Much remains to be known about offshore phenomena, despite the potential threat they pose to coastal communities and economically-important offshore infrastructure. The scientific and engineering community has a fairly good grasp of the mechanics governing these geohazards; for instance, we can model tsunami run-ups over entire oceans, evaluate the stability of slopes, and predict the runout of a given landslide. Much of the uncertainty arising in applications of such models stems from the sparsity and error in offshore data. Such datasets are often sparse because the ocean is so large, and contain values with potentially significant measurement error because of the complexities involved in collecting data in such extreme conditions (e.g., sampling sediment under miles of water). Stochastic techniques and statistics quantify these types of uncertainty. In the first chapter of this dissertation, I apply a stochastic optimization method to a geophysical model to achieve estimates of sub-seabed gas concentrations from remotely-sourced seismic reflection data. In the second chapter, I combine geostatistics and first-order, second-moment uncertainty analysis to map the probability of slope failure along the entire U.S. Atlantic margin. My third and final chapter statistically characterizes offshore wind speeds using an unprecedented amount of data collected over the northwestern hemisphere.
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