Detection of nonstationarities in geological time series: Wavelet transform of chaotic and cyclic sequences

Abstract

Wavelet analysis is used to detect and localize unconformities, events, or chaotic and periodic-cyclic sequences in marine sedimentary successions. Computer modeling using a single nonlinear algorithm provides a quantitative approach to a better understanding of chaotic, cyclic and monotonous sedimentation, and the preservation of unconformities. To model cyclic and chaotic sequences, we consider nonlinear and cyclic fluctuations in the rate of sedimentary supply, simple climatic feedback processes, variations of the Earth's orbit and sea-level changes. Controlled by superimposed sinusoidal fluctuations of sea-level, four stages of deterministic sedimentary pattern may be detectable: (1) chaotic sedimentation at relatively low sea-level and early transgression; (2) stable sedimentation with well-pronounced cyclicity or monotonous sequences at relatively high sea-level during late transgression and early regression; (3) a pre-chaotic zone with absence of significant cyclicity during decreasing sea-level; and (4) chaotic signals in the sea-level lowstand. These patterns have also been found in a Cretaceous sedimentary succession. Additionally, the exact localization of transitions and abrupt changes (events and unconformities) in the sequences permit a sufficient and simple zonation of the datasets. These transitions can be correlated to stratigraphical boundaries or changes in the depositional environment as well as to changes of the sedimentation rate.