Understanding models of the geomagnetic field by Fourier analysis.

Wang, Zhigang

doi:10.5636/jgg.39.333

Cited by 8 publications

(5 citation statements)

References 15 publications

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“…Even a small surface anomaly will contain weak low degree components as shown by Wang [1987]. Indeed, Meyer et al [1983], using very rough estimates of susceptibilities for Earth, generated a fairly flat spectrum that tailed off but was still extant at low degree.…”

Section: Model Resultsmentioning

confidence: 99%

An n = 90 internal potential function of the Martian crustal magnetic field

2003

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[1] A potential function using spherical harmonics up to degree and order 90 was derived from a selection of Mars Global Surveyor vector data. These included all three components of those taken below 200 km altitude during the two aerobraking phases (AB1 and AB2), the Science Phase Orbits (SPO), and the higher-altitude (367-435 km) data taken on the nightside during the Mapping Phase Orbits (MPO). The merger of these sets of data provided total global coverage. The technique used was a least squares minimization developed for Earth field analysis whereby the relative weighting of each data source was determined by the width of a Gaussian fit to the residual distribution about the potential function. Also, data selection by area and area weight functions were used to improve normalization. The residual misfit distributions for the vertical component for different data sources are (nT) AB1, 6.5; AB2 (in shadow), 6.7; AB2 (sunlit), 10.3; SPO, 6.4; and MPO, 5.9. The horizontal component misfits are about the same for MPO and AB2 in shadow, but for data taken in sunlight the scatter of horizontal component residuals increases by 50% for AB1, a factor of two for SPO, and 30% for AB2. The energy density spectrum evaluated at 3535 km radius (the mean altitude of the AB and SPO data) decreased from a high of 0.2 J/km 3 near n = 20 to an order of magnitude less at n = 90. Most of the power in the spectrum lies between n = 15 and n = 40. The dipole moment was only 8 Â 10 16 A Á m 2 , which is likely close to the noise of the coefficients. This spectrum is 40 times greater than that of Earth at the scale sizes represented by values of n from 20 to 40. Comparisons with other published maps and models for Mars show general agreement with the field representations at MPO altitudes, but disagreements up to several hundred nT in components calculated for areodetic altitudes below 200 km.

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Section: Model Resultsmentioning

confidence: 99%

An n = 90 internal potential function of the Martian crustal magnetic field

2003

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“…that spectrum derived from the sum squares of spherical harmonics so as to compute the energy density function) is the one useful for separation of the core and crustal components. Wang (1987) recently clarified these issues, and showed that it is not possible to make such a separation by filtering track lines, even of observations of a single vector component. Alldredge & Benton (1986) also discussed the subject.…”

Section: -mentioning

confidence: 99%

The Geomagnetic Spectrum For 1980 and Core-Crustal Separation

Cain¹,

Wang

Schmitz

et al. 1989

Geophysical Journal International

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The spectrum of a high degree spherical harmonic model of the geomagnetic field is analysed to compute the constants for the core and crustal field contributions. Using a noise estimate of 0.091 nT2 at the mean Magsat radius of 6791 km, the power reduced to the Earth's surface is found to be 9.66 X 10' (0.286)" nT2 for the core, and 19.1 (0.996)" nT2 for the crust. These values show half the crustal power extrapolated to n = 0 compared with a previously published n = 23 model, and a white noise depth of only 14 km below the mean surface. The core spectrum power is 30 per cent less than previously estimated and becomes flat 80 km below the core-mantle boundary. The crustal power level is an eighth of that of an estimate based on one-dimensional analyses of Project MAGNET survey lines. The point where the energy density of the core and crustal components become equal at the Earth's surface is n = 14.2.

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“…4.4 for a review). We do not discuss these approaches but refer to Wang (1987) for an overview of the issues raised by Fourier analysis along circular profiles. We focus instead on the SH analysis along the satellite orbits because it is apparently physically convincing for global studies of a planetary magnetic field outside the sources.…”

Section: Definitions and Hypotheses Of The Along‐track Analysismentioning

confidence: 99%

The satellite along-track analysis in planetary magnetism

Thébault

Vervelidou

Lesur

et al. 2011

Geophysical Journal International

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S U M M A R YMany physical characteristics of planets, such as their topography, magnetic and gravitational fields, are routinely detected and measured by spacecrafts. At satellite altitudes, even if little is known about the measured signal, it is possible to separate the large-scale components from other contributions by a spectral analysis carried out along the spacecraft orbit. This procedure, which dates back to the early age of the satellite era, is routinely applied with spherical harmonics analysis for the study of large-scale planetary magnetic fields, particularly those that vary rapidly in time. In this paper, we review the approximations of this procedure for investigating internal and external magnetic fields of planets. We show that the magnetic field analyses along the orbits are limited by a finite frequency resolution that is known to introduce a spectral leakage. This leakage may lead to artificial spatio-temporal variations of the magnetic field, such as an apparent internal field secular variation, an asymmetry of the magnetospheric field and a regional distortion of the lithospheric field structures. We quantify the errors for the Earth's lithospheric field and display its distribution in the spatial and the spectral domains. We also discuss these limits for the Moon and Mars lithospheric magnetic fields. Our analytical results illustrate the pros and cons of the orbit-by-orbit analyses and should allow us to avoid the pitfall of geophysical overinterpretation of some artificial magnetic field variations.

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Understanding models of the geomagnetic field by Fourier analysis.

Cited by 8 publications

References 15 publications

An n = 90 internal potential function of the Martian crustal magnetic field

An n = 90 internal potential function of the Martian crustal magnetic field

The Geomagnetic Spectrum For 1980 and Core-Crustal Separation

The satellite along-track analysis in planetary magnetism

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