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.

中文翻译：

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具有改进的古粒子变异再现的协变巨型高斯过程模型

常用的统计磁场模型族基于巨型高斯过程（GGP），该过程假定每个高斯系数都可以通过独立的正态分布实现。GGP模型能够生成一组合理的高斯系数，从而可以针对由时间平均地磁场产生的预期分布来测试古磁数据。但是，现有的GGP模型无法同时重现过去一千万年报告的场强分布和古粒子变化估计，并且除非在低纬度条件下进行了折衷，否则往往会低估高纬度的虚拟地磁极（VGP）色散。纬度。在这里，我们介绍一个新的GGP模型系列，BB18和BB18.Z3（后者包括球谐度2和3的非零均值纬向项）。我们的模型与之前的GGP模型不同，它同时从较高阶项中分别处理轴向偶极子方差，应用奇偶方差结构，并在某些高斯系数之间合并了协方差。高斯系数之间的协方差，既是发电机理论所期望的特性，也是在数值发电机仿真中观察到的特性，以前并未包含在GGP模型中。从“类地”发电机模拟的整体中推断出并通过理论预测的某些高斯系数之间的协方差，可以减少对VGP色散的不匹配，