Some rocks contain multiple remanence “components”, each of which preserves a record of a different magnetic field. The temperature ranges over which these remanence components demagnetize can overlap, making it difficult to determine their directions. We present a data analysis tool called Thermal Resolution Of Unblocking Temperatures (TROUT) that treats the process of thermal demagnetization as a function of temperature (or alternating field demagnetization as a function of coercivity). TROUT models the unblocking temperature distributions of components in a demagnetization experiment, allowing these distributions to overlap. TROUT can be used to find the temperatures over which paleomagnetic directions change and when two directional components overlap resulting in curved demagnetization trajectories. When applied to specimens given multi-component Thermoremanent Magnetizations (TRMs) in the laboratory, the TROUT method estimates the temperature at which the partial TRMs were acquired to within one temperature step, even for specimens with significant overlap. TROUT has numerous applications: knowing the temperature at which the direction changes is useful for experiments in which the thermal history of a specimen is of interest (e.g. emplacement temperature of pyroclastic deposits, re-heating of archaeological artifacts, reconstruction of cooling rates of igneous bodies). The ability to determine whether a single component or multiple components are demagnetizing at a given temperature is useful for choosing appropriate ranges of temperatures to use in paleointensity experiments. Finally, the width of the range of temperature overlap may be useful for inferring the domain state of magnetic mineral assemblages.

The assumptions of paleointensity experiments are violated in many natural and archaeological 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 non linear Arai plots from the analysis, but there is little consensus in the paleomagnetic community on which set to use. In this paper, 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 $\vec{k}$) on the Arai plot. We can use this empirical relationship to estimate the recorded paleointensity for a specimen where $\vec{k}=0$, i.e., 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.