Improving the analysis of well-logs by wavelet cross-correlation

The concept of wavelet cross-correlation is used to provide a new approach to identify similar patterns in related data sets, which largely improves the confidence of the results. The method amounts to decompose the data sets in the wavelet space so that correlations between wavelet coefficients can be analyzed in every scale. Besides the identification of the scales in which two independent measures are correlated, the method makes it possible to find patches of data sets where correlations exist simultaneously in all scales. This allows to extend the information of a small number of spots to larger regions. Well-log data sets from two neighboring oil wells are used. We compare similar measures at different probe sites, and also measurements of different physical quantities taken on the same place. Although this is a typical scenario for the application of classical geostatistical methods, it is well known that such methods erase out local differences in favor of smoother variability. In contraposition, this wavelet cross-correlation takes advantage of the fluctuations to give information about the continuity of the geological structures in space. It works even better if no filtering procedure has been applied to the original raw data.