# Erratum to: Earth's core internal dynamics 1840-2010 imaged by inverse geodynamo modelling

Julien Aubert

► To cite this version:

Julien Aubert. Erratum to: Earth's core internal dynamics 1840-2010 imaged by inverse geodynamo modelling. Geophysical Journal International, 2014, pp.1683-1683. 10.1093/gji/ggu235. insu-03581104

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Submitted on 19 Feb 2022

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Erratum to: Earth's core internal dynamics 1840–2010 imaged by inverse geodynamo modelling

by Julien Aubert

Dynamique des Fluides Géologiques, Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris-Diderot, UMR 7154 CNRS, 1 rue Jussieu, F-75005 Paris, France. E-mail: aubert@ipgp.fr

A spurious contribution has been noticed in the residuals of inver-
sions using the COV-OBS main magnetic field. This arose from an
erroneous transcription of the covariance matrix **R**<sub>B</sub>. Being several
orders of magnitude below the magnetic field signal, the error does
not affect the inversion results themselves but only has an impact
on the computation of the misfits (Figs 1 and 2) at epochs where

<figure><img src="image_2.png" /></figure>

**Figure 1.** Mauersberger and Lowes energy spectra (black lines) of the main magnetic field (MF, top) and secular variation (SV, bottom) from COV-OBS in 1850 (left-hand side) and 2000 (right-hand side). Also shown are the inversion residuals obtained with prior CE (red lines), together with the typical data error levels (purple zones) prescribed by COV-OBS. These error levels are obtained by summing the diagonal variances in **R**<sub>B</sub> and **R**<sub>B̂</sub>. In the lower panels corresponding to the secular variation, the spectra of the estimated magnetic diffusion η∇<sup>2</sup>**W**<sub>lm</sub>(r<sub>CMB</sub>) are also reported (green lines), together with the spectra of fit residuals to the secular variation **M**<sub>xfs</sub> − **b** (red lines). The frozen-flux misfits to the secular variation data in dashed blue lines then correspond to **M**<sub>xfs</sub> − **b** − η[∇<sup>2</sup>**W**<sub>lm</sub>(r<sub>CMB</sub>)]<sub>f≤13</sub><sup>Tr</sup>.

<figure><img src="image_3.png" /></figure>

**Figure 2.** Normalized misfits to the data (prior misfits) Δ<sub>B</sub> (top) and Δ<sub>B̂</sub> (bottom, see text for definitions), obtained by inverting models COV-OBS, gufm-sat-Q3 and CM4 with priors CE and G. A misfit of 1 (dashed grey line) denotes an acceptable fit (0 is optimal).

the data accuracy is higher than the spurious signal. The corrected
figures presented here show that the misfits to the main magnetic
field data are now acceptable throughout 1840–2010. Points made
in the main text concerning anomalously high misfits to the main
magnetic field data should thus be discarded. Results concerning
misfits to the secular variation data remain unchanged.

REFERENCE

Aubert, J., 2014. Earth's core internal dynamics 1840–2010 imaged by inverse geodynamo modelling, *Geophys. J. Int.*, **197**, 1321–1334.