Ergodicity of the recent geomagnetic field

The geomagnetic field is a fundamental property of our planet: its study would allow us to understand those processes of Earth’s interior, which act in its outer core and produce the main field. Knowledge of whether the field is ergodic, i.e. whether time averages correspond to phase space averages, is an important question since, if this were true, it would point out a strong spatio-temporal coupling amongst the components of the dynamical system behind the present geomagnetic field generation. Another consequence would be that many computations, usually undertaken with many difficulties in the phase space, can be made in the conventional time domain. We analyse the temporal behaviour of the deviation between predictive and definitive geomagnetic global models for successive intervals from 1965 to 2010, finding a similar exponential growth with time. Also going back in time (at around 1600 and 1900 by using the GUFM1 model) confirms the same findings. This result corroborates previous chaotic analyses made in a reconstructed phase space from geomagnetic observatory time series, confirming the chaotic character of the recent geomagnetic field with no reliable prediction after around 6 years from definitive values, and disclosing the potentiality of estimating important entropic quantities of the field by time averages. Although more tests will be necessary, some of our analyses confirm the efforts to improve the representation of the geomagnetic field with more detailed secular variation and acceleration.