Evaluation of periodicities and fractal characteristics by wavelet analysis of well log data

Stratigraphic cycles are controlled by both deterministic and stochastic factors and commonly have both cyclic periodicities and fractal characteristics. A significant issue in stratigraphy is to be able both to evaluate the stochastic fractal trend and to detect periodic components such as Milankovitch cycles in stratigraphic records. In this context we propose the use of the relative wavelet spectrum, the wavelet-based spectral ratio, and the relative scalogram to detect dominant periods against fractal trends in stratigraphic records. Our method uses the relationships of the various kinds of wavelet-based spectra and classical power spectra. Application of the proposed method to synthetic data (periodic signal with red noise) and to well log data shows that the wavelet-based spectra, scalogram and their ratios are effective and convenient for evaluating periodicities and fractal characteristics of stratigraphic records characterized by a low signal-to-noise ratio in cyclostratigraphic study. The analyzed well log data appear to have both a fractal trend and important cycle periods at spatial scales greater than 1.6-2.5 m, corresponding potentially to parasequences consisting of alternation of beds.