²¹⁰Pb-dating of recent sediments with the χ-mapping CF and CSAR models. On the attractors

Conventional ²¹⁰Pb-dating models use assumptions on sedimentary conditions that allow for analytical formulations. The novel χ-mapping models use numerical methods to generate and test a large number (∼10⁶) of potential solvers. Empirical data (excess ²¹⁰Pb vs. mass depth profile) serve to attract the solver that minimizes the χ function (the attractor), and it has been assumed that it also defines the most likely chronology. This work aims to test this assumption in a deep way. In synthetic and varved sediments, the performance of each solver can be quantified through a parameter ξ_a accounting for the deviation of the model and the true ages. This work studies the complex relationships between χ and ξ_a using the constant flux (χ-CF) and the constant sediment accumulation rate (CSAR) models, which operate in a parametric 3D space. The full mapping of the 3D χ function serves to find the absolute minimum, for the graphical representation of the complex topology of the attractors, which is model-specific, and for plotting clouds of chronological lines from solvers with varying χ values. The minimum value of ξ_a (the best chronology) is achieved for a wide range of χ values, including the region of the absolute minimum. In complex cases, tiny changes in χ can result in quite different chronologies. Alternative attractors that include a reference date and an objective function are studied. The results provide guidelines for strengthening the ²¹⁰Pb-based chronologies.