Approximation methods for the solution of inverse problems in lake and sea sediment core analysis

A theoretical model employing one-dimensional (depth) transport equations to describe vertical redistribution of ocean-floor and lake-floor sediment (particulates, volcanic ash, microtektites, or radioactive tracers) by episodic and nonepisodic events including bioturbation is developed analytically and demonstrated. The principles underlying the model are explained; the model equations are derived; the inverse problem of identifying the depth-dependent bioturbation coefficient is addressed; two approximation theorems are presented; and numerical results for two sample problems are presented graphically. It is suggested that compatification, porosity effects, and depth-dependent sedimentation be taken into account when formulating future models.