The interdisciplinary work that I have started at the University of British Columbia would not of been possible without the enthusiastic support from a tremendous and diverse group of individuals. First and foremost, Dr. Eldad Haber, who is a trailblazer in the computational geosciences and whose guidance and expertise has not only been invaluable, but is foundational to almost every paragraph of this thesis. Thank you for all your investment in me. Next, Dr. Doug Oldenburg, whose infectious enthusiasm and curiosity is able to both motivate and mobilize a team of passionate students around him that are able to tackle grand goals that we wholeheartedly believe will change our field of study. Next, Dr. Adam Pidlisecky, who introduced me to scientific programming and hydrogeophysics and who is able to weave scientific narratives that inspire and broker innovation. Next, my parents for, among so many other things, perspective in this process. Next, my committee and examiners who improved the quality and focus of this dissertation. Thank you all for your unwavering support and encouragement.

The funding for this interdisciplinary work was provided from several sources. A special thanks to the University of British Columbia, the Natural Sciences and Engineering Research Council of Canada, the Vanier Graduate Canada Scholarship program, the Gilles Brassard Doctoral Prize for Interdisciplinary Research, the Killam Scholarship program, the University of British Columbia Library, and the Banff International Research Station for their generous support.

A special thanks to my colleagues, friends and family who are always willing to talk through ideas and have supported me throughout this process. To name a few of these wonderful people: Dom Fournier, Gudni Rosenkjaer, Michael Mitchell, Thibaut Astic, Brendan Smithyman, Dave Marchant, Julie Nutini, Michael Wathen, Franklin Koch, Teddi Herring, Michael Firmin, Lars Ruthotto, Jenn Fohring, Luz Angelica Caudillo-Mata, Klara Steklova, Pieter Aukes, Kristyn Adams, Leonardo Uieda, Matt Hall, and many others. Also, a special thanks to the current and future users and contributors of SimPEG, and to those who are pioneering connected and open geoscience communities.

Finally, this dissertation would not have been possible without the continued emotional and educational support and encouragement from Lindsey Heagy and Seogi Kang. You have been partners in thought and have been integral in nurturing many of the ideas that fill the following pages.