Automatic detection of lithologic boundaries using the Walsh transform: A case study from the KTB borehole

An automatic method of lithologic boundary detection based on Walsh transform theory is developed and applied to the German Continental Deep Drilling Project (KTB) borehole well log data. Walsh functions are natural choices for describing binary waveforms; hence a Walsh transform-based scheme is most appropriate for detecting lithologic boundaries. The Walsh transform technique involves low-pass filtering augmented by a “Skilled Algorithm” to identify the correct boundary depths. In Walsh domain filtering, the step width of a low-pass image of the original signal is a function of cutoff sequency and also constant over a binary width. This makes the method more suitable to attune and resolve appropriately the minimum thickness of lithologic successions. The application of the method to the best available KTB data yields results that confirm the current geophysical model and also resolve additional finer scale boundaries embedded within larger geological units. The Walsh transform-based detection scheme renders an effective means for resolving and understanding structural inhomogeneity within complex geologic signals, particularly borehole geophysical logs.