The borehole proved 11.2m of upper Oligocene, carbonate-rich muds at the base, unconformably overlain by 2.85 m of middle to upper Miocene, glauconitic sands. This is in turn unconformably overlain by 89.25 m of predominantly Plio-Pleistocene sands and muds, with a Holocene sea-bed veneer. The post-Miocene succession is subdivided into two units: the sand-dominated, Pliocene to lower middle Pleistocene, Lower MacLeod sequence between 89.25 and 67.82 m, and the mud-dominated, middle Pleistocene to Holocene, Upper MacLeod sequence above 67.82 m. Regional mapping indicates that these sequences are commonly associated with large-scale shelf-margin progradation and slope-front fan construction. The borehole core provides an excellent record of the transition from pre-glacial to glacial conditions in the mid-latitude NE Atlantic Ocean. Climatic conditions warmer than present prevailed in the late Oligocene, mid- to late Miocene and Pliocene, although the influx of ice-rafted detritus in the late Pliocene marks the onset of climatic deterioration. This deterioration continued, in a fluctuating manner, until the early mid-Pleistocene (0.44 Ma) when fully glacial conditions were established on the Hebridean Margin.
Recent palaeomagnetic studies on Devonian and Carboniferous rocks have resulted in a time re-calibration of the Apparent Polar Wander Path (APWP) for Europe, and revision of the shape of the APWP for North America. Differences between previously published versions of these paths are now much reduced. The APWP for southern Britain is different from those for North America and Armorica, thus southern Britain is believed to have been an isolated block within the pre-Hercynian ocean. New continental reconstructions are presented to take account of these conclusions. A lack of sufficient reliable palaeomagnetic data from Baltica make its position on the map uncertain, and hence the significance of the Tornquist Sea between Baltica and Palaeo-Europe remains incompletely understood.
K-Ar age determinations, mainly whole rock, with some corroboration from mineral separates, are presented for lava flows, domes, minor intrusives and blocks in tuffs from 95 localities in the Lesser Antilles. Together with the much smaller number of previously published data, these show a distinction between a range 38-10 million years (Ma) in the outer arc (Limestone Caribbees) and less than 7.7 Ma in the inner arc (Volcanic Caribbees). From southern Martinique southwards, the two arcs are superposed, and the whole range is fragmentarily represented. The observed age ranges in the outer and inner arcs fit between discontinuities in sea floor spreading in the North Atlantic at ca. 38 and ca. 9 Ma and a causal connection between spreading change and relocation of arc volcanicity is suggested. Palaeomagnetic directions at 108 localities in ten of the islands fall into normal ( N = 56, k = 13.8, D = 359°, I = + 22°, pole position 229° E, 89° N with drjr = 3°, d X = 6°) and reversed groups ( N = 41, k = 14.1, D = 178°, I = -22°, pole position 18° E, 88° S with d xjr = 3°, dx = 6°) plus six sites of intermediate polarity and five sites indeterminate. The mean dipole axis is within 2° of the present rotation axis and is likely to be identical with it with a probability of 99%. The data are generally in accord with the established geomagnetic polarity time scale, but there is some suggestion of a normal polarity event at ca. 1.18 Ma within the Matuyama Reversed Epoch. The palaeomagnetic data relate mainly to be past 10 Ma and suggest that within that time the Lesser Antilles have not changed their latitude or geographic orientation, and that the geomagnetic field has averaged that of a centred axial dipole. The few older palaeomagnetic data are consistent with these same conclusions (though with less certainty) back to ca. 20 Ma ago. There is no evidence for oroclinal bending of the arc since then.
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