Radiocarbon ages have been published for nine basaltic lava flows on the island of Hawaii; the ages range from 2600 to somewhat older than 17,900 years B.P. By using the Thelliers' method in vacuum, geomagnetic paleointensity values were obtained from eight of the lavas; the ninth proved unsuitable. The paleointensities for the four youngest flows (2600–4600 years B.P.) yield virtual dipole moments (VDM's) that are 20% greater to more than twice the worldwide values for those times obtained by V. Bucha from archeomagnetic data. The dispersion of virtual geomagnetic poles for the eight lavas is 15.5°, appreciably larger than the average for older lava flows on Hawaii. These results contrast with the historic magnetic field in the region of Hawaii, in which both secular variation and nondipole components are very low. At about 10,000 years B.P. the measured VDM is not very different from the long-term worldwide average but differs considerably from a smooth extrapolation of Bucha's average curve. At about 18,000 years B.P. the measured VDM is very low and is associated with an unusually shallow paleomagnetic inclination for the latitude of Hawaii. These new paleointensity and paleodirectional data strongly suggest that sizable nondipole geomagnetic fields have existed in the vicinity of Hawaii at various times during the Holocene epoch and perhaps earlier.

Geomagnetic paleointensities from radiocarbon‐dated lava flows on Hawaii and the question of the Pacific nondipole low

As part of a comprehensive, nationwide evaluation of geothermal resources for Japan, the first of the Curie point depth maps, covering the island of Kyushu, has been prepared. The map was created by inverting gridded, regional aeromagnetic data. Two satisfactory algorithms were developed to invert the gridded data based upon a distribution of point dipoles. The first algorithm estimates x0,y0, and z0, the coordinates of the centroid of the distribution, by computing a least‐squares fit to the radial frequency of the Fourier transform; the second algorithm estimates centroid depth only by computing a least‐squares fit to the squared amplitude of the frequency estimates. The average depth to the top, zt of the collection of point dipoles, was estimated by a variation of the second algorithm. The depth to the bottom of the dipoles, inferred Curie point depth, is zb=2z0-zt. The depth estimates are hand contoured to produce the final map. The Curie point depth map is then compared to regional geology and heat ...

Curie point depths of the Island of Kyushu and surrounding areas, Japan

Summary

The spatial ‘power’ spectrum of the main geomagnetic field has been estimated for harmonics up to n= 500. It is shown to consist of two components, long wavelengths being dominated by fields originating in the core, and short wavelengths by fields originating in the crust; the cross-over occurs at n≥ 11, a wavelength ≤ 3600 km.



The core field is often approximated by a set of spherical harmonic coefficients. It is shown that at present main field coefficients for n≤ 9, and secular variation coefficients for n≤ 6, are not known with significant accuracy. Estimates are made of the standard deviations of the IGRF coefficients, and the standard deviation of the IGRF field deduced. This field is known to about 0.5 per cent at the surface but only to about 10 per cent at the core. Its time variation is known only to about 20 per cent at the surface, and is very uncertain at the core.

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Spatial Power Spectrum of the Main Geomagnetic Field, and Extrapolation to the Core

Variations in the lengths of geomagnetic polarity, intervals are analyzed by means of a probability model based on the theory of Bernouli trials. Polarity reversals are assumed to occur as the result of the interaction between steady oscillations of the geomagnetic dipole and secular variations of the nondipole field. The particular cycle on which a polarity inversion occurs is determined by the magnitude of the nondipole field, which is assumed to vary randomly and independently of dipole variations. The reversal properties of the geomagnetic dynamo are characterized by the single parameter p, the probability that a polarity inversion will occur during one cycle of change in the geomagnetic dipole moment. From an analysis of polarity changes during the past 10 m.y., the value of p is estimated to be 0.05. During the Permian period, it was at least two orders of magnitude smaller. The analysis suggests that within the past 10 m.y. there have occurred hitherto undiscovered short geomagnetic polarity events with durations shorter than 0.05 m.y.

Lengths of geomagnetic polarity intervals

A spherical harmonic model of the earth's internal magnetic field of degree and order 23 is derived from selected Magsat data, and its power spectrum, computed with terms developed by Mauersberger (1956) and Lowes (1974), is found to exhibit a change of a slope at n = 14 which is interpreted as an indication that the core field dominates at values lower than 13 while the crust field dominates above a value of 15. The representations of the two portions of the spectrum obtained can be used to establish order-of-magnitude inaccuracies due to both crustal fields and the inability to observe core field wavelengths beyond n = 13, at which point they are obscured by the crustal field, in core field models.

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A geomagnetic field spectrum

An around-the-world profile of magnetic total field intensity has been analyzed. Local anomalies are almost totally absent from Lisbon through the Mediterranean Sea, across the Arabian peninsula, and along the coast of the Arabian Sea to Bombay. Magnetic sources appear to be shallow across the entire Pacific Ocean and in the vicinity of the mid-Atlantic ridge. The major sources under continental areas are much deeper. The Fourier coefficients decrease in amplitude very rapidly up to order 7; beyond that, the envelope of the coefficients slowly decreases, reaching a magnitude of approximately 1 γ at the 2000th harmonic. The harmonics are summed according to fixed wavelength-width intervals. This results in a bimodal distribution indicating crustal sources and core sources. If the single around-the-world profile studied here is typical of all great-circle profiles, it is concluded that spherical harmonic coefficients of order and degree greater than 10 are probably not required to describe the main part of the earth's field to within limits acceptable for world charts.

A magnetic profile around the world

It is assumed that magnetic dipoles are useful as a first approximation to the electrical currents in the core that produce the earth's main magnetic field. For simplicity the model is restricted to a central dipole and several additional radial dipoles at equal distances from the center of the earth. A least-squares method is used to adjust the amplitude, latitude, and longitude of each dipole for a best fit to the observed field components on the earth's surface. In the first of four studies the observed field was the field of the United States 1945 world charts. Originally 11 dipoles, 10 of them at the core-mantle interface at 0.54 earth radii, were used. Progressively better fits were obtained as the dipoles were placed deeper, and two of the dipoles were eliminated at greater depths. The 29-parameter, 9-dipole model, with the radial dipoles at 0.28 earth radii, produced nearly as good a fit to the 1945 field as Vestine's 48 spherical harmonic coefficients. Models were also fitted to the United States 1955 world chart field, to the British Admiralty 1955 world chart field, and to the field synthesized from the Finch-Leaton spherical harmonic coefficients for 1955. The last model produced the best fit.

In all cases the radial dipoles are surprisingly deep and the central dipole is considerably stronger than the centered dipole given by the first three spherical harmonic coefficients. The great depth of the radial dipoles is qualitatively explained by a shielding effect from currents in the mantle and core. The spherical harmonic coefficients from the analyses of Vestine and of Finch and Leaton are compared with the spherical harmonic coefficients computed from the dipole parameters.

Radial dipoles as the sources of the Earth's main magnetic field

An automatic standard magnetic observatory (ASMO) has been built and operated with excellent results. The observatory uses a rubidium total field-intensity detector. The detector is placed at the center of two mutually perpendicular pairs of coils which control bias fields in a plane perpendicular to the mean magnetic field vector. Use of the bias fields permits a determination of the magnetic components. A preliminary calibration procedure involving reversals of the bias fields and a mechanical rotation of the coil system eliminates uncertainties in coil geometry. Measurements are automatically recorded in digital form so that the precise value of each magnetic component and all of the usual statistical analyses can be computed automatically. Tests made so far indicate that the statistical results from the new observatory are at least as accurate as those from normal observatories. Having the data in digital form simplifies subsequent analysis of the data for research purposes.

An automatic standard magnetic observatory

The characteristics of several long magnetic total field intensity profiles have been determined. Only track lines which were nearly straight and longer than 2000 miles were considered. First, the centered dipole field total intensity was subtracted from the measured total intensity to obtain a real nondipole field. A smooth curve was then drawn through this nondipole field using a stiff spline curve. The distance between crossover points of the smooth field and the nondipole field was determined and a histogram of the results plotted. The results confirm the earlier results of Serson and Hannaford that most of the anomalies have a very short wavelength. Ninety-three per cent of the cases had crossover distances less than 60 nautical miles. The simple form of the smooth curves indicated a nearly sinusoidal departure from a dipole field having crossover points between 2100 and 5200 nautical miles.

The most natural unforced explanation of the above results is that short-wavelength anomalies are due to crustal effects and the long-wavelength anomalies are due to causes within the core of the earth. The large gap between the short- and long-wavelength groupings supports the hypothesis that the mantle is a forbidden region for magnetic sources. This conclusion is illustrated by calculations based on simple models.

Depth to sources of magnetic anomalies

Characteristics of the geomagnetic field are shown by plotting equivalent current functions J on successively deeper spherical surfaces within the earth. As the depth increases, the amplification of the higher-order spherical harmonic terms increases, so that, in effect, higher-order terms successively are brought into focus. Maps of J reveal that negative extrema of J are much more prominent than positive extrema and are equally so in the northern and southern hemispheres. Coriolis forces are surely important in the generation of the earth's magnetic field. Since the Coriolis forces are of opposite sign in the northern and southern hemispheres, we have to seek a second factor that changes sign between the two hemispheres. It is suggested that this factor implies a general circulation pattern in the core that is antisymmetric between the two hemispheres.

Leroy R. Alldredge

Papers

A magnetic profile around the world

Radial dipoles as the sources of the Earth's main magnetic field

An automatic standard magnetic observatory

Depth to sources of magnetic anomalies

A peculiar property of the geomagnetic field