Covariant Giant Gaussian Process Models With Improved Reproduction of Palaeosecular Variation

A commonly used family of statistical magnetic field models is based on a giant Gaussian process (GGP), which assumes each Gauss coefficient can be realized from an independent normal distribution. GGP models are capable of generating suites of plausible Gauss coefficients, allowing for palaeomagnetic data to be tested against the expected distribution arising from a time-averaged geomagnetic field. However, existing GGP models do not simultaneously reproduce the distribution of field strength and palaeosecular variation estimates reported for the past 10 million years and tend to underpredict virtual geomagnetic pole (VGP) dispersion at high latitudes unless trade-offs are made to the fit at lower latitudes. Here we introduce a new family of GGP models, BB18 and BB18.Z3 (the latter includes non-zero-mean zonal terms for spherical harmonic degrees 2 and 3). Our models are distinct from prior GGP models by simultaneously treating the axial dipole variance separately from higher degree terms, applying an odd-even variance structure, and incorporating a covariance between certain Gauss coefficients. Covariance between Gauss coefficients, a property both expected from dynamo theory and observed in numerical dynamo simulations, has not previously been included in GGP models. Introducing covariance between certain Gauss coefficients inferred from an ensemble of Earth-like dynamo simulations and predicted by theory yields a reduced misfit to VGP dispersion, allowing for GGP models which generate improved reproductions of the distribution of field strengths and palaeosecular variation observed for the last 10 million years.