Numerical Solution of Next Generation Inverse Problems for Geophysical Applications

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The broad objective of my research is to advance geophysical inversion technology and thereby improve non-invasive investigation of the Earth's subsurface. Geophysical inversion generates models (three-dimensional spatial representations) of the subsurface that could have given rise to measured data from a geophysical survey, for example, seismic, gravity, magnetic, electrical and electromagnetic measurements taken on airborne systems, at ground level, or down drillholes. Inversion is a computationally intensive procedure, relying on accurate numerical solution of the differential equations that describe the physical phenomena involved, and development of numerical optimization routines tailored to the specific inverse problem at hand. It is very much an interdisciplinary field, combining aspects of mathematics, computer science, physics and Earth sciences, but the former two are of primary significance to my research. Geophysical inverse problems are generally nonunique: because of data uncertainty and other aspects inherent to the physical phenomena or mathematics of the inverse problem, there are an infinite number of models that can fit the measured geophysical data to the desired degree. Hence, the measured data alone are not enough to find a unique solution that is meaningful, interpretable and reliable. Additional information must be incorporated to reduce the nonuniqueness, provide mathematically well-behaved problems and, most importantly from an applied perspective, generate solutions that are consistent with any existing information regarding the subsurface. One of the central research questions in geophysical inversion, and one which guides my research, is how to best reduce the nonuniqueness of the inverse problem and thereby reduce ambiguity in the solutions obtained. Geophysical inversion provides a non-invasive method for providing models of the subsurface that can be used to inform decision makers before more invasive inspection is undertaken. These techniques have proven helpful for addressing a wide variety of practical problems in various fields of application, including resource exploration, natural hazard mitigation, archaeology, agriculture and many other environmental and civil engineering investigations, all of which are important across Canada. Geophysical inversion is a fundamental tool for advancing knowledge of the world we live in and the history of our civilization. My research program will develop new geophysical inversion methods and research best practices for applying those methods to various important worldwide problems.