scholarly journals Enhanced magnetic fields within a stratified layer

2020 ◽  
Vol 222 (3) ◽  
pp. 1686-1703
Author(s):  
Colin M Hardy ◽  
Philip W Livermore ◽  
Jitse Niesen

SUMMARY Mounting evidence from both seismology and numerical experiments on core composition suggests the existence of a layer of stably stratified fluid at the top of Earth’s outer core. In such a layer, a magnetostrophic force balance and suppressed radial motion lead to stringent constraints on the magnetic field, named Malkus constraints, which are a much more restrictive extension of the well known Taylor constraints. Here, we explore the consequences of such constraints for the structure of the core’s internal magnetic field. We provide a new simple derivation of these Malkus constraints, and show solutions exist which can be matched to any external potential field with arbitrary depth of stratified layer. From considerations of these magnetostatic Malkus constraints alone, it is therefore not possible to uniquely infer the depth of the stratified layer from external geomagnetic observations. We examine two models of the geomagnetic field defined within a spherical core, which obey the Taylor constraints in an inner convective region and the Malkus constraints in an outer stratified layer. When matched to a single-epoch geomagnetic potential field model, both models show that the toroidal magnetic field within the outer layer is about 100 times stronger compared to that in the inner region, taking a maximum value of 8 mT at a depth of 70 km. The dynamic regime of such a layer, modulated by suppressed radial motion but also a locally enhanced magnetic field, may therefore be quite distinct from that of any interior dynamo.

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.


2021 ◽  
Author(s):  
Felix Gerick ◽  
Dominique Jault ◽  
Jerome Noir

<p> Fast changes of Earth's magnetic field could be explained by inviscid and diffusion-less quasi-geostrophic (QG) Magneto-Coriolis modes. We present a hybrid QG model with columnar flows and three-dimensional magnetic fields and find modes with periods of a few years at parameters relevant to Earth's core. These fast Magneto-Coriolis modes show strong focusing of their kinetic and magnetic energy in the equatorial region, while maintaining a relatively large spatial structure along the azimuthal direction. Their properties agree with some of the observations and inferred core flows. We find additionally, in contrast to what has been assumed previously, that these modes are not affected significantly by magnetic diffusion. The model opens a new way of inverting geomagnetic observations to the flow and magnetic field deep within the Earth's outer core.</p>


2018 ◽  
Vol 216 (1) ◽  
pp. 123-129 ◽  
Author(s):  
R J Teed ◽  
C A Jones ◽  
S M Tobias

SUMMARY Turbulence and waves in Earth’s iron-rich liquid outer core are believed to be responsible for the generation of the geomagnetic field via dynamo action. When waves break upon the mantle they cause a shift in the rotation rate of Earth’s solid exterior and contribute to variations in the length-of-day on a ∼6-yr timescale. Though the outer core cannot be probed by direct observation, such torsional waves are believed to propagate along Earth’s radial magnetic field, but as yet no self-consistent mechanism for their generation has been determined. Here we provide evidence of a realistic physical excitation mechanism for torsional waves observed in numerical simulations. We find that inefficient convection above and below the solid inner core traps buoyant fluid forming a density gradient between pole and equator, similar to that observed in Earth’s atmosphere. Consequently, a shearing jet stream—a ‘thermal wind’—is formed near the inner core; evidence of such a jet has recently been found. Owing to the sharp density gradient and influence of magnetic field, convection at this location is able to operate with the turnover frequency required to generate waves. Amplified by the jet it then triggers a train of oscillations. Our results demonstrate a plausible mechanism for generating torsional waves under Earth-like conditions and thus further cement their importance for Earth’s core dynamics.


2003 ◽  
Vol 21 (8) ◽  
pp. 1709-1722 ◽  
Author(s):  
E. J. Bunce ◽  
S. W. H. Cowley ◽  
J. A. Wild

Abstract. We calculate the azimuthal magnetic fields expected to be present in Saturn’s magnetosphere associated with two physical effects, and compare them with the fields observed during the flybys of the two Voyager spacecraft. The first effect is associated with the magnetosphere-ionosphere coupling currents which result from the sub-corotation of the magnetospheric plasma. This is calculated from empirical models of the plasma flow and magnetic field based on Voyager data, with the effective Pedersen conductivity of Saturn’s ionosphere being treated as an essentially free parameter. This mechanism results in a ‘lagging’ field configuration at all local times. The second effect is due to the day-night asymmetric confinement of the magnetosphere by the solar wind (i.e. the magnetopause and tail current system), which we have estimated empirically by scaling a model of the Earth’s magnetosphere to Saturn. This effect produces ‘leading’ fields in the dusk magnetosphere, and ‘lagging’ fields at dawn. Our results show that the azimuthal fields observed in the inner regions can be reasonably well accounted for by plasma sub-corotation, given a value of the effective ionospheric Pedersen conductivity of ~ 1–2 mho. This statement applies to field lines mapping to the equator within ~ 8 RS (1 RS is taken to be 60 330 km) of the planet on the dayside inbound passes, where the plasma distribution is dominated by a thin equatorial heavy-ion plasma sheet, and to field lines mapping to the equator within ~ 15 RS on the dawn side outbound passes. The contributions of the magnetopause-tail currents are estimated to be much smaller than the observed fields in these regions. If, however, we assume that the azimuthal fields observed in these regions are not due to sub-corotation but to some other process, then the above effective conductivities define an upper limit, such that values above ~ 2 mho can definitely be ruled out. Outside of this inner region the spacecraft observed both ‘lagging’ and ‘leading’ fields in the post-noon dayside magnetosphere during the inbound passes, with ‘leading’ fields being observed both adjacent to the magnetopause and in the ring current region, and ‘lagging’ fields being observed between. The observed ‘lagging’ fields are consistent in magnitude with the sub-corotation effect with an effective ionospheric conductivity of ~ 1–2 mho, while the ‘leading’ fields are considerably larger than those estimated for the magnetopause-tail currents, and appear to be indicative of the presence of another dynamical process. No ‘leading’ fields were observed outside the inner region on the dawn side outbound passes, with the azimuthal fields first falling below those expected for sub-corotation, before increasing, to exceed these values at radial distances beyond ~ 15–20 RS , where the effect of the magnetopause-tail currents becomes significant. As a by-product, our investigation also indicates that modification and scaling of terrestrial magnetic field models may represent a useful approach to modelling the three-dimensional magnetic field at Saturn.Key words. Magnetospheric physics (current systems; magnetosphere-ionosphere interactions; solar wind-magnetosphere interactions)


Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. J1-J13 ◽  
Author(s):  
Pauline Le Maire ◽  
Marc Munschy

The shape of an anomaly (magnetic or gravity) along a profile provides information on the geometry, horizontal location, depth, and magnetization of the source. For a 2D source, the horizontal location, depth, and geometry of a source are determined through the analysis of the curve of the analytic signal. However, the amplitude of the analytic signal is independent of the dips of the structure, the apparent inclination of magnetization, and the regional magnetic field. To better characterize the parameters of the source, we have developed a new approach for studying 2D potential field equations using complex algebra. Complex equations for different geometries of the sources are obtained for gravity and magnetic anomalies in the spatial and spectral domains. In the spatial domain, these new equations are compact and correspond to logarithmic or power functions with a negative integer exponent. We found that modifying the shape of the source changes the exponent of the power function, which is equivalent to differentiation or integration. We developed anomaly profiles using plots in the complex plane, which is called mapping. The obtained complex curves are loops passing through the origin of the plane. The shape of these loops depends only on the geometry and not on the horizontal location of the source. For source geometries defined by a single point, the loop shape is also independent of the source depth. The orientation of the curves in the complex plane is related to the order of differentiation or integration, the geometry and dips of the structures, and the apparent inclination of magnetization and of the regional magnetic field. The application of these equations and mapping on total field magnetic anomalies across a magmatic dike in Norway shows coherent results, allowing us to determine the geometry and the apparent inclination of magnetization.


Author(s):  
A.A Bachtiar ◽  
D.J Ivers ◽  
R.W James

The Earth's main magnetic field is generally believed to be due to a self-exciting dynamo process in the Earth's fluid outer core. A variety of antidynamo theorems exist that set conditions under which a magnetic field cannot be indefinitely maintained by dynamo action against ohmic decay. One such theorem, the Planar Velocity Antidynamo Theorem , precludes field maintenance when the flow is everywhere parallel to some plane, e.g. the equatorial plane. This paper shows that the proof of the Planar Velocity Theorem fails when the flow is confined to a sphere, due to diffusive coupling at the boundary. Then, the theorem reverts to a conjecture. There is a need to either prove the conjecture, or find a functioning planar velocity dynamo. To the latter end, this paper formulates the toroidal–poloidal spectral form of the magnetic induction equation for planar flows, as a basis for a numerical investigation. We have thereby determined magnetic field growth rates associated with various planar flows in spheres. For most flows, the induced magnetic field decays with time, supporting a planar velocity antidynamo conjecture for a spherical conducting fluid. However, one flow is exceptional, indicating that magnetic field growth can occur. We also re-examine some classical kinematic dynamo models, converting the flows where possible to planar flows. For the flow of Pekeris et al . (Pekeris, C. L., Accad, Y. & Shkoller, B. 1973 Kinematic dynamos and the Earth's magnetic field. Phil. Trans. R. Soc. A 275 , 425–461), this conversion dramatically reduces the critical magnetic Reynolds number.


Author(s):  
Christian Gerhards

AbstractAny square-integrable vector field $$\mathbf {f}$$ f over a sphere $$\mathbb {S}$$ S can be decomposed into three unique contributions: one being the gradient of a function harmonic inside the sphere (denoted by $$\mathbf {f}_+$$ f + ), one being the gradient of a function harmonic in the exterior of the sphere (denoted by $$\mathbf {f}_-$$ f - ), and one being tangential and divergence-free (denoted by $$\mathbf {f}_{df}$$ f df ). In geomagnetic applications this is of relevance because, if we consider $$\mathbf {f}$$ f to be identified with a magnetization, only the contribution $$\mathbf {f}_+$$ f + can generate a non-vanishing magnetic field in the exterior of the sphere. Thus, we call $$\mathbf {f}_-$$ f - and $$\mathbf {f}_{df}$$ f df “silent” and $$\mathbf {f}_+$$ f + “nonsilent”. If $$\mathbf {f}$$ f is known to be spatially localized in a subregion of the sphere, then $$\mathbf {f}_+$$ f + and $$\mathbf {f}_-$$ f - are coupled due to their potential field nature. In this short paper, we derive an approach that makes use of this coupling in order to compute the contribution $$\mathbf {f}_-$$ f - from knowledge of the contribution $$\mathbf {f}_+$$ f + .


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