Hydrocarbon deposits in the form of petroleum, natural gas, and natural gas hydrates occur offshore worldwide. Electromagnetic methods that measure the electrical resistivity of sediments can be used to map, assess, and monitor these resistive targets. In particular, quantitative assessment of hydrate content in marine deposits, which form within the upper few hundred meters of seafloor, is greatly facilitated by complementing conventional seismic methods with EM data. The North-East Pacific Time-series Undersea Network Experiment (NEPTUNE) is an underwater marine observatory that provides power and network connection to a host of instruments installed on the seafloor on the Cascadia Margin offshore Vancouver Island. The observatory’s aim is to provide a platform for very long-term studies in which access to data is available on a continuous basis. For this thesis project, a transient dipole-dipole time-domain EM system was constructed and deployed on the NEPTUNE network with the goal of long-term monitoring of a well-studied hydrate deposit in the area. The instrument includes a source transmitter of electrical current and individual receivers to measure small electric field variations. The instrument is powered by the NEPTUNE observatory and data can be collected remotely by connecting to the instrument through the web. Data collected so far from the instrument are consistent with a resistive structure. The best fitting model from 1D inversion is a 36 ± 3 m thick layer of 5.3 ± 0.3 Ωm resistivity, overlaying a less resistive 0.7 ± 0.1 Ωm halfspace. Average hydrate concentration, deduced with the aid of ODP-889 well-log derived Archie’s parameters, is approximately 72% of pore space in the resistive layer, consistent with the very high concentration of gas hydrates (~80%) recovered from seafloor cores. The weekly collection of data from the instrument shows that the resistive structure has changed little since monitoring began in October of 2010.

Hydrocarbon deposits in the form of petroleum, natural gas, and natural gas hydrates occur offshore worldwide. Electromagnetic methods that measure the electrical resistivity of sediments can be used to map, assess, and monitor these resistive targets. In particular, quantitative assessment of hydrate content in marine deposits, which form within the upper few hundred meters of seafloor, is greatly facilitated by complementing conventional seismic methods with EM data. The North-East Pacific Time-series Undersea Network Experiment (NEPTUNE) is an underwater marine observatory that provides power and network connection to a host of instruments installed on the seafloor on the Cascadia Margin offshore Vancouver Island. The observatory’s aim is to provide a platform for very long-term studies in which access to data is available on a continuous basis. For this thesis project, a transient dipole-dipole time-domain EM system was constructed and deployed on the NEPTUNE network with the goal of long-term monitoring of a well-studied hydrate deposit in the area. The instrument includes a source transmitter of electrical current and individual receivers to measure small electric field variations. The instrument is powered by the NEPTUNE observatory and data can be collected remotely by connecting to the instrument through the web. Data collected so far from the instrument are consistent with a resistive structure. The best fitting model from 1D inversion is a 36 ± 3 m thick layer of 5.3 ± 0.3 Ωm resistivity, overlaying a less resistive 0.7 ± 0.1 Ωm halfspace. Average hydrate concentration, deduced with the aid of ODP-889 well-log derived Archie’s parameters, is approximately 72% of pore space in the resistive layer, consistent with the very high concentration of gas hydrates (~80%) recovered from seafloor cores. The weekly collection of data from the instrument shows that the resistive structure has changed little since monitoring began in October of 2010.

Uncertainty Quantification (UQ) has been an active area of research in recent years with a wide range of applications in data and imaging sciences. In many problems, the source of uncertainty stems from an unknown parameter in the model. In physical and engineering systems for example, the parameters of the partial differential equation (PDE) that model the observed data may be unknown or incompletely specified. In such cases, one may use a probabilistic description based on prior information and formulate a forward UQ problem of characterising the uncertainty in the PDE solution and observations in response to that in the parameters. Conversely, inverse UQ encompasses the statistical estimation of the unknown parameters from the available observations, which can be cast as a Bayesian inverse problem. The contributions of the thesis focus on examining the aforementioned forward and inverse UQ problems for the low-frequency, time-harmonic Maxwell equations, where the model uncertainty emanates from the lack of knowledge of the material conductivity parameter. The motivation comes from the Controlled-Source Electromagnetic Method (CSEM) that aims to detect and image hydrocarbon reservoirs by using electromagnetic field (EM) measurements to obtain information about the conductivity profile of the sub-seabed. Traditionally, algorithms for deterministic models have been employed to solve the inverse problem in CSEM by optimisation and regularisation methods, which aside from the image reconstruction provide no quantitative information on the credibility of its features. This work employs instead stochastic models where the conductivity is represented as a lognormal random field, with the objective of providing a more informative characterisation of the model observables and the unknown parameters. The variational formulation of these stochastic models is analysed and proved to be well-posed under suitable assumptions. For computational purposes the stochastic formulation is recast as a deterministic, parametric problem with distributed uncertainty, which leads to an infinite-dimensional integration problem with respect to the prior and posterior measure. One of the main challenges is thus the approximation of these integrals, with the standard choice being some variant of the Monte-Carlo (MC) method. However, such methods typically fail to take advantage of the intrinsic properties of the model and suffer from unsatisfactory convergence rates. Based on recently developed theory on high-dimensional approximation, this thesis advocates the use of Sparse Quadrature (SQ) to tackle the integration problem. For the models considered here and under certain assumptions, we prove that for forward UQ, Sparse Quadrature can attain dimension-independent convergence rates that out-perform MC. Typical CSEM models are large-scale and thus additional effort is made in this work to reduce the cost of obtaining forward solutions for each sampling parameter by utilising the weighted Reduced Basis method (RB) and the Empirical Interpolation Method (EIM). The proposed variant of a combined SQ-EIM-RB algorithm is based on an adaptive selection of training sets and a primal-dual, goal-oriented formulation for the EIM-RB approximation. Numerical examples show that the suggested computational framework can alleviate the computational costs associated with forward UQ for the pertinent large-scale models, thus providing a viable methodology for practical applications.