Eccentric dipoles and spherical harmonic analysis

Hurwitz, Louis

doi:10.1029/jz065i008p02555

Cited by 46 publications

(22 citation statements)

References 3 publications

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“…Notice that the second degree harmonic term is relatively low if a straight line were to be drawn through the lower degree harmonics. The straight line is the best fit to the power spectrum derived by LANGEL and ESTES (1982) from data collected by MAGSAT. BENTON and ALLDREDGE (1987) investigated the depths of dipole sources which give the correct power spectrum, but instead of using the Lowes-Mauersberger function, they used a function in which the plot of log(power) versus degree of harmonic is a straight line.…”

Section: Dipole and Current Loop Modelsmentioning

confidence: 99%

“…Rather than using the general statement of BULLARD (1967) concerning the wavelength represented by each degree of harmonic, it is possible to calculate directly the effect of moving a core surface source at a certain rate. HURWITZ (1960) has shown how to calculate the spherical harmonic coefficients of an offset dipole located at an arbitrary position and pointing in an arbitrary direction. It has been assumed here that the off centered dipole is vertical.…”

Section: Tn Prementioning

confidence: 99%

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An Alternative Picture of the Geomagnetic Field.

Harrison

1994

J. geomagn. geoelec

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Spherical harmonic models of the Earth's magnetic field are a convenient way of describing the characteristics of the field. It has been common practice to use the Lowes/Mauersberger function to describe the power of the field in each degree of harmonic. There are several characteristics of this power spectrum which are well known from recent analyses of the geomagnetic field. Firstly, there is a general decrease of power as the degree of harmonic is increased. This general pattern is that the power varies as a function of a constant raised to the power n where n is the degree of the harmonic. However, there are some exceptions to this rule of thumb. Firstly, the dipole term (n = 1) is higher than expected. Secondly, the degree two term is lower than expected. Thirdly, the degree eight term is lower than expected. Although these facts might be considered to be just a 'chance happening, characteristic of today's field but not of other fields, it is shown that these characteristics are true for the last 200 years, during which time both the degree two and the degree eight individual harmonic terms change drastically. It is therefore suggested that these patterns represent a more permanent feature of the field, which may be caused by the sources approximating current loops located close to the core-mantle boundary (CMB). Another interesting fact about the spherical harmonic analyses of the field over the past 200 years is that the low order harmonics tend to be significantly stronger than the high order harmonics. This probably reflects sources which are preferentially located at higher latitudes, or are stronger at higher latitudes than at lower latitudes. The rates of change ofthe field are also studied, and it is shown that these rates of change are similar to what might be expected if the foci of the field at the CMB moved without changing their strength greatly. These simple observations based on analysis of the Gauss coefficients give information which may be useful for dynamo theories of Earth's magnetic field.

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Section: Dipole and Current Loop Modelsmentioning

confidence: 99%

Section: Tn Prementioning

confidence: 99%

An Alternative Picture of the Geomagnetic Field.

Harrison

1994

J. geomagn. geoelec

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“…The spherical harmonic representation of a given dipole distribution may be expressed in closed form for comparison with standard spherical harmonic field and a spatial position (1) Similar expressions were presented by HURWITZ (1960). The coefficients may be calculated up to any order.…”

Section: Introductionmentioning

confidence: 99%

Equivalent source modeling of the core magnetic field using magsat data.

Mayhew

Estes

1983

J. geomagn. geoelec

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An iterative least squares estimation algorithm with the capability for including a priori statistical information has been implemented to recover multiple magnetic dipole models of the Earth's main magnetic field. The dipoles are fixed to a specified radius at or below the core-mantle boundary and centered on equal area blocks. The algorithm can solve for dipole magnitudes only (fixed orientations), or allow full freedom of orientation and solve for vector components. First-order external field parameters can be estimated simultaneously, as well as magnetic observatory biases when observatory annual means data is used. Secular variation is modeled by making the dipole components linear functions of time. Single-epoch and time dependent dipole models are derived using Magsat and observatory annual means data. Equivalent spherical harmonic representations are computed in closed form from the dipole models for comparison with truncated spherical harmonic models estimated in the standard way from the same data sets. A model consisting of 93 dipoles arranged 1977 and a selected Magsat data set and is compared with candidate IGRF 1975 models and their 1984 secular variation. The equivalent dipole source representation is shown to be comparable to the standard spherical harmonic approach in accuracy and, for high resolution models, to be superior in computational efficiency for field model evaluation when three degree-of-freedom dipoles (i.e., unconstrained by direction) are utilized. Fixing of the dipole positions results in rapid convergence of the dipole solutions for single-epoch models. For time-dependent models, a sufficiently long time interval of data or a priori values and statistics must be available for the derivatives to achieve convergence. In contrast to spherical harmonic models incorporating secular variation parameters based on the same data, the correlation structure of dipole magnetic moment derivatives with the constant magnetic moment parameters is small, indicating the ability to strongly separate the constant field and the secular variation.

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“…1, is the longitude of the element dA. According to HURWITZ (1960) this differential dipole will produce a potential at P of dWr(r,0,A)=a-(dgm cos mA+dhn sin mA)Pm(cos 0)…”

Section: Shc Of Circular Current Loopsmentioning

confidence: 99%

Circular Current Loops, Magnetic Dipoles and Spherical Harmonic Analyses

Alldredge

1980

J. geomagn. geoelec

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Eccentric dipoles and spherical harmonic analysis

Cited by 46 publications

References 3 publications

An Alternative Picture of the Geomagnetic Field.

An Alternative Picture of the Geomagnetic Field.

Equivalent source modeling of the core magnetic field using magsat data.

Circular Current Loops, Magnetic Dipoles and Spherical Harmonic Analyses

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