Extraction of geological information from acoustic well-logging waveforms using time-frequency wavelets

Recently developed classification and regression methods are applied to extract geological information from acoustic well-logging waveforms. First, acoustic waveforms are classified into the ones propagated through sandstones and the ones propagated through shale using the local discriminant basis (LDB) method. Next, the volume fractions of minerals are estimated (e.g., quartz and gas) at each depth using the local regression basis (LRB) method. These methods first analyze the waveforms by decomposing them into a redundant set of time-frequency wavelets, i.e., the orthogonal wiggle traces localized in both time and frequency. Then, they automatically extract the local waveform features useful for such classification and estimation or 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 data set, 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.