TY - JOUR
T1 - Space-time dynamics of depositional systems
T2 - Experimental evidence and theoretical modeling of heavy-tailed statistics
AU - Ganti, Vamsi
AU - Straub, Kyle M.
AU - Foufoula-Georgiou, Efi
AU - Paola, Chris
PY - 2011/6/1
Y1 - 2011/6/1
N2 - 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. In this study, 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 extreme events. We show that the periods of inactivity, when neither deposition nor erosion occurs, follow 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 the erosional and depositional 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 with a nonlinear spectrum of scaling exponents (multifractality) quantifying the complex dynamics of the system. Finally, we show how the results of this study can lead to improved diffusional models for surface evolution using the tools of fractional calculus.
AB - 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. In this study, 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 extreme events. We show that the periods of inactivity, when neither deposition nor erosion occurs, follow 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 the erosional and depositional 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 with a nonlinear spectrum of scaling exponents (multifractality) quantifying the complex dynamics of the system. Finally, we show how the results of this study can lead to improved diffusional models for surface evolution using the tools of fractional calculus.
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U2 - 10.1029/2010JF001893
DO - 10.1029/2010JF001893
M3 - Article
AN - SCOPUS:79957459938
SN - 2169-9003
VL - 116
JO - Journal of Geophysical Research: Earth Surface
JF - Journal of Geophysical Research: Earth Surface
IS - 2
M1 - F02011
ER -