Spectral Analysis based on Wavelet Transform Maxima: Identification of Multi-order Stratigraphic Boundaries and Cycles

Abstract

In sedimentology, stratigraphic sequences and cycles are ordered by time spans and physical scales, such as thickness, and bounded by discontinuities, including unconformities or flooding surfaces. Spectral analysis based on wavelet transform (WT) maxima is proposed and used as a quantitative tool to identify multi-order stratigraphic boundaries and cycles in well log data. The proposed spectral analysis is based on quantitative analysis on the center frequencies and resolutions of Gaussian wavelets in time and frequency, and uses a combination of the WT maxima based on both the first order Gaussian wavelet having a high time resolution and the seventh order Gaussian wavelet having a high frequency resolution. WT maxima spectra, which can characterize the evolution of WT maxima across scales and periods along WT maxima lines concerned with sequence boundaries, are used to detect dominant spectral peaks corresponding to the time-period domain WT maxima and to determine WT maxima spectral slopes. The WT maxima spectral slopes are helpful for discriminating sequence boundaries from intrasequence cyclic variations in well log data, and the time-period domain WT maxima are used to relate the detected boundaries to relevant cycles. The interval WT maxima spectra and the stationary index, related to the WT maxima spectra, are introduced as indicators that can be used for the hierarchical ordering of the boundaries and cycles. Application of the proposed method to well log data shows that the suggested method is efficient in identifying multi-order sequences that relate well to the Milankovitch cycles.