Bias Corrected Estimation of Paleointensity (BiCEP): An Improved Methodology for Obtaining Paleointensity Estimates

Abstract

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.

New Paleointensity Data From Aniakchak Volcano, Alaska, USA

“…We apply the Bias Corrected Estimation of Paleointensity (BiCEP) method of Cych et al (2021) as a different means of estimating the paleointensity and uncertainty from the 1931 CE samples. BiCEP is a Bayesian method which accounts for bias in paleointensity estimates of specimens, effectively weighting the paleointensity of different specimens using the curvature of the Arai plot as a metric of nonlinearity (where linearity is measured by the 𝐴𝐴 ⃖ ⃗ 𝑘𝑘 statistic) and a predictor of bias (Cych et al, 2021). Specimen paleointensity and bias are estimated using a range of selected temperature steps in the Arai plot.…”

“…For the BiCEP calculation, we provided temperature steps for all specimens from samples NA02-1B and NA97-10, including those that failed the CCRIT selection criteria (Table 4). For the specimens that passed CCRIT, we used the temperature steps from the Thellier-GUI (Cych et al, 2021) estimation (Table 3). For the specimens that failed CCRIT we provided the temperature steps that represented the characteristic NRM/TRM of the paleointensity experiment, excluding low-temperature steps that deviate from the characteristic remanent magnetization direction on the Zijderveld plots, and high-temperature steps where thermochemical alteration occurred as evidenced by failed pTRM checks in the Arai plot.…”

“…The BiCEP estimation using all specimens from samples NA02-1B and NA97-10 generated "B-Grade" results (Cych et al, 2021), which are shown in Figure 6. The range of individual specimen paleointensity estimates relative to the range of estimated 𝐴𝐴 ⃖ ⃗ 𝑘𝑘 is shown on the left plot of Figure 6.…”

Changes in Non‐Dipolar Field Structure Over the Plio‐Pleistocene: New Paleointensity Results From Hawai'i Compared to Global Data Sets

“…Additionally, although pTRM checks are used to detect alteration, they themselves may be caused by multi‐domain carriers (Wang et al., 2013). Fortunately, the source of curvature is unlikely to matter for the BiCEP method, as it has been shown to yield accurate results when applied naively to a large test dataset, including passed and failed pTRM checks with no selection (Cych et al., 2021). However, the term “thermochemical alteration” describes a wide range of processes, and so in this study we cautiously excluded temperature steps where pTRM checks failed.…”

Artificial Intelligence for Earth System Predictability (AI4ESP) (2021 Workshop Report)

“…Note that the methods of data assimilation for spatially dependent problems or stationary problems are usually Gauss-Markov estimation. In applications, especially those that combine dynamics at different scales, research into ways to remove biases as well as ways to couple the scales in a Bayesian framework have received a great deal of attention (see Penny et al 2019;Berry and Harlim 2017;Cych, Morzfeld, and Tauxe 2021). How to deal with parametrizations of phenomena that are not well understood, and the formulation of statistical parametrizations of epistemic errors, are also very current topics of research.…”