Lithologic characterization of a reservoir using continuous-wavelet transforms

We consider the problem of characterizing the lithology of a reservoir using gamma ray logs as well as seismic traces around the well. We first calculate the continuous-wavelet transform of the the data and then use the fact that the energy of such transformation is proportional to a power of its scale. The technique consists in estimating the power transformation obtaining a set of values of the same size as the original data and then modeling the distribution of these values using a double exponential. We find that wells that are predominantly sand correspond to distributions that are significantly different from those that correspond to wells that are predominantly gravel. This happens in both cases: gamma rays and seismic traces. We use this characterization to classify other points in the reservoir.