A Bayesian iterative geomagnetic model with universal data input: Self-consistent spherical harmonic evolution for the geomagnetic field over the last 4000 years

Changes of the Earth's magnetic field have been observed with varying spatial and temporal resolution since the middle ages by means of compasses, and later by refined mechanical inclination and intensity instruments, until the modern use of quantum mechanical devices and satellite observations. Ancient records, on the other hand, rely on the natural magnetization of archaeological artifacts and other materials, such as rocks and sediments, being therefore indirect, less accurate and sparser. The combination of such heterogeneous records into a single, self-consistent, global model of the geomagnetic field is very challenging: the highly uneven data coverage, both in space and time, requires a careful handling of data uncertainties and error correlations. Previous models dealt with this problem using separated treatments of instrumental data and indirect records, respectively, as well as a different handling of the dipole field component, with respect to non-dipole terms. Here we present a global geomagnetic field model based, for the first time, on the simultaneous inversion of historical, archaeomagnetic, and volcanic records, using a Bayesian approach with minimal-committing time regularization that minimizes the energy of secular variation. A detailed assessment of data uncertainty and error correlation is used to minimize artifacts generated by the appearance of an overwhelming number of incomplete, mostly declination only records, associated with shipboard measurements in the early colonial period. Our model yields lower dipole energies, which better match modern values, as well as higher non-dipole energies and a stronger secular variation of the dipole moment. Some model artifacts associated with extremely heterogeneous distributions of records in time and space are not completely eliminable and might be caused by incorrect a-priori uncertainty assessments. Alternatively, they might represent an intrinsic limit that can be overcome only by adding new records at critical locations and times.