The strength of the geomagnetic field has been a focus of geophysical research since the 1930s, starting with the work of Königsberger (1936) and Thellier (1938) and continuing today (see review of Tauxe and Yamazaki, 2015). Absolute paleointensity experiments rely on the assumption from Néel theory (Néel, 1949) that thermal remanent magnetizations (TRMs) are related quasilinearly to the field in which a sample cooled and are generally based on normalization of remanences in controlled laboratory fields. Despite decades of effort, fundamental problems remain with the methods used to extract reliable records of field strength. Paleointensity experiments involve a variety of protocols and there is no consensus on what materials might

The assumptions of paleointensity experiments are violated in many natural and archeological materials, leading to Arai plots which do not appear linear and yield inaccurate paleointensity estimates, leading to bias in the result. Recently, paleomagnetists have adopted sets of “selection criteria” that exclude specimens with nonlinear Arai plots from the analysis, but there is little consensus in the paleomagnetic community on which set to use. In this study, we present a statistical method we call Bias Corrected Estimation of Paleointensity (BiCEP), which assumes that the paleointensity recorded by each specimen is biased away from a true answer by an amount that is dependent a single metric of nonlinearity (the curvature parameter truek⃗) on the Arai plot. We can use this empirical relationship to estimate the recorded paleointensity for a specimen where truek⃗=0, that is, a perfectly straight line. We apply the BiCEP method to a collection of 30 sites for which the true value of the original field is well constrained. Our method returns accurate estimates of paleointensity, with similar levels of accuracy and precision to restrictive sets of paleointensity criteria, but accepting as many sites as permissive criteria. The BiCEP method has a significant advantage over using these selection criteria because it achieves these accurate results without excluding large numbers of specimens from the analysis. It yields accurate, albeit imprecise estimates from sites whose specimens all fail traditional criteria. BiCEP combines the accuracy of the strictest selection criteria with the low failure rates of the less reliable “loose” criteria.

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A foundational assumption in paleomagnetism is that the Earth's magnetic field behaves as a geocentric axial dipole (GAD) when averaged over sufficient timescales. Compilations of directional data averaged over the past 5 Ma yield a distribution largely compatible with GAD, but the distribution of paleointensity data over this timescale is incompatible. Reasons for the failure of GAD include: (a) Arbitrary “selection criteria” to eliminate “unreliable” data vary among studies, so the paleointensity database may include biased results. (b) The age distribution of existing paleointensity data varies with latitude, so different latitudinal averages represent different time periods. (c) The time‐averaged field could be truly non‐dipolar. Here, we present a consistent methodology for analyzing paleointensity results and comparing time‐averaged paleointensities from different studies. We apply it to data from Plio/Pleistocene Hawai'ian igneous rocks, sampled from fine‐grained, quickly cooled material (lava flow tops, dike margins and scoria cones) and subjected to the IZZI‐Thellier technique; the data were analyzed using the Bias Corrected Estimation of Paleointensity method of Cych et al. (2021, https://doi.org/10.1029/2021GC009755), which produces accurate paleointensity estimates without arbitrarily excluding specimens from the analysis. We constructed a paleointensity curve for Hawai'i over the Plio/Pleistocene using the method of Livermore et al. (2018, https://doi.org/10.1093/gji/ggy383), which accounts for the age distribution of data. We demonstrate that even with the large uncertainties associated with obtaining a mean field from temporally sparse data, our average paleointensities obtained from Hawai'i and Antarctica (reanalyzed from Asefaw et al., 2021, https://doi.org/10.1029/2020JB020834) are not GAD‐like from 0 to 1.5 Ma but may be prior to that.