### Abstract

Motivated by the high degree of correlation between the variable parts of the magnetic and gravitational potentials of the Earth discovered by Hide and Malin (using a harmonic analysis approach and utilizing the geomagnetic data) when one field is suitably displaced relative to the other, Moffatt and Dillon (1976) studied a simple planar model in an attempt to find a quantitative explanation for the suggestion that this high degree of correlation may be due to the influences produced by bumps on the core-mantle interface. Moffatt and Dillon assumed that the core-mantle interface was z = η(x) where |∂η/∂χ| ≪ 1 and such that in the core [z <η(x)] a uniform flow (U_{0}, 0, 0) prevails in the presence of a uniform 'toroidal' field (B_{0}, 0, 0); (here z is the vertical coordinate and x is the eastward distance). The whole system rotates uniformly about the vertical with angular velocity Ω. The present work extends the model discussed by Moffatt and Dillon to include a horizontal component of angular velocity Ω_{H} and a uniform small poloidal field B_{p}. In addition, the uniform toroidal field is here replaced by one which vanishes everywhere in the mantle and increases linearly, from zero on the interface, with z. It is shown that the presence of Ω_{H} and B_{p}, together with the present choice of toroidal magnetic field, has a profound effect both on the correlation between the variable parts of the magnetic and gravitational fields of the Earth, and on how far the disturbances caused by the topography of the interface [which is necessarily three-dimensional i.e. z = η(x, y) here] can penetrate into the liquid core. In particular it is found that the highest value of the correlation function is +0.79 which corresponds to a situation in which the magnetic potential is displaced both latitudinally and longitudinally relative to the gravitational potential.

Original language | English |
---|---|

Pages (from-to) | 239-254 |

Number of pages | 16 |

Journal | Physics of the Earth and Planetary Interiors |

Volume | 19 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1979 |

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### ASJC Scopus subject areas

- Geophysics
- Space and Planetary Science
- Physics and Astronomy (miscellaneous)
- Astronomy and Astrophysics

### Cite this

*Physics of the Earth and Planetary Interiors*,

*19*(3), 239-254. https://doi.org/10.1016/0031-9201(79)90025-6

**On the effects of a bumpy core-mantle interface.** / Eltayeb, I. A.; Hassan, M. H A.

Research output: Contribution to journal › Article

*Physics of the Earth and Planetary Interiors*, vol. 19, no. 3, pp. 239-254. https://doi.org/10.1016/0031-9201(79)90025-6

}

TY - JOUR

T1 - On the effects of a bumpy core-mantle interface

AU - Eltayeb, I. A.

AU - Hassan, M. H A

PY - 1979

Y1 - 1979

N2 - Motivated by the high degree of correlation between the variable parts of the magnetic and gravitational potentials of the Earth discovered by Hide and Malin (using a harmonic analysis approach and utilizing the geomagnetic data) when one field is suitably displaced relative to the other, Moffatt and Dillon (1976) studied a simple planar model in an attempt to find a quantitative explanation for the suggestion that this high degree of correlation may be due to the influences produced by bumps on the core-mantle interface. Moffatt and Dillon assumed that the core-mantle interface was z = η(x) where |∂η/∂χ| ≪ 1 and such that in the core [z <η(x)] a uniform flow (U0, 0, 0) prevails in the presence of a uniform 'toroidal' field (B0, 0, 0); (here z is the vertical coordinate and x is the eastward distance). The whole system rotates uniformly about the vertical with angular velocity Ω. The present work extends the model discussed by Moffatt and Dillon to include a horizontal component of angular velocity ΩH and a uniform small poloidal field Bp. In addition, the uniform toroidal field is here replaced by one which vanishes everywhere in the mantle and increases linearly, from zero on the interface, with z. It is shown that the presence of ΩH and Bp, together with the present choice of toroidal magnetic field, has a profound effect both on the correlation between the variable parts of the magnetic and gravitational fields of the Earth, and on how far the disturbances caused by the topography of the interface [which is necessarily three-dimensional i.e. z = η(x, y) here] can penetrate into the liquid core. In particular it is found that the highest value of the correlation function is +0.79 which corresponds to a situation in which the magnetic potential is displaced both latitudinally and longitudinally relative to the gravitational potential.

AB - Motivated by the high degree of correlation between the variable parts of the magnetic and gravitational potentials of the Earth discovered by Hide and Malin (using a harmonic analysis approach and utilizing the geomagnetic data) when one field is suitably displaced relative to the other, Moffatt and Dillon (1976) studied a simple planar model in an attempt to find a quantitative explanation for the suggestion that this high degree of correlation may be due to the influences produced by bumps on the core-mantle interface. Moffatt and Dillon assumed that the core-mantle interface was z = η(x) where |∂η/∂χ| ≪ 1 and such that in the core [z <η(x)] a uniform flow (U0, 0, 0) prevails in the presence of a uniform 'toroidal' field (B0, 0, 0); (here z is the vertical coordinate and x is the eastward distance). The whole system rotates uniformly about the vertical with angular velocity Ω. The present work extends the model discussed by Moffatt and Dillon to include a horizontal component of angular velocity ΩH and a uniform small poloidal field Bp. In addition, the uniform toroidal field is here replaced by one which vanishes everywhere in the mantle and increases linearly, from zero on the interface, with z. It is shown that the presence of ΩH and Bp, together with the present choice of toroidal magnetic field, has a profound effect both on the correlation between the variable parts of the magnetic and gravitational fields of the Earth, and on how far the disturbances caused by the topography of the interface [which is necessarily three-dimensional i.e. z = η(x, y) here] can penetrate into the liquid core. In particular it is found that the highest value of the correlation function is +0.79 which corresponds to a situation in which the magnetic potential is displaced both latitudinally and longitudinally relative to the gravitational potential.

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U2 - 10.1016/0031-9201(79)90025-6

DO - 10.1016/0031-9201(79)90025-6

M3 - Article

VL - 19

SP - 239

EP - 254

JO - Physics of the Earth and Planetary Interiors

JF - Physics of the Earth and Planetary Interiors

SN - 0031-9201

IS - 3

ER -