Uncertainty in Automated Well-Log Correlation Using Stochastic Dynamic Time Warping

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Well-log correlation is used extensively to generate subsurface cross sections from sparse well data. This is commonly done by a subject matter expert such as stratigraphers and exploration geophysicists. Several methodologies exist for automating the procedure with varying success. Dynamic time warping (DTW) is a signal-processing technique where one signal is locally stretched and squeezed to maximize the similarity between a reference second signal. This is done by calculating a similarity cost matrix that is traversed to minimize the cumulative distance. The technique produces reasonable results when applied to the well correlation problem. The produced correlation, however, is deterministic, and thus, it does not allow for studying the associated uncertainty. This study presents an extension of traditional dynamic time warping to allow the generation of multiple realizations of correlations. To accomplish this, the cost matrix is traversed deterministically or probabilistically based on a local correlation metric, e.g., the local correlation coefficient. The resultant realizations show stability in the correlation markers where the signals are similar and instability where they are not. The methodology is applied to two adjacent wells. Multiple well-log types (gamma ray, sonic, and resistivity) are used to construct the similarity cost matrix between the two wells. The cost matrix is traversed multiple times to produce multiple realizations. The produced realizations are geologically acceptable. By generating a large number of realizations, the uncertainty in the solutions is quantified. While the application presented here relates to well-log correlation, the presented stochastic dynamic time warping methodology can be applied to other types of signals and data, such as seismic, chemostratigraphy data, and real-time drilling measurements.