FROM EXPERIMENTAL BASINS TO DELTAS: STATISTICAL CHARACTERIZATION OF SURFACE DYNAMICS IN DELTAIC SYSTEMS

In depositional systems, channels migrate from one location to another, causing erosion and deposition at any given point in the domain. The durations of depositional and erosional events, as well as their magnitudes, control the structure of the stratigraphic record. The goal of this study is to use data from a small-scale laboratory experiment to understand and quantify the statistical structure of surface evolution of deltaic systems. For this purpose, we use high-resolution temporal surface elevation data from a controlled experiment to quantify the probability distributions of the processes that govern the evolution of depositional deltaic systems. Heavy-tailed statistics of erosional and depositional events are documented, indicating that a small but significant chance exists for the occurrence of extremely large events. We show that the periods of inactivity, when neither erosion nor deposition occurs, is well described by a truncated Pareto Distribution whose truncation scale is set by the mean characteristic avulsion time scale in the system. Further, we show that the heavy-tails in the magnitudes of depositional and erosional events are not preserved in the stratigraphic record, resulting instead in an exponential distribution for the bed sediment thickness. It is also shown that the temporal evolution of surface elevation exhibits self-similarity. Finally, we show how the results of this study can lead to improved diffusional models for surface evolution using tools of fractional calculus.