INCORPORATING RADIOMETRIC CONSTRAINTS IN DYNAMIC PROGRAMMING ALGORITHMS TO ALIGN CHEMOSTRATIGRAPHIC TIME SERIES

Dynamic programming algorithms can optimize the alignment of two geochemical time series (Lisiecki and Lisiecki, 2002; Hay et al., 2019). As written, these algorithms do not leverage stratigraphic tie points when generating a library of plausible alignments. Here we present a modified version of the algorithm that incorporates stratigraphic tie points, such as a shared radiometric constraint. Following Hay et al. (2019), the algorithm first constructs a matrix with dimensions equal to the number of (isotopic) values in each time series. Each matrix element is then populated by the value of the squared difference between a data point in each of the time series. A path comprised of the contiguous set of matrix elements that minimizes the cumulative sum of squared differences between the time series dictates an optimal alignment. Two geologically relevant penalty functions encourage/discourage temporal overlap of the two time series and relative changes in the rate of sediment accumulation and thereby produce a multitude of paths, herein referred to as a 'library' of plausible alignments. Here we explore the alignment of synthetic δ¹³C_carb signals (both sinusoidal and randomly generated waveforms) with randomly assigned stratigraphic tie points of normally distributed time uncertainty as well as a case study of aligning Cambrian Series 1–2 δ¹³C_carb curves with ID-TIMS U-Pb radiometric dates (Maloof et al., 2005; 2010). We explore the merit of (i) generating a library of alignments without heed to temporal control and then eliminating those that do not conform to the stratigraphic tie point versus (ii) following the method proposed by Haam and Huybers (2010) that imposes a bell-curve–shaped ‘bonus’ function to attract the warping path through a gateway in the matrix whose location is determined by the stratigraphic tie point. The inclusion of tie points in the least-squares calculation reduces the number of non-unique alignments between the time series.