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Figure 2.
Illustration of the dynamic time warping technique for aligning simple, synthetic δ13Ccarb sequences. (A–G) Step-by-step matrix operations to align the two synthetic δ13Ccarb sequences (target, original candidate) shown in frame (H). The target and original candidate δ13Ccarb sequences populate the columns and rows of the target (A) and candidate (B) matrices, respectively; subtracting the candidate matrix from the target matrix yields the difference matrix (C). Squaring the values in the difference matrix generates the squared-difference matrix (D), a measure of the similarity of all pairs of δ13Ccarb from the target and candidate sections. Multiplying the edges of the squared-difference matrix by the adopted value of the edge parameter yields the edge-modified matrix (E). The cumulative difference matrix (F) incorporates the accumulation of cost arising from the adopted value of the g parameter. The alignment path, which reveals the temporally equivalent target and candidate strata/δ13Ccarb values, begins in the lower right corner of the cumulative difference matrix and proceeds to the lowest cost cell looking two steps ahead (G). For these synthetic data, the alignment path shifts the aligned candidate section stratigraphically higher on the target sequence relative to the original candidate meterage (H). Abbreviations: Difference = the difference matrix; Sq. Diff. = the squared-difference matrix; min(aug. 8 preceding) = the minimum value of the eight preceding cumulative difference matrix cells; Edge = the edge-modified matrix.
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