GP23A-01
Magnetic Dipole Reversals in Dynamo Simulations
Although 3D MHD simulations of convective dynamos continue to improve as computers become faster and resources become more available, we are still far from being able to produce a realistic geodynamo simulation in terms of the input parameters. Modelers are compelled to choose between as much spatial and temporal resolution that is currently practical in order to reach smaller Ekman numbers and more turbulent (i.e., realistic) dynamics or to use very coarse resolution and less Earth-like parameters in order to simulate enough time to study reversals. Here we present results from the latter approach. We use the Glatzmaier-Roberts anelastic model with a finitely conducting inner core that is free to rotate. The Ekman number, ν/(2 Ømega D2), is set to 5 × 10-4. Here, ν is the viscous diffusivity, Ømega is the angular velocity and D is the depth of the fluid outer core. We set the magnetic diffusivity to 2 m2/s and the other three to 20 m2/s. No hyperdiffusion is employed. With the correct core size, this Ekman number requires the rotation rate to be 20,000 times smaller than the Earth's. The coarse resolution (66x72x144) produces large-scale laminar flows and fields. Magnetic reversals do occur, although the vast difference between model and Earth parameters complicates their interpretation.
GP23A-02
Geomagnetic Estimates of the Mean Rates of Paleomagnetic Dipole Power Excursions and Reversals
To further and better test some kinematic, dynamical, and statistical hypotheses about the core geodynamo, previous predictions for the mean rates and durations of dipole power excursions and axial dipole reversals [Voorhies & Conrad, 1996] are re-examined and refined. The hypotheses yield a theoretical form for the low degree, core-source part of the Lowes-Mauersberger spectrum R(n) - the mean square field, averaged over the sphere of radius a, in spherical harmonics of degree n. This form is \{R(n)\} = K[(n + 1/2)/n(n + 1)](c/a)**(2n+4); core radius c = 3.5 +/- 0.1 Mm is recovered with no significant error by fitting log-theoretical to log-observational spectra for Earth [Voorhies, 2004]. Jupiter may also have a "1/n" spectrum, but Mercury's field seems too weak and for its core dynamo to be very Earth-like. Our statistical hypothesis distributes (2n+1)R(n)/\{R(n)\} as chi-square with 2n+1 degrees of freedom. The implied field is usually mainly dipolar and can be primarily axial. During a small fraction of geologic time, however, dipole power R(1) is expected to be quite small. An unusually weak axial dipole might reverse during such an interval. So we defined "dipole power excursion" as an interval when absolute dipole moment is less than or equal to a threshold value, taken to be the absolute equatorial dipole moment at 1980. Our amplitude estimate implied that such excursions would occupy 2.5% of geologic time. We used the 1945-1980 dipole power time scale to convert this fraction into mean duration, hence mean rate. For dipole power excursions, we predicted a mean duration of 2767 years and a mean rate of 9.04 per million years; for reversals, we predicted a mean duration of 5534 years and a mean rate of 2.26 per million years [Voorhies & Conrad, 1996]. The method and results are critically reviewed and updated, with special attention to definitions, calibration, time scale, the one quarter rule for reversal/excursion rates, and uncertainty estimates. For example, amplitude K has now been calibrated by a self-consistent fit to satellite-era spectra for degrees 1-12 and used to estimate mean intensity [Voorhies, 2006 JGR-SE]. The expected Virtual (Axial) Dipole Moment, 6.5 +/- 1.0 (x 10**22 Am**2), is centered in the range of published mean paleointensities. The calibrated model also predicts large intensity variations: 80% of the time, absolute dipole moment is expected to be between 2.7 and 9.0, but non-dipole fields broaden the 80% range for Virtual Axial Dipole Moment to about 2 - 12 (x 10**22 Am**2).
GP23A-03 INVITED
Statistical Views of Long Term Geomagnetic Field Variations
Paleomagnetic data are not easily assimilated into geodynamical models of Earth's core, but statistical descriptions of paleomagnetic field behavior can provide a basis for determining whether geodynamo models are basically compatible with long term observations of the geomagnetic field. Such statistical descriptions generally include some kind of average field state and variability about the mean, and have often been parameterized in terms of a so-called Giant Gaussian Process, in which spherical harmonic coefficients describing the poloidal part of the geomagnetic field are represented as samples from specific normal probability distributions. The time-averaged field at any location can be determined from the means, while the anticipated variability over time is reflected in the standard deviations of these statistical distributions, and the spherical harmonic representation in principle allows for arbitrary spatial complexity in the paleofield. In practice the number and quality of paleomagnetic data available limit the parameters that can be determined, along with simplifying hypotheses about overall field structure. Data used to assess field variability for these models are usually derived from lava flows and reflect instantaneous quasi-independent observations of the field at random times determined by the associated igneous processes. A two step process is presented for inverting globally distributed data to find a suitable Giant Gaussian Process, first discovering parameters to describe local or regional field variations, and then proceeding to a global inversion. Such models can be extended by using estimates of the geomagnetic power spectrum to accommodate temporal correlations in the spherical harmonic structures. A simplified model for frequency dependence of the geomagnetic dipole spectrum is derived from recent estimates of the paleomagnetic power spectrum, and could be merged with simple parametrizations for secular variation at higher spherical harmonic degree.
GP23A-04 INVITED
Statistically Assessing Time-Averaged and Paleosecular Variation Field Models Against Paleomagnetic Directional Data Sets. Can Likely non-Zonal Features be Detected in a Robust way ?
We recently introduced a method to rigorously test the statistical compatibility of combined time-averaged (TAF) and paleosecular variation (PSV) field models against any lava flow paleomagnetic database (Khokhlov et al., 2001, 2006). Applying this method to test (TAF+PSV) models against synthetic data produced from those shows that the method is very efficient at discriminating models, and very sensitive, provided those data errors are properly taken into account. This prompted us to test a variety of published combined (TAF+PSV) models against a test Bruhnes stable polarity data set extracted from the Quidelleur et al. (1994) data base. Not surprisingly, ignoring data errors leads all models to be rejected. But taking data errors into account leads to the stimulating conclusion that at least one (TAF+PSV) model appears to be compatible with the selected data set, this model being purely axisymmetric. This result shows that in practice also, and with the data bases currently available, the method can discriminate various candidate models and decide which actually best fits a given data set. But it also shows that likely non-zonal signatures of non-homogeneous boundary conditions imposed by the mantle are difficult to identify as statistically robust from paleomagnetic directional data sets. In the present paper, we will discuss the possibility that such signatures could eventually be identified as robust with the help of more recent data sets (such as the one put together under the collaborative "TAFI" effort, see e.g. Johnson et al. abstract #GP21A-0013, AGU Fall Meeting, 2005) or by taking additional information into account (such as the possible coincidence of non-zonal time-averaged field patterns with analogous patterns in the modern field).
GP23A-05 INVITED
Understanding Core-Mantle Coupling Through Dynamo Models
Core-mantle interaction in the Earth is studied using convection-driven dynamo models. We begin by considering an idealized regime that supports locking of the fluid motion and magnetic field to external inhomogeneities. In perfect locking, the azimuthal velocity in the fluid core has the profile of a thermal wind imposed by the boundary. In strongly convective dynamos, the competition between buoyancy-driven and boundary-driven thermal winds determines the extent of fluid-boundary coupling. We go on to show that dynamos with weakly convecting outer layers support locking, whereas strongly convecting outer regions swamp any influence of the lateral variations at the boundary. Finally, we investigate the tomographic boundary condition to see how its individual harmonic components may affect the morphology of the geomagnetic field. http://earth.leeds.ac.uk/~earbs
GP23A-06
A Quadrupolar Magnetic Field at Mercury?
During the Mariner 10 flybys Mercury's global magnetic field was detected. The available observations can be fitted by a nearly axial dipole, but the field geometry including the quadrupole-to-dipole ratio is poorly constrained. The surface field strength is only 1% of the geomagnetic field strength. For an Earth-like dynamo a thirty times stronger field is expected based on an assumed balance of Lorentz and Coriolis forces. We suggest that the dynamo operates only in a deep sublayer of the fluid part of the core, whereas its upper part is stably stratified because the temperature gradient is subadiabatic. Depending on the heat flow at the core mantle boundary, the sulphur concentration, and the size of the solid inner core, we estimate that the unstable layer has 20-60% of the outer core's thickness. Because Mercury rotates 60 times slower than Earth, the local Rossby number Rol, measuring the role of inertial forces relative to the Coriolis force, is estimated to be of order 10 compared to 0.1 in the geodynamo. Numerical dynamo models show that for high Rol the contribution of the dipole to the magnetic field is weak in the dynamo region, where higher multipole components dominate. They vary rapidly in time and are strongly attenuated in the stable conducting layer. The weak but slowly varying dipole and quadrupole components pass this layer to some degree and dominate the field geometry at the planetary surface. We have varied the basic control parameters, inner core size, and stable layer thickness in over 20 dynamo models. In some models the axial dipole and in others the axial quadrupole dominate the surface field whose strength is of the right order. While the dipole is more preferred for a larger size of the inner core, there is a trend towards quadrupolar solutions with an increasing value of Rol. Because our model values fall short of the estimated Mercury value for numerical reasons, we conclude that it is possible that Mercury's magnetic field is dominantly quadrupolar at the planet's surface. The Messenger flyby in January 2008 offers an opportunity to test this hypothesis as well as other model predictions, such as a high degree of axisymmetry of the field.
GP23A-07
Variation of the Dynamo region and sudden termination of Mars Dynamo
Numerical simulation showed that the Mars dynamo could be subcritical towards the end of it history: as the Rayleigh number (measuring the driving force of the dynamo) decreases from the strong-field dynamo domain, the numerical Mars magnetic field remains comparable in magnitude. It vanishes suddenly when the Rayleigh number is lower than a critical value. However, the Mars dynamo will not be reactivated until the Rayleigh number increases to a value much higher than the critical point for the termination of the dynamo. To better understand the termination of the Mars dynamo, it is important to understand first the variation of the dynamo region in which the emf offsets the Joule dissipation. Our initial analysis shows that the dynamo region is often around the tangent cylinder (a co-axial cylindrical surface across the outer core tangent to the inner core boundary at the equator) and extended outward significantly. As the Rayleigh number decreases, the dimension of the region is reduced, and tends to fluctuate stronger in time. These two combined may suggest that there is probably a critical dimension, below which the dynamo region can no longer be sustained by core convection.