Reflection extraction from sonic log waveforms using Karhunen-Loeve transform

Junxiao Li, Kristopher A. H. Innanen, Guo Tao, Laurence R. Lines

Sonic reflection logging, a recently developed borehole geophysical scheme, is in principle capable of providing a clear view of structures up to 40 m away from well site theoretically. Under acoustic well logging conditions, reflected wave signals used in sonic reflection logging are generally lost in the full waveform records, hidden by the dominant direct waves (direct P- and S- waves, and the Stoneley wave). It is critical, therefore, to effectively extract the reflection signals from the acoustic full waveforms in acoustic reflection well logging data processing. The Karhunen-Loeve (KL) transformations combined with a band limiting filter is used to extract reflections of interest out of dominant direct waves. Based on energy difference of each wave component, the direct Stoneley wave, S wave and P wave are to be eliminated separately from high to low energy component. Therefore, the extracted reflections can then be used in migration so as to get a clear image of the structures outside borehole.