Bayesian geochemical correlation and tomography

To accurately reconstruct palaeoenvironmental change through time it is important to determine which rock samples were deposited contemporaneously at different sites or transects, as erroneous correlation may lead to incorrectly inferred processes and rates. To correlate samples, current practice interpolates geological age between datable units along each transect, then temporal signatures observed in geochemical logs are matched between transects. Unfortunately spatiotemporally variable and unknown rates of sedimentary deposition create highly nonlinear space-time transforms, significantly altering apparent geochemical signatures. The resulting correlational hypotheses are also untestable against independent transects, because correlations have no spatially-predictive power. Here we use geological process information stored within neural networks to correlate spatially offset logs nonlinearly and geologically. The same method creates tomographic images of geological age and geochemical signature across intervening rock volumes. Posterior tomographic images closely resemble the true depositional age throughout the inter-transect volume, even for scenarios with long hiatuses in preserved geochemical signals. Bayesian probability distributions describe data-consistent variations in the results, showing that centred summary statistics such as mean and variance do not adequately describe correlational uncertainties. Tomographic images demonstrate spatially predictive power away from geochemical transects, creating novel hypotheses attributable to each geochemical correlation which are testable against independent data.