Extraction of Geological Information from Acoustic Well-Logging Waveforms Using Time-Frequency Wavelets, (with R. R. Coifman), Geophysics, vol. 62, no. 6, pp. 1921-1930, 1997.

Abstract

We apply recently developed classification and regression methods to extract geological information from acoustic well-logging waveforms. First, we classify acoustic waveforms into the ones propagated through sandstones and the ones through shale using the Local Discriminant Basis [LDB] method.  Next, we estimate the volume fractions of minerals (e.g., quartz andgas) at each depth using the Local Regression Basis [LRB] method. These methods first analyze the waveforms bydecomposing them into a redundant set of time-frequency wavelets, i.e., the orthogonal wiggles localized both in time and frequency. Then, these automatically extract the local waveform features useful for such classification and estimation/regression. Finally, these features are fed into conventional classifiers or predictors.  Because these extracted features are localized in time and frequency, they allow intuitive interpretation. Using the field dataset, we found that it was possible to classify the waveforms without error into sandstone and shale classes using the LDB method.  It was more difficult, however, to estimate the volume fractions,in particular, that of gas, from the extracted waveform features. We also compared the performance of the LRB method with the prediction based on the commonly used ratio of compressional and shear wave velocities, Vp/Vs and found that our method performed better than the Vp/Vs method.

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