Detecting Stratigraphic Discontinuities using Wavelet and S-Transform Analysis of Well Log Data

Detecting stratigraphic discontinuities using well log data is a fundamental task in petroleum geosciences projects. Wavelet transforms (WT) and S-transform (ST) of well log data can provide objective identification of lithological interfaces to aid in this effort. The continuous wavelet transform (CWT) of a time series gives the wavelet correlation coefficients (i.e. similarity) between the given time series and the wavelet at different spatial scales. In comparison, S-transform (ST) is a hybrid form of short-time Fourier transform and wavelet transform that provides a measure of the local Fourier frequency spectrum of the time series (in this case well log data). We applied Haar continuous wavelet (HCWT) and S-transform on five types of well log data (Gamma Ray (GR), Spontaneous Potential (SP), Deep Resistivity (RD), Bulk Density (RHOB) and Neutron Porosity (NPHI) logs) from an oil sands evaluation well in the Cold Lake area of Alberta to evaluate autonomous detection of lithological interfaces. The wavelet analysis of well log data delivered two-dimensional output (i.e. depth vs. scale) of the given one-dimensional (depth only) well log record. The results of HCWT are presented in terms of wavelet coefficients at different scales whereas the results of ST are shown at different frequencies. The Haar wavelet with its rectangular shape is able to identify the abrupt change in the well log signal encountered at bed boundaries, and therefore it is effective in extracting lithological discontinuities from the well log data analysis. Stransform was applied to median filtered data in order to suppress signal noise. It was observed that in the HCWT of noisy data, there was no appearance of high values of wavelet coefficients (i.e. the HCWT fails to identify change in the noisy log data even after filtering), whereas ST is able to identify the changes in the data. Both, CWT and ST show good depth-frequency resolution in detecting interfaces, however they produce different outputs. These transformation methods are additional and efficient approaches to identify stratigraphic interface boundaries using well log data and useful in the quantitative division of geological layers in the petroleum reservoir characterization.