A. T. Price

Bio: A. T. Price is an academic researcher. The author has contributed to research in topics: Magnetic field & Field (physics). The author has an hindex of 2, co-authored 2 publications receiving 96 citations.

The Electric and Magnetic State of the Interior of the Earth, as Inferred from Terrestrial Magnetic Variations

Abstract: 1.1. By spherical harmonic analysis it is possible, as was shown by GAUSS, to distinguish between the parts of the earth’s magnetic field, at any time, which originate respectively within and above the earth’s surface. In this way GAUSS confirmed and extended GILBERT’s conclusion that the field is almost entirely of internal origin. 1.2. Sir ARTHUR SCHUSTER applied the method to the field of the daily magnetic variation at the earth’s surface, and found that the major part is of external origin, but that there is also a part produced within the earth. He attributed the latter to electric currents induced in the earth by the outer varying field, which he regarded as primary. In co-operation with Prof. H. LAMB he showed that the relation between the two parts of the field is consistent with this hypothesis ; the calculations referred to currents induced in a uniformly conducting sphere. They showed that the conducting sphere must be distinctly smaller than the earth, that is, it is an inner core, and not the whole earth, which is effective.

On Line-Integrals of the Diurnal Magnetic Variations

Abstract: 1. According to electromagnetic theory, the line-integral ∫ H . ds of the magnetic force H taken round any closed curve is equal to 4πI, where I is the electric current threading the curve, H and I being measured in c.g.s. units. Such line-integrals have been calculated by Gauss and many later investigators for various curves on the earth’s surface, in order to determine whether any electric current flows upwards or downwards across the surface. Modern computations for large areas lead in general to values of ∫ H . ds differing from zero by amounts that correspond to current-densities of the order 3·10-2 ampere/km.2. The magnetic field of such currents would account for 2 or 3 per cent, of the earth’s surface field. These results are inconsistent with the direct measurements of the atmospheric electric potential gradient and the ionisation of the air, which indicate a verticalcurrent-density of the order 3·10-6 amp./km.2. If the magnetic estimates are reliable, the discrepancy indicates either that atmospheric electric currents exist which escape measurement, though they are 10,000 times as great as those which are measured, or that the relation ∫ H . ds = 4πI, which is one of the foundations of electromagnetic theory, is not strictly correct. These alternatives are so remarkable that the magnetic evidence must be above suspicion if it is to gain credence. Dr. L. A. Bauer holds that the results got from independent sets of data, for different epochs, and the mutual accordance of the results from neighbouring areas, justify the acceptance of the non-zero line-integrals, and that to explain them away it is necessary to assume quite unlikely systematic errors in the magnetic data. Other investigators show less conviction: for example, Sir Frank Dyson and H. Furner conclude that “though there is some evidence for Prof. Bauer’s results, the existence of vertical electric currents is not indicated with any great certainty.” But though the magnetic evidence may not be conclusive, it cannot be lightly dismissed, and in view of the importance of the question Sir Arthur Schuster has recently urged the desirability of a detailed magnetic survey of a small area as the best means of obtaining a definite conclusion.

Geomagnetic Variations and the Electrical Conductivity of the Upper Mantle

Abstract: Summary The electrical conductivity of the upper mantle can be determined by comparing the measured response of the Earth to magnetic variations of all frequencies with the theoretical response of particular conductivity distributions. On the basis of a limited amount of data the response has been estimated at frequencies in the range 0.003 to 0.25 c day−1. In this range of the geomagnetic spectrum, line spectra at frequencies of 1 and 2 c yr−1 and 1, 2, and 3 cycles per 27 days can be used. Investigations of the continuum spectrum show that it also occurs on a worldwide scale, and must correspond to a real geophysical process. Meaningful estimates of the response can therefore be made over the whole of the frequency range considered. The entire magnetic variation spectrum in the range 2 c yr−1 to 0.25 c day−1 appears to be generated by fluctuations in the strength of the ring current, and a P10 spherical harmonic adequately describes the variation of the magnetic field over the surface of the Earth.

The theory of magnetotelluric methods when the source field is considered

Abstract: The theory of the relationship between the tangential components of E and H for geomagnetic fluctuations over a stratified earth is extended to take account of the distribution of the ionospheric inducing field. It is shown that Cagniard's simple formulas on which magnetotelluric methods are generally based need modification to take account of the dimensions of this field. This is so even when the inducing field is much more extensive than the region under consideration and when the depth of the probe is quite moderate. It is further shown that, for deep probing, magnetotelluric methods can be satisfactorily applied only if an analysis of the field over a region having dimensions comparable with those of the inducing field is first made. The relation between these methods and the earlier methods of determining the conductivity distribution from analyses of the components of the surface magnetic field is discussed. The evaluation of the amplitude and phase relations of E and H over the oceans is also discussed, and it is shown that some results obtained recently by Fonarev need extending and amending.

The electrical conductivity of the mantle beneath Europe derived from C-responses from 3 to 720 hr

Abstract: SUMMARY The C-response, which connects the magnetic vertical component and the horizontal gradient of the horizontal components of electromagnetic fluctuations, forms the basis for estimating the conductivity‐depth profile of the Earth. This paper describes new estimates of the C-response obtained from observatory hourly mean values. The Z: Y-method is applied, which means that the vertical component is used locally whereas the horizontal components are used globally by expansion into terms of spherical harmonics. A special eVort is made to obtain unbiased estimates of C. When applied to 90 months of hourly mean values from about 90 observatories, the method yields consistent results for European observatories in the entire period range from 3 to 720 hr, and for two diVerent source mechanisms (S and D st ). A good description of the source structure for individual time segments is essential. This was achieved by a separate spherical harmonic analysis of the data for each month (for D st ) or each day (for S), and by estimating a large number (120) of expansion coeYcients. The results are interpreted by means of 1-D conductivity models, which show that the upper mantle has remarkably little structure, with a monotonic decrease of resistivity from 100 V m near z=200 km to 0.7 V m below z=1000 km.

Penetration of the geomagnetic secular field through a mantle with variable conductivity

Abstract: The work reported on here is an investigation of the radial distribution of electrical conductivity σ in the earth's mantle. Previously this function had been inferred only to about the 800-km depth from the geomagnetic transient variations of external origin (see Lahiri and Price). Throughout the remaining lower portion of the mantle, we make use here of the longer wave periods which characterize the geomagnetic secular variation. Choosing a power law for σ, the wave attenuation and phase retardation after propagation through the mantle are investigated, using sinusoidal input functions, and an equivalent conductivity is established on the basis of amplitude attenuation. Aperiodic models at the core are solved by the method of Laplace transforms and a time discontinuity in Hr. (δ-function in Hr) is treated in detail. The elapsed time for a pulse to reach the earth's surface is expressed in terms of an equivalent conductivity. The latter quantity is then gotten indirectly from a study of the time-dependent magnetic observatory records. Judged somewhat better than an order of magnitude, in these calculations, σ is shown plotted throughout the mantle.

Large‐scale, near‐field magnetic fields from external sources and the corresponding induced internal field

Abstract: Data from MAGSAT analyzed as a function of the Dst index to determine the first degree/order spherical harmonic description of the near-Earth external field and its corresponding induced field. The analysis was done separately for data from dawn and dusk. The MAGSAT data was compared with POGO data. A local time variation of the external field persists even during very quiet magnetic conditions; both a diurnal and 8-hour period are present. A crude estimate of Sq current in the 45 deg geomagnetic latitude range is obtained for 1966 to 1970. The current strength, located in the ionosphere and induced in the Earth, is typical of earlier determinations from surface data, although its maximum is displaced in local time from previous results.