Date of Award

1-2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Advisor

Khan, Taufiquar

Committee Member

Medlock , Jan

Committee Member

Schmoll , Martin

Abstract

Obtaining accurate images of solute plumes in the subsurface is important to understand site-specific subsurface flow and transport processes. Since image reconstruction is an inverse problem, its ill-posed nature makes obtaining an accurate, high-resolution image difficult. Further, current geophysical methods for plume imaging do not take into account models of the specific process being targeted for imaging.
The main objective of the research is to find a suitable basis that gives a sparse representation of the plume. In future work, we seek to use this basis as a physical constraint during the inversion so as to increase accuracy in imaging. We use three different methods to find the best coefficients for the basis given the concentration values at sampled points in the domain.
We then compare these results to the current geo-statistical technique to estimate these values known as kriging. Kriging produced slightly better results for our simulation but we suspect that our multi-scale library l0 approach, which promotes sparsity, will outperform kriging as the heterogeneity of the subsurface increases.

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