Can bi-coherence spectral analysis be used as test for the astronomical origin of sedimentary cycles?

Many geological datasets exhibit distinct lithological cycles at high-frequencies (e.g., ~30 kyr, ~15 kyr, ~13 kyr) that often lack a definitive explanation for their origin. While such cycles are frequently hypothesized to be tied to astronomical forcing, the identification of periodicities alone is insufficient to confirm their astronomical origin. This challenge underscores the need for robust analytical frameworks capable of probing the underlying forcing mechanisms of these cycles. Recently, amplitude variations are the standard tool to assess the possible orbital origin of quasi-cyclic sediment sequences. Bi-coherence spectral analysis, a technique commonly used to identify nonlinear interactions and energy transfer between frequencies in complex systems, offers a promising complementary approach for addressing this issue. By assessing the coherence between two primary frequencies and their interaction-generated secondary frequency in the astronomical solutions, bi-coherence spectra provide insights into the complex relationships between orbital cycles. Here, we utilize bi-coherence analysis as a tool to evaluate whether specific periodicities observed in geological records stem from nonlinear interactions consistent with astronomical forcing. We test this approach using several datasets from the Quaternary to the Paleozoic and assess Milanković and sub-Milanković frequencies. This study proposes a novel test for the astronomical origin of cycles in geological records.