On flow magnitude and field-flow alignment at Earth's core surface

We present a method to estimate the typical magnitude of flow close to Earth's core surface based on observational knowledge of the geomagnetic main field (MF) and its secular variation (SV), together with prior information concerning field-flow alignment gleaned from numerical dynamo models. An expression linking the core surface flow magnitude to spherical harmonic spectra of the MF and SV is derived from the magnetic induction equation. This involves the angle γ between the flow and the horizontal gradient of the radial field. We study γ in a suite of numerical dynamo models and discuss the physical mechanisms that control it. Horizontal flow is observed to approximately follow contours of the radial field close to high-latitude flux bundles, while more efficient induction occurs at lower latitudes where predominantly zonal flows are often perpendicular to contours of the radial field. We show that the amount of field-flow alignment depends primarily on a magnetic modified Rayleigh number Raη=αg0ΔTD/ηΩ, which measures the vigour of convective driving relative to the strength of magnetic dissipation. Synthetic tests of the flow magnitude estimation scheme are encouraging, with results differing from true values by less than 8 per cent. Application to a high-quality geomagnetic field model based on satellite observations (the xCHAOS model in epoch 2004.0) leads to a flow magnitude estimate of 11-14 km yr−1, in accordance with previous estimates. When applied to the historical geomagnetic field model gufm1 for the interval 1840.0-1990.0, the method predicts temporal variations in flow magnitude similar to those found in earlier studies. The calculations rely primarily on knowledge of the MF and SV spectra; by extrapolating these beyond observed scales the influence of small scales on flow magnitude estimates is assessed. Exploring three possible spectral extrapolations we find that the magnitude of the core surface flow, including small scales, is likely less than 50 km yr−

Imaging Earth's crustal magnetic field with satellite data: a regularized spherical triangle tessellation approach

We present a method for imaging the global crustal magnetic field at Earth's surface using a local basis representation and a minimum norm model regularization approach. The local basis consists of a spherical triangle tessellation (STT) parametrization of the radial component of the crustal field at Earth's reference spherical surface. The Green's function for Laplace's equation in spherical geometry with Neumann boundary conditions provides the necessary forward modelling scheme. We solve the inverse problem of estimating the crustal field from satellite magnetic observations by minimizing an objective function comprising a mean absolute deviation (L1-norm) measure of misfit plus a norm measuring model complexity. Both quadratic and entropy measures of field complexity are investigated. We report results from synthetic tests performed on a geophysically motivated scenario; these include a successful benchmark of the method and a comparison between quadratic and entropy regularization strategies. Applying our technique to real observations collected by the CHAMP, Ørsted and SAC-C satellites, we obtain stable images of the crustal magnetic field at Earth's surface that include sharp features with high amplitudes. We present details of two prototype crustal field models STT-CRUST-Q and STT-CRUST-E regularized using quadratic and entropy norms respectively; these provide a perspective complementary to that given by conventional spherical harmonic crustal field model

Maximum entropy regularization of time-dependent geomagnetic field models

We incorporate a maximum entropy image reconstruction technique into the process of modelling the time-dependent geomagnetic field at the core-mantle boundary (CMB). In order to deal with unconstrained small lengthscales in the process of inverting the data, some core field models are regularized using a priori quadratic norms in both space and time. This artificial damping leads to the underestimation of power at large wavenumbers, and to a loss of contrast in the reconstructed picture of the field at the CMB. The entropy norm, recently introduced to regularize magnetic field maps, provides models with better contrast, and involves a minimum of a priori information about the field structure. However, this technique was developed to build only snapshots of the magnetic field. Previously described in the spatial domain, we show here how to implement this technique in the spherical harmonic domain, and we extend it to the time-dependent problem where both spatial and temporal regularizations are required. We apply our method to model the field over the interval 1840-1990 from a compilation of historical observations. Applying the maximum entropy method in space—for a fit to the data similar to that obtained with a quadratic regularization—effectively reorganizes the magnetic field lines in order to have a map with better contrast. This is associated with a less rapidly decaying spectrum at large wavenumbers. Applying the maximum entropy method in time permits us to model sharper temporal changes, associated with larger spatial gradients in the secular variation, without producing spurious fluctuations on short timescales. This method avoids the smearing back in time of field features that are not constrained by the data. Perspectives concerning future applications of the method are also discusse

LCS-1: A High-Resolution Global Model of the Lithospheric Magnetic Field Derived from CHAMP and \u3cem\u3eSwarm\u3c/em\u3e Satellite Observations

We derive a new model, named LCS-1, of Earth’s lithospheric field based on four years (2006 September–2010 September) of magnetic observations taken by the CHAMP satellite at altitudes lower than 350 km, as well as almost three years (2014 April–2016 December) of measurements taken by the two lower Swarm satellites Alpha and Charlie. The model is determined entirely from magnetic ‘gradient’ data (approximated by finite differences): the north–south gradient is approximated by first differences of 15 s along-track data (for CHAMP and each of the two Swarm satellites), while the east–west gradient is approximated by the difference between observations taken by Swarm Alpha and Charlie. In total, we used 6.2 mio data points. The model is parametrized by 35 000 equivalent point sources located on an almost equal-area grid at a depth of 100 km below the surface (WGS84 ellipsoid). The amplitudes of these point sources are determined by minimizing the misfit to the magnetic satellite ‘gradient’ data together with the global average of |Br| at the ellipsoid surface (i.e. applying an L1 model regularization of Br). In a final step, we transform the point-source representation to a spherical harmonic expansion. The model shows very good agreement with previous satellite-derived lithospheric field models at low degree (degree correlation above 0.8 for degrees n ≤ 133). Comparison with independent near-surface aeromagnetic data from Australia yields good agreement (coherence \u3e 0.55) at horizontal wavelengths down to at least 250 km, corresponding to spherical harmonic degree n ≈ 160. The LCS-1 vertical component and field intensity anomaly maps at Earth’s surface show similar features to those exhibited by the WDMAM2 and EMM2015 lithospheric field models truncated at degree 185 in regions where they include near-surface data and provide unprecedented detail where they do not. Example regions of improvement include the Bangui anomaly region in central Africa, the west African cratons, the East African Rift region, the Bay of Bengal, the southern 90°E ridge, the Cretaceous quiet zone south of the Walvis Ridge and the younger parts of the South Atlantic

Polar ionospheric currents and high temporal resolution geomagnetic field models

Estimating high resolution models of the Earth's core magnetic field and its time variation in the polar regions requires that one can adequately account for magnetic signals produced by polar ionospheric currents, which vary on a wide range of time and length scales. Limitations of existing ionospheric field models in the challenging polar regions can adversely affect core field models, which in turn has important implications for studies of the core flow dynamics in those regions. Here we implement a new approach to co-estimate a climatological model of the ionospheric field together with a model of the internal and magnetospheric fields within the CHAOS geomagnetic field modelling framework. The parametrization of the ionospheric field exploits non-orthogonal magnetic coordinates and scales linearly with external driving parameters related to the solar wind and the interplanetary magnetic field. Using this approach we derive a new geomagnetic field model from measurements of the magnetic field collected by low Earth orbit satellites, which in addition to the internal field provides estimates of the typical current system in the polar ionosphere. We find that the time derivative of the estimated internal field is less contaminated by the polar currents, which is mostly visible in the zonal and near-zonal terms at high spherical harmonic degrees. Distinctive patches of strong secular variation at the core-mantle boundary, which have important implications for core dynamics, persist. Relaxing the temporal regularisation reveals annual oscillations, which could indicate remaining ionospheric field or related induced signals in the internal field model. Using principal component analysis we find that the annual oscillations mostly affect the zonal low-degree spherical harmonics of the internal field.Comment: 26 pages, 15 figures, 3 table

Time-dependent low-latitude core flow and geomagnetic field acceleration pulses

We present a new model of time-dependent flow at low latitudes in the Earth's core between 2000 and 2018, derived from magnetic field measurements made on board the {\it Swarm} and CHAMP satellites and at ground magnetic observatories. The model, called {\it CoreFlo-LL.1}, consists of a steady background flow without imposed symmetry plus a time-dependent flow that is dominated by geostrophic and quasi-geostrophic components but also allows weak departures from equatorial symmetry. We find that the equatorial region beneath the core-mantle boundary is a place of vigorous, localised, fluid motions; time-dependent flow focused at low latitudes close to the core surface is able to reproduce rapid field variations observed at non-polar latitudes at and above Earth's surface. Magnetic field acceleration pulses are produced by alternating bursts of non-zonal azimuthal flow acceleration in this region. Such acceleration sign changes can occur within a year or less, and when the structures involved are of large spatial scale they can give rise to geomagnetic jerks at the Earth's surface