Détection des transitions lithologiques par lʹanalyse de la composante fractale des diagraphies par transformée continue en ondelettes

The frequency analysis of many log data permits to verify that their stochastic component show ‘power-law-type’ spectral densities, characteristic of 1 / f noise. They can be modelled by fractional Brownian motions. Continuous Wavelet Transformation (CWT) provides us with very efficient methods to determine the local spectral exponents of these scaling laws. These new attributes are related to the local fractality of these signals. We first present some theoretical results and an application to a fractional Brownian motion. The second application concerns a dataset recorded in the MAR203 borehole. We show that clustering of these new pseudo-logs leads to a good resolution between different lithofacies. To cite this article: N. Zaourar et al., C. R. Geoscience 338 (2006).