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UBC Theses and Dissertations

Multiple dynamic matching and median filters applied to sonic well logs Leaney, W. Scott Powell


Nonlinear signal matching is a generalization of cross correlation in that a discrete lag between signals is replaced with a variable lag function or 'matching function', m(x). Two methods are reviewed which attempt to solve for m(x), namely the dynamic programming approach and the inverse theory approach. Both methods suffer from pitfalls and require the input of prior constraints to ensure convergence to the correct solution. The goal of this work has been to develop a method that can handle simple or complex matching problems and can succeed without any prior knowledge constraints. The multiple dynamic matching method is the result. It uses a significance threshold to extract a set of ridge points from a similarity matrix and applies dynamic programming to obtain a set of matched sections. These significant matched sections or 'subpaths' are then combined into a set of complete matching functions and a 'mean local confidence' norm is evaluated to determine the best overall match. It is argued through a model of change between signals, that given that the correct matching function is known, the presence of large amplitude changes between signals can cause the correct matching function to appear suboptimal under similarity norms. Multiple dynamic matching, because it generates suboptimal solutions as well, does not overlook the correct matching function. Typically the top three interpretations as ranked by mean local confidence will contain the expert's choice for the correct matching function. The use of median filters to preprocess the data and enhance well log features for matching has been investigated. A new 'median decomposition' is discussed as well, and in the context of a scale - space point of view to filtering, it is argued that median scale space is the proper choice for blocky waveforms. Finally, the connection between multiple dynamic matching and pattern recognition is explored, and matching iteratively through scale is proposed as a means of further generalizing the multiple dynamic matching method, making efficient high resolution matching possible.

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