A definitive model of the geomagnetic field and its secular variation for 1965 — I. Derivation of model and comparison with the IGRF

Summary. Using a very large body of post-1955 data, a spherical harmonic model of the geomagnetic field and its secular variation is derived for 1965.0. This model is compared with the original International Geomagnetic Reference Field (IGRF) and with individual models used, or proposed for use, in producing the IGRF. Positions of the dip-poles, the geomagnetic poles and the eccentric dipole are derived from the model, together with their rates of change, and comparisons are made with other estimates of these positions.     

Using geomagnetic secular variation to separate remanent and induced sources of the crustal magnetic field

Magnetic fields originating from magnetized crustal rocks dominate the geomagnetic spectrum at wavelengths of 0.1–100 km. It is not known whether the magnetization is predominantly induced or remanent, and static surveys cannot discriminate between the two. Long‐running magnetic observatories offer a chance, in principle, of separating the two sources because secular variation leads to a change in the main inducing field, which in turn causes a change in the induced part of the short‐wavelength crustal field. We first argue that the induced crustal field, b ^I( t ), is linearly related to the local core field, B ( t ), through a symmetric, trace‐free matrix A : b ^I( t )= A B ( t ). We then subtract a core field model from the observatory annual means and invert the residuals for three components of the remanent field, b ^R( t ), and the five independent elements of A . Applying the method to 20 European observatories, all of which have recorded for more than 50 years, shows that the most difficult task is to distinguish b ^R from the steady part of b ^I. However, for nine observatories a time‐dependent induced field fits the data better than a steady remanent field at the 99 per cent confidence level, suggesting the presence of a significant induced component to the magnetization.     

Spectral analysis of Quaternary palaeomagnetic data from British Columbia and its bearing on geomagnetic secular variation

Palaeomagnetic results obtained from a 7-m sedimentary sequence in southern British Columbia spanning approximately 9000 yr (˜ 22 000 to ˜31 000 yr BP based on radiocarbon dates) are reported and analysed. Remanence directions from 37 horizons spread throughout the section have been determined, and no evidence of the geomagnetic excursion observed at Lake Mungo, Australia (˜ 31 000–28 000 yr BP), or that observed at Mono Lake, California (25 000–24 000 yr BP) is present. However, regular oscillations in the remanence vectors are observed, and maximum entropy spectral analysis, after mapping the remanence directions on to the complex plane, reveals peaks at periods of approximately 2000 and 5000 yr. The 2000-yr peak is associated with clockwise looping of the geomagnetic vector, and therefore most likely represents the time associated with one full cycle of the westward drift of the non-dipole field. The 5000-yr peak is associated with elliptical counterclockwise looping of the local geomagnetic vector and may be indicative of counterclockwise motion of the geomagnetic dipole axis.     

Palaeosecular variation and the current loop model of the geomagnetic field

Summary. The geomagnetic palaeosecular variation has been studied in terms of two current loops which change their positions and orientations with time. The results broadly agree with the observed data. Comparison with the existing models is made.     

Time series analysis of the 10 000 yr geomagnetic secular variation record from SE Australia

Summary. A 10 000 yr continuous secular variation record from intensively dated lake sediments in SE Australia has been subjected to periodogram and maximum entropy method analysis. Tests on synthetic data reveal some of the limitations of the latter method, particularly when applied to complex number series. Anticlockwise precession of the magnetic vector at a period of 5000 ± 1000 yr is tentatively ascribed to dipole precession, and clockwise precession at a period of about 2800 yr is probably due to westward drift of features of the non-dipole field.
The effect of calibrating the radiocarbon time-scale is important and results in periodicity shifts of up to 25 per cent. Even for well-dated lacustrine sequences power spectra are poorly constrained: it is thus possible that the geomagnetic secular variation on a time-scale of thousands of years is more uniform than often supposed. Mismatches between declination and inclination spectra can arise as a natural consequence of certain types of source mechanism and should not be simply attributed to figments of the analysis employed.     

The subseismic approximation in core dynamics—II. Love numbers and surface gravity

This paper extends our earlier examinations of the utility of various approximations for treating the dynamics of the Earth's liquid core on time-scales of the order of 10⁴ to 10⁸ s. We discuss the effects of representing the response of the mantle and inner core by static (versus dynamic) Love numbers, and of invoking the subseismic approximation for treating core flow, used either only in the interior of the liquid core (SSA-1) or also at the boundaries (SSA-2). The success of each approximation (or combinations thereof) is measured by comparing the resulting surface gravity effects (computed for a given earthquake excitation), and (for the Slichter mode) the distribution of translational momentum, with reference calculations in which none of these approximations is made. We conclude that for calculations of the Slichter triplet, none of the approximations is satisfactory, i.e. a full solution (using dynamic Love numbers at elastic boundaries and no core flow approximation) is required in order to avoid spurious eigenfrequencies and to yield correct eigenfunctions (e.g. conserving translational momentum) and surface gravity. For core undertones, the use of static Love numbers at rigid boundaries is acceptable, along with SSA-1 (i.e. provided the subseismic approximation is not invoked at the core boundaries). Although the calculations presented here are for a non-rotating earth model, we argue that the principal conclusions should be applicable to the rotating Earth. Shortcomings of the subseismic approximation appear to arise because both SSA-1 and SSA-2 lower the order of the governing system of differential equations (giving rise to a singular perturbation problem), and because SSA-2 overdetermines the boundary conditions (making it impossible for solutions to satisfy all continuity requirements at core boundaries).