Abstract
Abstract. We consider a stochastic differential equation model for Earth's axial magnetic dipole field. Our goal is to estimate the model's parameters using diverse and independent data sources that had previously been treated separately, so that the model is a valid representation of an expanded paleomagnetic record on kyr to Myr timescales. We formulate the estimation problem within the Bayesian framework and define a feature-based posterior distribution that describes probabilities of model parameters given a set of features derived from the data. Numerically, we use Markov chain Monte Carlo (MCMC) to obtain a sample-based representation of the posterior distribution. The Bayesian problem formulation and its MCMC solution allow us to study the model's limitations and remaining posterior uncertainties. Another important aspect of our overall approach is that it reveals inconsistencies between model and data or within the various data sets. Identifying these shortcomings is a first and necessary step towards building more sophisticated models or towards resolving inconsistencies within the data. The stochastic model we derive represents selected aspects of the long-term behavior of the geomagnetic dipole field with limitations and errors that are well defined. We believe that such a model is useful (besides its limitations) for hypothesis testing and give a few examples of how the model can be used in this context.
Highlights
Earth possesses a time-varying magnetic field which is generated by the turbulent flow of liquid metal alloy in the core
To what we found in the context of power spectral densities (PSDs) computations and approximations, we find that estimates of the reversal rate, time average and standard deviation are subject to large errors unless the simulation time is very long
Similar to what we observed of the model–data fit in terms of PSDs, we find that the nominal parameter values lead to a “reasonable” fit of the model’s reversal rate, time average and standard deviation
Summary
Earth possesses a time-varying magnetic field which is generated by the turbulent flow of liquid metal alloy in the core. Variations on even longer timescales of millions of years are recorded by marine sediments (Valet et al, 2005; Ziegler et al, 2011) and by magnetic anomalies in the oceanic crust (Ogg, 2012; Cande and Kent, 1995; Lowrie and Kent, 2004). On such long timescales, we can observe the intriguing feature of Earth’s axial magnetic dipole field to reverse its polarity (magnetic North Pole becomes the magnetic South Pole and vice versa)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
