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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. For the simple poloidal magnetic field that we consider here they show a localization of kinetic and magnetic energy in the equatorial region. This concentration of energy near the equator and the high frequency make them a plausible mechanism to explain similar features observed in recent geomagnetic field observations. Our model potentially opens a way to probe the otherwise inaccessible magnetic field structure in the Earth's outer core. Plain Language Summary: Earth's magnetic field is evolving on many time scales. Here, we show that the changes of periods of a few years could possibly be explained by standing waves (modes) within the fluid outer core, which we model as not stratified. These modes are mostly in a balance between the magnetic and rotational forces. The numerically calculated modes show agreement with features of recent magnetic field observations through satellites, for example a stronger amplitude of the magnetic field near the equator. In a next step, our model might allow us to probe the magnetic field inside the liquid and conducting outer core. Key Points: Magneto‐Coriolis modes of periods close to torsional Alfvén modes could be present in Earth's core model without stratificationThe magnetic field changes of such modes show properties similar to geomagnetic observations, with fast changes localized near the equatorOur model could allow core‐flow inversions from geomagnetic field data to the flow and simultaneously the magnetic field within the core [ABSTRACT FROM AUTHOR]

The construction of geomagnetic, archaeomagnetic or palaeomagnetic field models requires some prior knowledge about the actual field, which can be gathered from the statistical properties of the field over a variety of length-scales and timescales. However, available geomagnetic data on centennial to millennial periods are too sparse to infer directly these statistical properties. We thus use high-resolution numerical simulations of the geodynamo to test a method for estimating the temporal power spectra (or equivalently the autocovariance functions) of the individual Gauss coefficients that describe the geomagnetic field outside the Earth's fluid outer core. Based on the spectral analysis of our simulations, we argue that a prior for the observational geomagnetic field over decennial to millennial periods can be constructed from the statistics of the field during the short satellite era. The method rests on the assumption that time-series of spherical harmonic coefficients can be considered as realizations of stationary and differentiable stochastic processes, namely order 2 autoregressive (AR2) processes. In the framework of these processes, the statistics of Gauss coefficients are well constrained by their variance and one or two timescales. We find that the time spectra in the dynamo simulations of all Gauss coefficients but the axial dipole are well approximated by the spectra of AR2 processes characterized by only one timescale. The process parameters can simply be deduced from instantaneous estimates of the spatial power spectra of the magnetic field and of its first time derivative. Some deviations of the Gauss coefficients statistics from this minimal model are also discussed. Characterizing the axial dipole clearly requires a more sophisticated AR2 process, with a second distinct timescale. [ABSTRACT FROM AUTHOR]

We report a new method to infer continuous time-series of the declination, inclination and intensity of the magnetic field from archaeomagnetic data. Adopting a Bayesian perspective, we need to specify a priori knowledge about the time evolution of the magnetic field. It consists in a time correlation function that we choose to be compatible with present knowledge about the geomagnetic time spectra. The results are presented as distributions of possible values for the declination, inclination or intensity. We find that the methodology can be adapted to account for the age uncertainties of archaeological artefacts and we use Markov chain Monte Carlo to explore the possible dates of observations. We apply the method to intensity data sets from Mari, Syria and to intensity and directional data sets from Paris, France. Our reconstructions display more rapid variations than previous studies and we find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archaeological artefacts. [ABSTRACT FROM AUTHOR]

Geomagnetic observations from satellites have highlighted interannual variations in the rate of change of the magnetic field originating from Earth's core. Downward continued to the core surface, these variations primarily show up in the equatorial belt. First, we recall the main characteristics of these patterns, addressing their spatio-temporal resolution, as seen from field models. We then review the several dynamical frameworks proposed so far to understand and model these observations, which populate the frequency spectrum on time scales close to the Alfvén time τ A ≈ 2 yr, much shorter than the vortex turnover time τ U ≈ 150 yr in Earth's core. Magnetic–Archimedes–Coriolis (MAC) waves in a stratified layer below the core surface constitute a first possibility in the case of a sub-adiabatic heat flux at the top of the core. Their period may reach the interannual range for a layer thickness less than ≈ 30 km, for a buoyancy frequency of the order of the Earth's rotation rate. An alternative has been proposed in a context where the Coriolis force dominates the momentum balance, rendering transient motions almost invariant along the rotation axis (quasi-geostrophy, QG). Torsional Alfvén waves, consisting of axisymmetric QG motions, operate at periods similar to the Alfvén time, but are not sufficient to explain the interannual field changes, which require non-axisymmetric motions. QG Alfvén waves (involving the Coriolis and magnetic forces) constitute another possibility, with inertia playing an important role. They have been detected in the latest generation of geodynamo simulations, propagating in a ubiquitous manner at a speed slightly less than the Alfvén velocity. They are localized in longitude and as a result their description requires high azimuthal wavenumber. But the branch of QG waves with large extent in azimuth is also worth considering, as it reaches interannual periods as their radial wavenumber is increased. The excitation of such high-frequency dynamics is discussed with respect to the temporal spectrum of the core field, which presents a slope ∼ f - 4 for periods approximately between τ A and τ U . We finally summarize the main geophysical implications of the existence of this interannual dynamics on core and lower mantle structure, properties, and dynamics. [ABSTRACT FROM AUTHOR]