Geomagnetic field variations and the accumulation of in-situ cosmogenic nuclides in an eroding landform

The analysis of cosmogenic nuclides in an eroding surface yields information concerning erosion rates and exposure times. Such analysis requires accurate knowledge of the nuclide production rate at the site in question. Here we develop a relatively simple analytic model for the time variation of the production rate caused by fluctuations in the geomagnetic field. This model contains three parameters, which have a clear physical meaning and which provide a convenient way to quantify information on the production rate variations. We use this model to compute the buildup of nuclides in an eroding surface, and derive an analytic formula for the nuclide concentration as a function of the exposure time and the erosion rate. Several representative applications of our results are presented.