Constraining autogenic smaller-scale stratigraphic variability via information theoretic relationships with larger-scale observations

Abstract:

Fluvial stratigraphy is a written history of temporal grain size fluctuations at the sediment surface, caused by a multitude of autogenic river processes including bedform translation, lateral migration, and channel avulsion. Smaller-scale subsurface heterogeneity due to autogenic channel and bedform dynamics (<1 m) is typically under-constrained, because it is below the resolution that can be imaged by geophysical techniques. Yet, this smaller-scale heterogeneity strongly influences flow pathways and thus rates of contaminant transport and groundwater aquifer recharge, which limits our ability to mitigate health risks and sustainably manage water resources in river-delta environments. Our study constrains smaller-scale heterogeneity produced by autogenic channel dynamics via information theoretic measures and observations of larger-scale stratigraphic variability. In particular, we use mutual information, a metric of similarity between two probability distributions, to document stratigraphic scale invariance and scale-breaks, thereby illuminating how autogenic channel processes are recorded in fluvial stratigraphy. We use the pyDeltaRCM numerical model to simulate fluvial-deltaic stratigraphy under varying model-input sand-to-mud ratios, and compute the probability distributions of bed thickness and sand-to-mud ratio for mutual information calculations. As expected, we find that different boundary conditions produce distinct stratigraphic patterns; importantly, our method attributes individual stratigraphic features to specific autogenic fluvial processes. Thus, our observations inform ongoing debate regarding the distinction of autogenic barform and bedform deposits in outcrop. Additionally, we determine that scale-breaks in stratigraphic scale invariance depend on boundary conditions, and suggest that this information can be applied to create quantitative links between observable larger-scale stratigraphic heterogeneity and smaller-scale variability.