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  • 1
    Electronic Resource
    Electronic Resource
    Optimized kinematic dynamos (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 124 (1996), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: A numerical optimization approach is introduced to the subject of dynamo theory. Conventional kinematic dynamo studies treat the induction equation as an eigenvalue problem by choosing a candidate velocity field and solving for a marginally stable solution of magnetic field and critical magnetic Reynolds number. The conventional approach has told us something about dynamo action and magnetic field morphology for specific velocities, but the arbitrary choice of fluid flow is a hit-or-miss affair; not all velocities sustain dynamo action, and of those that do, few yield mathematically tractable solutions. As a result, progress has been slow. Here we adopt a new approach, a non-linear numerical variational approach, which allows us to solve the induction equation simultaneously for both the magnetic field and the velocity field. The induction equation is discretized following the Bullard-Gellman formalism and the resulting algebraic equations solved by an iterative, globally convergent, Newton-Raphson method. The particular choice of optimization constraints allows one to design a dynamo which satisfies certain conditions; in this paper we minimize a linear combination of the kinetic energy (magnetic Reynolds number) and a smoothness norm on the magnetic field to produce efficient (low magnetic Reynolds number) well-converged (smooth magnetic field) solutions. We illustrate the optimization method by designing two dynamos based on a Kumar-Roberts velocity parametrization; a specific choice of the velocity parameters, KR, sustains a 3-D kinematic model of the geodynamo. Compared with KR, one of our new models, LG1, is designed to have a higher magnetic Reynolds number but smoother magnetic field, and the other, LG2, a lower magnetic Reynolds number and somewhat rougher magnetic field. We suggest that dynamo efficiency, defined by the magnetic Reynolds number, is achieved through reduced differential rotation and a favourable spatial distribution of the helicity. These examples demonstrate the value of the optimization method as a tool for exploring dynamo action with geophysically realistic flows. It can be extended to the dynamic dynamo problem and, by changing the constraints, be used to design dynamos with good numerical convergence, which match the observed geomagnetic surface field morphology and which place useful quantitative constraints on the physical nature of the geodynamo.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1996.tb05638.x
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  • 2
    Electronic Resource
    Electronic Resource
    Geomagnetic field analysis—V. Determining steady core-surface flows directly from geomagnetic observations (1995)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 122 (1995), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Geomagnetic secular variation is a result of inductive effects of fluid motion at the top of the Earth's liquid core, which can be mapped using the frozen-flux approximation and inverting mathematical models of the secular variation. Non-uniqueness may be removed by assuming the flow to be stationary. The use of an intermediate mathematical model of secular variation makes comparison of the derived models with observation unsatisfactory, and here we devise a new method, inverting the geomagnetic measurements directly to obtain steady core motion. The method is applied to observatory annual mean data for the 30 yr period 1960–1990 to produce six separate models of steady flow: three that are stationary over 10 yr intervals (1960–1970, 1970–1980 and 1980–1990), two 20 yr models (1960–1980 and 1970–1990), and one 30 yr model (1960–1990). The method is not restricted to continuous time series or linear (X, Y, Z) data. The 10 yr models fit the weighted data with misfits of 1.0–1.3, the 20 yr models fit less well, and the 30 yr model has a misfit of 1.7 when constrained to have the same norm as the 10 yr models. All models appear to fit the central decade with a gross misfit close to unity, suggesting that changes in core motion may be associated with the two geomagnetic jerks that occurred around 1969 and 1978. Furthermore, close inspection of the fits at individual observatories shows that steady core motions with this norm cannot produce the secular accelerations required at a large number of high-quality observatories. Steady flows can predict magnetic fields that follow the trend at most observatories, but cannot follow the detailed time variations of the past three decades.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1995.tb03556.x
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  • 3
    Electronic Resource
    Electronic Resource
    Kinematic magnetic-field morphology at the core-mantle boundary (1994)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 116 (1994), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The earth's magnetic field is generated by induction in fluid motions in the liquid iron core, a dynamo process that is not yet properly understood. The field changes on time-scales of years to centuries, and this change probably forms part of the fundamental regeneration process. A kinematic approach is used whereby the induction of fluid motions is modelled by choosing a flow and investigating the magnetic field that it generates. Using a novel matching condition, which is appropriate when the upper part of the liquid iron core is static, a set of kinematic dynamos is generated that belongs to the geophysically interesting class of flows with one cell in radius. The morphology of the radial component of the induced magnetic field is then mapped at the boundary of the core and compared with equivalent maps derived from observation to retrieve some essential, symmetric static features in the geomagnetic field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1994.tb01800.x
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  • 4
    Electronic Resource
    Electronic Resource
    On convection in the earth's core driven by lateral temperature variations in the lower mantle (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 108 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Lateral variations in heat flux or temperature in the lowermost mantle, associated with mantle convection, will drive fluid flow in the liquid core. The effect is modelled by a rotating spherical shell with uniform lower boundary temperature and a laterally varying upper surface temperature and the solutions found by numerical calculation, some for a density-stratified fluid. The problem depends upon two dimensionless numbers, a horizontal Rayleigh number and a stratification parameter. The calculations are restricted to surface temperatures which are symmetric about the equator and steady solutions are found. Induced toroidal flows near the surface are closely linked with the applied temperature profile through the thermal wind equation and Coriolis forces make the convection penetrate into the shell. Stratification acts mainly to suppress radial flow but the surface toroidal flow is relatively unaffected. The results illustrate the powerful influence exerted by the surface temperature but are difficult to apply directly to the earth's core because molecular values of the thermal diffusivity entail a very long time-scale. Assuming a turbulent thermal diffusivity equal to the magnetic diffusivity gives a more realistic time-scale and it is possible to recover, for specific simple imposed temperature profiles, flows similar to those found in the earth's core from inversion of geomagnetic secular change.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb00853.x
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  • 5
    Electronic Resource
    Electronic Resource
    On the use of horizontal components of magnetic field in determining core motions (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 98 (1989), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: Geomagnetic secular variation is caused by flow of fluid in the Earth's core. If electrical diffusion can be ignored, field lines are frozen to the core fluid and can be used as tracers for the flow at the top of the free stream, which lies beneath the diffusive boundary layer. In this paper we assume the flux is frozen-in and investigate the jump in the horizontal field across the boundary layer. Theoretical studies indicate that such a jump will be small (about 1000 nT); we test the hypothesis that the jump is zero within the errors of measurement of the magnetic field. Integral constraints, which are conserved if the horizontal components of field at the base of the mantle can be equated to the components at the top of the free stream, are derived and computed using seven main-field models from epochs 1935.5 to 1980.0. These main-field models have been forced to satisfy all the conditions of frozen-flux theory. The integral constraints are found to be constant within their expected errors, and we conclude that the observations are consistent with zero jump in horizontal field across the boundary layer. This result implies that use can be made of the horizontal components of field in determining core flow. We attempt to compute the flow along null-flux curves, which is not determined at all by the radial component of the field, for epoch 1970. The result is very noisy because of its reliance on gradients of the secular variation at the core-mantle boundary, which are poorly determined. We do not attempt to compute reasonable core flows consistent with these observations, although presumably many such flows exist, because they would be so poorly constrained by observation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1989.tb03353.x
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  • 6
    Electronic Resource
    Electronic Resource
    Seismic source parameters in New Zealand from broad-band data (1996)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 124 (1996), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The Leeds Tararua array of nine broad-band, three-component seismometers was deployed in southern North Island, New Zealand, from 1991 January to 1992 September and recorded many local events. We selected 111 events with local magnitude ≥ 2.5 and good station coverage, and attempted to find their source mechanisms by using conventional first motions and by matching of the vertical component waveforms to Rayleigh-mode synthetics. 90 source mechanisms were found: 32 from the method of first motions, 18 by waveform matching, and 40 using both methods. A comparison of mechanisms for events using both methods suggests that waveform matching is reliable even for small events where the coverage on the focal sphere does not allow a first-motion mechanism to be found. The mechanisms are of all types but with a predominance of normal faulting with one of the planes aligned approximately NE–SW. There are many dip-slip events. Deep (60–80 km) events are mostly thrusts, and there is some evidence of a trend from normal faulting in the shallow part of the subducted slab and upper seismic plane to thrusts in the deeper part, although the pattern is not clear cut. A complex stress pattern is to be expected in this region, which is near the southern end of the Tonga–Kermadec–Hikurangi subduction zone. The magnitude–moment relation ML= (0.84 ± 0.23) log M0– (7.53 ± 1.48) is found for the region, where ML is the local magnitude and M0 the seismic moment in N m.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1996.tb06371.x
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  • 7
    Electronic Resource
    Electronic Resource
    Thermal core–mantle interactions (1987)
    [s.l.] : Nature Publishing Group
    Nature 325 (1987), S. 511-513 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] In an earlier paper1 we presented models of the magnetic field at the core-mantle boundary (CMB) at approximately 60 yr intervals from 1715 to 1980. We showed that the secular variation (SV) is confined mainly to the hemisphere 90° E to 90° W, where its character has remained unaltered ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/325511a0
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  • 8
    Electronic Resource
    Electronic Resource
    Mapping the mantle and core (1987)
    [s.l.] : Nature Publishing Group
    Nature 325 (1987), S. 392-393 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] IT is common to talk of the effects of the plate tectonic revolution on geology; less so to speak of its effects on geophysics. It has left two obvious avenues of study open to the geophysicist interested in the study of the Earth's deep interior - either to view plate tectonics as a purely ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/325392a0
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  • 9
    Electronic Resource
    Electronic Resource
    Morphology of the geomagnetic field and implications for the geodynamo (1987)
    [s.l.] : Nature Publishing Group
    Nature 325 (1987), S. 509-511 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Fig. 1 Map of the radial component of the magnetic field at the core-mantle boundary for 1980 (ref. 3). Contour interval is 100 |xT; solid contours represent flux into the core, broken contours flux out of the core; bold contours represent zero radial field. The two main pairs of lobes (1,3) and ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/325509a0
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  • 10
    Electronic Resource
    Electronic Resource
    Mechanism for geomagnetic polarity reversals (1987)
    [s.l.] : Nature Publishing Group
    Nature 326 (1987), S. 167-169 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] A review of palaeointensity measurements4 has shown a clear fall in the dipole moment throughout the past 2,000 years; there is good evidence for growth in the preceding 2,000 years. Modern data also exhibit this fall in dipole moment: Fig. 1 shows the fall, in the twentieth century, of the Gauss ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/326167a0
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