Exact Analytical Solutions for Kinetic Equations Describing Thermochemical Remanence Acquisition for Single-Domain Grains: Implications for Absolute Paleointensity Determinations

Abstract

The magnetic record, preserved by igneous rocks in the form of thermoremanent magnetization (TRM) or thermo-chemical remanent magnetization (TCRM), is essential to reconstruct Earth's absolute paleointensity (API) but strongly depends on the kinetic conditions in which the remanence was acquired. In this paper, we present exact analytical solutions describing the time-dependent processes of acquisition and thermal demagnetization of various kinds of thermally activated remanences for non-interacting single-domain grains with uniaxial shape anisotropy. Our solutions, derived in less-restrictive conditions than previous studies, are also valid for TCRMs acquired either by growth of grain volume or by increase of the Curie point Tc. We first show that TCRMs by Tc increase and TRMs are of comparable intensity whereas TCRMs by volume growth are significantly less intense. We then model Arai-Nagata diagrams for assemblies of coercivity-variable grains and find that all Thellier-type protocols yield reliable API determinations for TRMs and TCRMs by Tc increase, with the peculiarity of the IZZI protocol to produce small zigzags in the Arai-Nagata diagram. In contrast, TCRMs by volume growth yield convex Arai-Nagata diagrams. The most conspicuous kinetic effect is the influence of cooling rate on API determinations due to a ∼5% increase of the remanent magnetization for a 10-fold increase in cooling time. We show that the situation is problematic when the cooling time of natural samples coincides with the geomagnetic secular-variation time scales. Natural samples with cooling times sufficient to average out secular variation conversely yield reliable API determinations provided a cooling-rate correction is applied.