Quantifying uncertainty in stratigraphic alignment of geological signals using probabilistic dynamic time warping

Aligning stratigraphic records is essential for constructing unified and coherent chronological frameworks for Earth's history and advancing our understanding of past environments and geological processes. However, the alignment process is often complicated by noise, hiatuses, and local accumulation dynamics, which introduce significant uncertainty. To address these challenges, we present the Probabilistic Dynamic Time Warping (P-DTW) algorithm, designed to align noisy stratigraphic signals, identify multiple plausible alignment scenarios, and quantify the associated uncertainty. The algorithm incorporates three transition probability factors, which are used to stochastically sample the alignment paths through the DTW cost matrix. The P-DTW algorithm is primarily aimed at aligning stratigraphic signals where peak-to-peak correlations are ambiguous.

Through synthetic test cases, we demonstrate the ability of the P-DTW algorithm to capture a range of plausible alignments, while quantifying the associated uncertainty. This stands in contrast to the traditional deterministic DTW algorithm, which provides a single solution that may overlook geologically plausible alternatives. Furthermore, we show the P-DTW algorithm's capacity to align signals with different amplitudes over the same intervals, and how to incorporate tie points derived from independent constraints.

When applied to real-world δ¹⁸O data from sediment cores GeoB7920-2 and MD95-2042, the P-DTW algorithm generates an alignment model consistent with established alignments while quantifying the associated uncertainties. Additionally, we demonstrate the algorithm's ability to align the magnetic susceptibility signal from the ENAM93-21 core in the North Atlantic with the δ¹⁸O record from the NorthGRIP ice core, resulting in an age-depth model that aligns with independent constraints. Finally, we showcase the algorithm's capacity to integrate chronological information across sites within a probabilistic inverse modeling framework, hereby facilitating the construction of a coherent multi-site age-depth model.