Tracer dynamics in ocean sediments and the deciphering of past climates

An analysis of tracer dynamics in ocean sediments taking into account the disordered, fractal, character of geological materials is performed. The complexity of the medium is modeled by augmenting the equation of motion of the tracer through the addition of a stochastic forcing. In the one-dimensional version of the model, it is found both analytically and numerically that the dynamics is characterized by a large dispersion of arrival times at a given depth of the sediment as deduced from the first passage time probability distribution of the tracer. Moreover, the trajectories of two initially close tracer particles deviate at later times according to a power law, thereby raising the question of reliability of climatic trends deduced from geological data. Numerical simulations in a more realistic, two-dimensional setting show that this uncertainty becomes even more pronounced entailing the formation of a fractal precipitation front whose width increases with time. The implications of the results on the interpretation of geological records are discussed.