Statistical Tuning via the Coherent Output Spectrum

Statistical tuning quantitatively evaluates the consistency between candidate timescales and the theoretical astronomical forcing using an explicit statistical criterion or probabilistic model. The developments in statistical tuning methods have greatly improved the objectivity and reproducibility of cyclostratigraphy. Recent advances have even moved beyond the optimization of sedimentation rates or an age-depth model toward the reconstruction of the orbital evolution within the Solar System. Conventional statistical tuning primarily relies on the linear correspondence between tuned series and target signal, either in the time domain or in the frequency domain. While the criteria are highly intuitive from the perspective of classical visual tuning, the methods somewhat suffer from limited formal interpretability. Here we propose a new statistical tuning criterion based on the coherent output spectrum, designed to quantify how much of the energy from the orbital forcing input is actually recoverable from a candidate tuned geological record. The phase coherence between the orbital parameters and the filtered signals were the earliest approach to assessing whether the sedimentary signal preserved identifiable astronomical imprints. With the widespread adoption of the amplitude modulation approach, the coherence approach gradually got deprecated for its high sensitivity to stratigraphic distortion and chronological uncertainty. We reformulate the concept of coherence with modern techniques including multitaper coherency and multiple coherence to quantify the ratio of recoverable coherent energy across orbital frequency bands. Our new statistical tuning method embeds the physical intuition and interpretability of the early coherence approach in a more robust statistical framework, suited to surrogate testing and even Bayesian inference for modern statistical tuning tasks.