Please use this identifier to cite or link to this item:
http://hdl.handle.net/2122/3978
DC Field | Value | Language |
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dc.contributor.authorall | Lowes, F. J.; Physics Department, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK | en |
dc.contributor.authorall | De Santis, A.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
dc.contributor.authorall | Duka, B.; Faculty of Natural Sciences, Department of Physics, University of Tirana, Tirana, Albania | en |
dc.date.accessioned | 2008-07-17T10:33:37Z | en |
dc.date.available | 2008-07-17T10:33:37Z | en |
dc.date.issued | 1995 | en |
dc.identifier.uri | http://hdl.handle.net/2122/3978 | en |
dc.description.abstract | For a vector field defined by a scalar potential outside a surface enclosing all the sources, it is well known that the potential is defined uniquely if either the potential itself, or its derivative normal to the surface, is known everywhere on the surface. For a spherical surface, the normal derivative is the radial component of the field; the horizontal (vector) component of the field also gives uniqueness (except for any monopole contribution). This paper discusses the way other partial information of the field on the spherical surface can give a unique, or almost unique, knowledge of the external potential/field, bringing together and correcting previous work. For convenience the results are given in the context of the geomagnetic field B. This is often expressed in terms of its local Cartesian components (X, Y, Z), equivalent to (-Bθ, BΦ, -Br); it can also be expressed in terms of Z and the vector horizontal component H = (X, Y). Alternatively, local "spherical polar" components (F, I, D) are used, where F = |B|, the inclination I is the angle in the vertical plane downward from H to B, and the declination D is the angle in the horizontal plane eastward from north to H. Knowledge of X over the sphere gives a complete knowledge of the potential, apart from that of any monopole (which is zero in geomagnetism), and Y gives the potential except for any axially symmetric part (which can be provided by a knowledge of X along a meridian, or of H along any path from pole to pole). In terms of (F, I, D) the situation is more complicated; either F or the total angle (I, D) needs to be known throughout a finite volume; for the latter, this paper shows how, in principle, the actual potential can be determined (except for an unknown scaling factor). Similarly D on the sphere also needs a knowledge of |H| on a line from (magnetic) pole to pole. We also discuss how these various properties affect the determination, by surface integration, of the Gauss coefficients of the field representation in terms of spherical harmonics. | en |
dc.language.iso | English | en |
dc.publisher.name | Blackwell Publishing | en |
dc.relation.ispartof | Geophysical Journal International | en |
dc.relation.ispartofseries | 2 / 121 (1995) | en |
dc.subject | geomagnetic field | en |
dc.subject | potential theory | en |
dc.subject | spherical harmonic analysis | en |
dc.subject | uniqueness | en |
dc.title | A discussion of the uniqueness of a Laplacian potential when given only partial field information on a sphere | en |
dc.type | article | en |
dc.description.status | Published | en |
dc.type.QualityControl | Peer-reviewed | en |
dc.description.pagenumber | 579-584 | en |
dc.subject.INGV | 04. Solid Earth::04.05. Geomagnetism::04.05.05. Main geomagnetic field | en |
dc.subject.INGV | 05. General::05.05. Mathematical geophysics::05.05.99. General or miscellaneous | en |
dc.relation.references | Backus, G.E., 1968. Applications of a non-linear boundary value problem for Laplace's equation to gravity and geomagnetic intensity surveys, Q. J. Mech. appl. Math., 21, 195-221. Backus, G.E., 1970. Non-uniqueness of the external geomagnetic field determined by surface intensity measurements. J. geophys. Res., 75,6339-6341. Backus, G.E., 1974. Detemination of the external geomagnetic field from intensity measurements, Geophys. Res. Lett., l, 21. Bloxham, J., 1985. Geomagnetic secular variation, PhD Thesis, Cambridge University, UK. Chapman, S. & Bartels, J., 1940. Geomagnetism, Vol II. Clarendon Press, Oxford. De Santis, A., Falcone, C. & Lowes, F.J., 1995. Remarks on the mean-square values of the geomagnetic field and its components, Annali di Geopica, submitted. Gubbins, D., 1986. Global models of the magnetic field in historical times: augmenting declination observations with archeo- and paleo-magnetic data, J. Geomagn. Geoelect., 38, 715-720, Kawasaki, K., Matsushita, S. & Cain, J.C., 1989. Least squares and integral methods for the spherical harmonic analysis of the Sq-field, Pure appl. Geophys., 131,357-370. Kono, M., 1976. Uniqueness problems in the spherical harmonic analysis of the geomagnetic field direction data, J. Geomagn. Geoelect., 28, 11-29. Langel, R.A., 1987. The main field, in Geomagnetism, Vol. I, pp 249-512, ed. Jacobs, J.A., Academic Press, London. Lowes, F.J., 1966, Mean-square values on sphere of spherical harmonic vector fields, J. geophys, Res., 7l, 2179. Lowes, F.J., 1975. Vector errors in spherical harmonic analysis of scalar data, Geophys. J. R. astr. Soc., 42, 637-651. Lucke, Q., 1957. Über Mittelwerte von Energiedichten der Kraftfelder, in Wiss. Z. der Päd. Hochschule Potsdam, Jahrgang 3, Heft l, 39-467. Proctor, M.R.E. & Gubbins, D,, 1990. Analysis of geomagnetic directional data, Geophys. J. Int., l00, 69-77. Schmidt, A., 1889. Mathematische Entwicklungen zur allgemeinen Theorie des Erdmagnetismus, in Archiv det Deuischen Seewarte, XII annual edition, no. 3, 1-29, Hamburg. Schmidt, A., 1895. Mitteilungen über eine neue Berechnung des Erdmagnetischen Potentials, Abhandl. Bayer. Akad. Wiss., 19, 1-66. Vestine, E.H., 1941. On the analysis of surface magnetic fields by integrals, Part 1, Terr. Magn. Atm. Electr., 46, 2741. | en |
dc.description.journalType | N/A or not JCR | en |
dc.description.fulltext | reserved | en |
dc.contributor.author | Lowes, F. J. | en |
dc.contributor.author | De Santis, A. | en |
dc.contributor.author | Duka, B. | en |
dc.contributor.department | Physics Department, University of Newcastle, Newcastle upon Tyne NE1 7RU, UK | en |
dc.contributor.department | Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma2, Roma, Italia | en |
dc.contributor.department | Faculty of Natural Sciences, Department of Physics, University of Tirana, Tirana, Albania | en |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.languageiso639-1 | en | - |
item.grantfulltext | restricted | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.fulltext | With Fulltext | - |
crisitem.author.dept | Physics Department, University of Newcastle Upon Tyne, NE1 7RU, U.K. | - |
crisitem.author.dept | Istituto Nazionale di Geofisica e Vulcanologia (INGV), Sezione Roma2, Roma, Italia | - |
crisitem.author.dept | Department of Physics, Faculty of Natural Sciences, University of Tirana, Albania | - |
crisitem.author.orcid | 0000-0002-3941-656X | - |
crisitem.author.orcid | 0000-0002-2014-1316 | - |
crisitem.author.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
crisitem.classification.parent | 04. Solid Earth | - |
crisitem.classification.parent | 05. General | - |
crisitem.department.parentorg | Istituto Nazionale di Geofisica e Vulcanologia | - |
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