In this thesis, I adopt ideas of finding the structure from randomness to recover the low-rank representations of the full subsurface extended image volumes which can give us access to any elements and image gathers. I derived the time-domain wave-equation based factorization via randomly probing which helps to remove the computational bottlenecks in both wave-equation solves and the imaging conditions. Also, I designed the framework combined with power iterations to increase the recovered accuracy without increasing the probing size.

Nitrous oxide (N2O) is a potent greenhouse gas that can destroy stratospheric ozone. In marine environments, N2O is assumed to be produced and consumed solely by nitrogen-metabolizing microbes. It has been shown, however, that intermediate metabolites from these microbes can potentially leak out of cells and react with metal oxides to produce N2O. Recent studies have shown that the nitrification intermediate hydroxylamine (NH2OH) can chemically react with manganese (Mn) oxides in soils to yield N2O. Little is known about these interactions in marine systems.

Manganese oxides (MnO2) are ubiquitous in the environment and play an important role in the transformation and transport of contaminants in the environment and the biogeochemical cycling of carbon. This study investigated both aspects of these roles using a combination of laboratory experiments and field work. First, the kinetics of oxidation of the more toxic arsenic form, arsenite (As(III)), to the less mobile form, arsenate (As(V)), by MnO2 was determined and the mechanism of the reaction investigated.