Evaluation of geomagnetic dynamo integrals.

Winch, D. E.

doi:10.5636/jgg.26.87

Cited by 10 publications

(2 citation statements)

References 7 publications

(2 reference statements)

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“…To complete the decomposition of the induction equation, we substitute these equations into equation ( depend on Elsasser and Gaunt integrals respectively, and on the magnetic field B,. The form of these matrix elements is given by Whaler (1986) and Bloxham (1988a); Winch (1974) discusses their efficient evaluation as combinations of Wigner 3-j coefficients.…”

Section: The Inverse Problemmentioning

confidence: 99%

Simple models of fluid flow at the core surface derived from geomagnetic field models

Bloxham

1989

Geophysical Journal International

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We examine the problem of determining the fluid flow at the core surface given a model of the temporal variation of the magnetic field, seeking to fit the field over a finite time interval. The flow is assumed steady over the time interval, and we adopt the frozen-flux approximation. We produce a range of solutions of varying complexity and subject to different constraints, estimate the errors on the solutions, and assess their consistency with the underlying assumptions. We find both direct evidence for ageostrophic flow in the form of flow across the geographical equator, and indirect evidence in the form of poorer fits to the field when the flow is contained to be geostrophic. On account of this evidence we do not adopt the geostrophic approximation. However, we find that unconstrained flows are poorly determined, and consider the various alternatives for producing better determined solutions. We choose to restrict our attention to determining the large-scale toroidal part of the flow, and find a simple pattern of flow which is nearly symmetric about the equator. From a sequence of maps of the flow over 5-year time intervals back to 1915 we are still able to identify many of the basic aspects of this simple pattern, but changes in the flow pattern are discernible. Although our models of the flow explain a large proportion of the signal (typically 95 per cent of the variance), the fits which we obtain are not as good as might be expected. Failure of the underlying assumptions, together with our decision to map only the large-scale toroidal part of the flow, explains the poorer than expected fit.

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Section: The Inverse Problemmentioning

confidence: 99%

Simple models of fluid flow at the core surface derived from geomagnetic field models

Bloxham

1989

Geophysical Journal International

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“…Equations (6) Winch (1974) has expressed the Gaunt and Elsasser integrals in closed form in terms of the Wigner 3jcoefficients of quantum mechanics (Wigner 1959), and has written a FORTRAN function t o evaluate the 3-j coefficients. For the normalization of spherical harmonics he chose, the results can be relatively simply recast into Schmidt quasi-normalization recommended in geomagnetism (Winch 1974;Winch & Bamber , unpublished manuscript). Thus, the elements of the matrices E and G in (7) could be rapidly and accurately calculated using the supplied FORTRAN function, with published values of the spherical harmonic coefficients of the main field.…”

Section: Stochastic Inversion For Velocity Coefficientsmentioning

confidence: 99%

Geomagnetic evidence for fluid upwelling at the core-mantle boundary

Whaler

1986

Geophysical Journal International

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Previous studies, both geomagnetic and seismic, have been unable to show conclusively whether or not there is fluid upwelling at the coremantle boundary. Here a new method is developed, in which an attempt is made to invert geomagnetic secular variation data measured at the Earth's surface for a frozen-flux purely toroidal core-mantle boundary (CMB) velocity field, under the assumption that the mantle is electrically insulating and flux is frozen in at the CMB. These data have previously been inverted for the core-mantle boundary radial secular variation, from which the appropriate fit between model and data is known. Two different main field models were used t o assess the effect of uncertainty in its radial component at the CMB. The conclusions were the same in both cases: frozen-flux purely toroidal motions provide a poor fit. A statistical test allows very firm rejection of the hypothesis that the residuals are not significantly larger, whereas there is no statistical difference between the residuals of inversions for radial secular variation and frozen-flux velocity fields at the CMB if upwelling and downwelling is included. The inherent non-uniqueness in the velocity field obtained is not of concern, since only their statistical properties are utilized and no physical significance is attached to the flows obtained.

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The determination of fluid flow at the core surface from geomagnetic observations

Bloxham

1988

Mathematical Geophysics

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Evaluation of geomagnetic dynamo integrals.

Cited by 10 publications

References 7 publications

Simple models of fluid flow at the core surface derived from geomagnetic field models

Simple models of fluid flow at the core surface derived from geomagnetic field models

Geomagnetic evidence for fluid upwelling at the core-mantle boundary

The determination of fluid flow at the core surface from geomagnetic observations

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