Improving methods to search for signatures of astronomical chaos in time series

Incoming solar radiation (insolation) received on Earth is controlled by Earth's rotational parameters and its distance from the sun. These quasi-cyclic variations in the Earth's eccentricity, axial tilt, and precession, also called Milankovitch cycles, alter the local and global climate on Earth in time scales of 104 to 106 years. As astronomically forced climate variation is imprinted in sediments, this information can be utilized in combination with other stratigraphic and dating methods to establish precise and high-resolution geological time scales. Astronomical time scales have been constructed by tuning cyclic climatic records to theoretical orbital solutions. These astronomical models are calculated with present (initial) conditions. However, the chaotic dynamics of the Solar System pose limits on the prediction and calculation of an accurate solution for the orbital and precessional motion of the Earth over more than 50 Ma. One main manifestation of astronomical chaos is quantifiable in resonance changes of the secular (fundamental) frequencies between Mars (g4, s4) and Earth (g3, s3). The frequencies g3 and g4 are associated with the precession of the perihelion, the closest approach to the Sun. The frequencies s3 and s4 relate to the precession of the nodes, the intersection of the orbital plane with the reference plane. The resonance of 2:1 defined as 2(s4 - s3) = (g4 - g3) changes into a 1:1 resonance expressed as (g4 - g3) = (s4 - s3). The challenge is to detect resonance changes induced by astronomical chaos in the geological record in order to test and extend the applicability of theoretical astronomical models. This would contribute to the precision of astronomically tuned age models which are needed to reconstruct Earth history.