ALBERT

Notes: There are many techniques for modelling the geomagnetic field, any one of which may be suitable for a particular application depending on its associated modelling goals. Each method combines a choice of functions and an approach to fitting data so that, in general, it is best suited to a particular type of field modelling, e.g. core versus crustal, regional versus global, downward continuation versus interpolation. Those few approaches such as spherical cap harmonic analysis (Haines 1985a) that possess any true flexibility in this respect suffer from mathematical and computational complexity. In addition, regularization is still a somewhat overlooked issue. Regularization is essential for downward continuing geomagnetic data because shorter wavelength field components and their errors blow up in this process. Approaches such as harmonic spline modelling (Shure, Parker & Backus 1982) which include regularization do so while significantly complicating the task of inversion. We present a new regularized modelling scheme which employs magnetic monopoles as representing functions. We apply regularizing norms of the type introduced by Shure et al. (1982). Owing to the mathematical simplicity of the monopoles, the expressions for the norms are themselves very simple and flexible, and the monopole models very easy to compute. Moreover, the conceptual simplicity of this representation allows for easy modification to accommodate most geomagnetic modelling problems. We apply the technique to problems on three different length scales, each application having distinctly different modelling goals: globally we model the radial core field at the core-mantle boundary (CMB) from satellite data; on a large regional scale we model the radial crustal field at the earth's surface from satellite data; on a small regional scale we model the radial crustal field at the earth's surface from surface data. For each of these varied applications we are able to generate monopole models which produce smooth, plausible fields that fit the data.

Notes: Techniques for modelling the geomagnetic field at the surface of Earth's core often penalize contributions at high spherical harmonic degrees to reduce the effect of mapping crustal fields into the resulting field model at the core-mantle boundary (CMB). Ambiguity in separating the observed field into crustal and core contributions makes it difficult to assign error bounds to core field models, and this makes it hard to test hypotheses that involve pointwise values of the core field. The frozen-flux hypothesis, namely that convective terms dominate diffusive terms in the magnetic-induction equation, requires that the magnetic flux through every patch on the core surrounded by a zero contour of the radial magnetic field remains constant, although the shapes, areas and locations (but not the topology) of these patches may change with time. Field models exactly satisfying the conditions necessary for the hypothesis have not yet been constructed for the early part of this century. We show that such models must exist, so testing the frozen-flux hypothesis becomes the question of whether the models satisfying it are geophysically unsatisfactory on other grounds, for example because they are implausibly rough or complicated. We introduce an algorithm to construct plausible field models satisfying the hypothesis, and present such models for epochs 1945.5 and 1980.Our algorithm is based on a new parametrization of the field in terms of its radial component Br at the CMB. The model consists of values of Br at a finite set of points on the CMB, together with a rule for interpolating the values to other points. The interpolation rule takes the specified points to be the vertices of a spherical triangle tessellation of the CMB, with Br varying linearly in the gnomonic projections of the spherical triangles onto planar triangles in the planes tangent to the centroids of the spherical triangles. This parametrization of Br provides a direct means of constraining the integral invariants required by the frozen-flux hypothesis.Using this parametrization, we have constructed field models satisfying the frozen-flux hypothesis for epochs 1945.5 and 1980, while fitting observatory and survey data for 1945.5 and Magsat data for 1980. We use the better constrained 1980 CMB field model as a reference for 1945.5: we minimize the departure of the 1945.5 CMB field model from a regularized 1980 CMB field model, while constraining the 1945.5 model to have the same null-flux curves and flux through those curves as the 1980 model. The locations, areas and shapes of the curves are allowed to change. The resulting 1945.5 CMB field model is nearly as smooth as that for 1980, fits the data adequately, and satisfies the conditions necessary for the frozen-flux hypothesis.

Notes: Accounting historians have shown considerable interest in the first printed books published on accounting (from 1494 onwards) in various countries. This paper provides a detailed study of the first Australian book, published in sets between 1871 and 1873. It examines the factors determining the date and place of such first authorship. James Dimelow's life and career in Britain and Australia are discussed and his books (which were published in Britain as well as Australia) are systematically described. These books are placed within the contexts of the economic and cultural environment of colonial Australia and the nineteenth-century British and Australian accounting literature. The differences between Dimelow's and John Scouller's books are explored and explained and possible influences of Dimelow on the later development of Australian accounting are proposed.