Classification of geophysical acoustic waveforms using time-frequency atoms,
1996 Proc. Computing Section of Amer. Statist. Assoc., pp.322-327,
Acoustic waveforms recorded in boreholes carry important information for oil and gas exploration and development. For example, classifying such waveforms to the ones propagated through sandstone layers and the ones through shale layers is helpful for identifying the reservoir region. We apply recently developed Local Discriminant Basis (LDB) method to this classification problem. Given the training dataset consisting of the reference waveforms and the corresponding geological information, the LDB method first analyzes the waveforms by decomposing them into a redundant set of time-frequency atoms, i.e., the orthogonal wiggles localized both in time and frequency (e.g., wavelet packets, local sine/cosine bases, and local Fourier bases). Then, this method automatically extracts the local waveform features (expansion coefficients into a subset of such atoms) useful for classifying the waveforms. Finally a small number of these features (e.g., 10 to 20 % of the dimension of the input signals) are fed into a classifier such as linear discriminant analysis or classification trees. Because these extracted features are localized in time and frequency, they allow intuitive interpretation of the results and may provide new insights and understanding of the problem.
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