The importance of optimum mother wavelet selection for data decomposition in earth sciences

Analysis of earth science data using different transform methods such as Fourier and wavelet transform, are useful for the extraction of hidden information imbedded in the data. Fortunately, the uses of such transforms have been expanding as reported in recent studies. Wavelets and wavelet transform in signal processing, offer important advantages that are highly useful in transient data analysis. These include multiresolution analysis of data for extraction of different information that reside in different frequency bands as well as extraction of localized features, a distinct property of wavelet transform as compared with other transforms. Furthermore, in wavelet transform, availability of alternative mother wavelets each with its own distinct featuremakes wavelets highly suitable for their usage in different application environment for maximal information extraction. Therefore selection of appropriate mother wavelet for maximal information extraction in a given data analysis, is considered to be an important and necessary step when working with wavelets.Areview of literature in earth science on the subject of optimal wavelet selection reveals little work has been done on the subject. In this paper, we have attempted to overcome this shortcoming in which we have investigated various approaches and considerations for the selection of optimum mother wavelet. In this investigation the results of a case study for selection of optimum mother wavelet for decomposition of set of petrophysical logs gathered from one of the Iranian south oil elds are presented. The signicance of optimum mother wavelet selection in this oil eld is shown.