Accurate subsurface imaging is critical for appraisal and development of several hydrological, environmental, and energy resources. These subsurface systems are complex, heterogeneous, and inherently uncertain due to costly and inconvenient sampling. In addition, simulations of fluid flow and transport in these systems typically involves models with strong nonlinearity, high dimensionality, and considerable computational complexity. However, geologic formations often exhibit large-scale spatial continuity and correlations that make them amenable to low-dimension or compressed representations, a property that we exploit in estimating them from nonlinear data. In this talk, I will review several popular image compression techniques for sparsifying subsurface property maps and show how these compact descriptions transform the imaging problem into sparse reconstruction from limited nonlinear flow measurements. I will discuss the solution of the resulting nonlinear imaging problems using guidelines provided by recent developments in sparse signal processing under linear measurements, e.g. compressed sensing.
Behnam Jafarpour is an assistant professor in the Viterbi School of Engineering at USC. He obtained an S.M. in Electrical Engineering and Computer Science, and a Ph.D. in Environmental Engineering both from Massachusetts Institute of Technology in February 2008. Before joining USC, he was an assistant professor at Texas A&M University from October 2007 to August 2011. His current research interests focus on the application of signal processing, estimation and control to characterization, modeling, and management of energy resources and environmental systems.