Regularity analysis applied to sonic logs data: a case study from KTB borehole site

Borehole logs provide in situ information about the fluctuations of petrophysical properties with depth and thus allow the characterization of the crustal heterogeneities. A detailed investigation of these measurements may lead to extract features of the geological media. In this study, we suggest a regularity analysis based on the continuous wavelet transform to examine sonic logs data. The description of the local behavior of the logs at each depth is carried out using the local Hurst exponent estimated by two (02) approaches: the local wavelet approach and the average–local wavelet approach. Firstly, a synthetic log, generated using the random midpoints displacement algorithm, is processed by the regularity analysis. The obtained Hurst curves allowed the discernment of the different layers composing the simulated geological model. Next, this analysis is extended to real sonic logs data recorded at the Kontinentales Tiefbohrprogramm (KTB) pilot borehole (Continental Deep Drilling Program, Germany). The results show a significant correlation between the estimated Hurst exponents and the lithological discontinuities crossed by the well. Hence, the Hurst exponent can be used as a tool to characterize underground heterogeneities.