Abstract

We propose a global geomagnetic field model for the last fourteen thousand years, based on thermoremanent records. We call the model ArchKalMag14k. ArchKalMag14k is constructed by modifying recently proposed algorithms, based on space-time correlations. Due to the amount of data and complexity of the model, the full Bayesian posterior is numerically intractable. To tackle this, we sequentialize the inversion by implementing a Kalman-filter with a fixed time step. Every step consists of a prediction, based on a degree dependent temporal covariance, and a correction via Gaussian process regression. Dating errors are treated via a noisy input formulation. Cross-correlations are re-introduced by a smoothing algorithm and model parameters are inferred from the data. Due to the specific statistical nature of the proposed algorithms, the model comes with space and time dependent uncertainty estimates. The new model ArchKalMag14k shows less variation in the large scale degrees than comparable models. Local predictions represent the underlying data and agree with comparable models, if the location is sampled well. Uncertainties are bigger for earlier times and in regions of sparse data coverage. We also use ArchKalMag14k to analyze the appearance and evolution of the South Atlantic anomaly together with reverse flux patches at the core mantel boundary, considering the model uncertainties. While we find good agreement with earlier models for recent times, our model suggests a different evolution of intensity minima prior to 1650 CE. In general, our results suggest that prior to 6000 BCE the database is not strong enough to support global models.