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Episodic Erosion With a Power Law Probability Density, and the Accumulation of Cosmogenic Nuclides
Author(s) -
Muzikar Paul
Publication year - 2019
Publication title -
journal of geophysical research: earth surface
Language(s) - English
Resource type - Journals
eISSN - 2169-9011
pISSN - 2169-9003
DOI - 10.1029/2019jf005095
Subject(s) - cosmogenic nuclide , pareto distribution , power law , nuclide , spall , erosion , spallation , pareto principle , range (aeronautics) , statistical physics , geology , mechanics , law , mathematics , physics , statistics , materials science , nuclear physics , geomorphology , cosmic ray , neutron , composite material , political science
In steady state, the concentration n of a cosmogenic nuclide in a surface can be used to study the local erosion rate. When the erosion is due to episodic spalling events, this concentration is not constant in time but has a statistical distribution which reflects the underlying spallation process. In this paper, we study a model in which slabs of rock of depth w are removed in instantaneous events; the time intervals t between these events are random variables. The probability density for t , p ( t ), is taken to have a Pareto distribution, with a power law decrease at large values of t . This case is interesting to study, since the Pareto distribution can lead to the occurrence of a wide range of time intervals, which can lead to a broad distribution of measured values of n . We derive analytic expressions for the average and the variance of n in steady state and compare our results to previous work, which took p ( t ) to decrease exponentially with t . We also show results from simulations of the Pareto model, which allow us to gain insight into the time‐dependent behavior of the nuclide concentration.