A review of: “Free oscillations of the earth”

Abstract

By E. R. Lapwood and T. Usami, Cambridge University Press, 1981. xii + 243 pp. $25 (ISBN 0 521 23563 7).     

Some models of the geomagnetic field in western Europe from 1960 to 1980

Achache et al.'s averages over 10 west European observatories of the annual mean magnetic components X, Y, Z are studied from 1953 to 1979. A 1970 jerk is fitted to the data by least squares, and the fit is quantitatively compared with that of a polynomial having the same number of free parameters as the jerk (a quintic). A crude correction for the 11-y sunspot cycle is also attempted. The jerk and quintic are equally good fits to X, the jerk is clearly better for Y, and the quintic is modestly better for Z. The jerk amplitudes of X and Z but not Y depend heavily on whether a sunspot correction is made, and such a correction may be required to estimate the energy of the internal part of the jerk in the manner of Malin and Hodder. The sunspot correction to Y probably cannot be brought above the noise because it is small and highly correlated with both the jerk and the quintic. The sunspot corrections to X and Z are statistically significant but depend on whether the core signal is taken as a jerk or a quintic. Courtillot and Le Mouël's physical model for the jerk predicts that the jerk amplitudes of X, Y, Z will be proportional to the longitudinal derivatives of X, Y and Z. This prediction is roughly verified for the magnitudes but not the signs; it is just possible that the signs in X and Z are not statistically significant.     

The occultation of κ geminorum by Eros

The predictions and observations of the occultation of κ Gem by Eros on January 24, 1975, are described. At least eight positive and several critical negative observations were made in western New England. The paucity of observations on the western side of the track makes the analysis somewhat ambiguous, but a circular cross section of diameter up to 23 km gives a good fit to most of the available data. Consideration of a crucial, unconfirmed negative observation indicates that an elliptical solution 17 by 7 km (with the long axis in the direction of motion of the “shadow” of Eros) may be preferable, but this does not represent the positive observations so satisfactorily. The ellipse was therefore distorted into a more irregular shape about 20 km long and 7 km wide, rounded on one long side and flattened on the other. Both this irregular shape and the ellipse yield geometric albedos near 0.5, which is considerably higher than has been derived for most other planets or satellites lacking an atmosphere. The albedo that corresponds to the circular solution (0.1) is less than the polarimetric albedo of 0.21 for Eros. It is suggested either that the circle should be warped into an ellipse of dimensions 21 by 13 km, or, if some weight is given to the critical negative observation and the westernmost positive observation, that the profile is a kind of dumbbell.     

FLAT SPOT EXPLORATION*

The hydrocarbon-brine contact produces a flat reflection, unconformable with the lithologic reflections from the trap boundaries, and over a limited area bounded by structural contours. When it can be reliably detected and mapped, the flat spot can provide (i) a reasonably unambiguous indication and areal extent of a reservoir and (ii) an estimate of reservoir thickness. The gas-brine contact in thick reservoirs in offshore elastic sections is the easiest target. An example of gas mapping is presented in the paper. Other reservoirs represent a continuum of increasingly elusive targets. Increasing the range of applicability of flat spot exploration will require (i) increases in signal/noise and multiple ratio, increases in the three dimensional depth point density (or grid density), increased resolution and static and dynamic correction accuracy, and (ii) processing and interpretation aimed directly at flat spot mapping. Low relief structural and stratigraphic traps should provide the most attractive targets. The approach should be at least theoretically feasible, though not necessarily cost effective, for most major reservoirs with a well-behaved hydrocarbon brine contact.     

Harmonic splines for geomagnetic modelling

Which features of a geomagnetic field model on the surface of the core are really necessary in order to fit, within observational error, the field observations at and above the Earth's surface? To approach this question, we define ‘roughness’ in various ways as a norm on an appropriate Hilbert space of field models which is small when the field is smooth on the core surface. Then, we calculate the model with least norm (the smoothest model) which fits the data, sources outside the core being treated as noise. Sample calculations illustrate the effects of noise, of the choice of norm and of an uneven distribution of observing stations.