Total Variation Method for Finding Non-Smooth Solutions to the Inverse Gravity Problem by Hugo Bertete-Aguirre with Elena Cherkaeva and Aaron Fogelson JTB320, 3:20pm Monday, October 27, 1997 Abstract This work deals with the problem of reconstruction of non-smooth solutions of the inverse gravimetric problem. The developed approach is based on minimization of the Tikhonov functional with the total variation of the density function taken as the stabilization functional. An adaptive gradient minimization scheme is used to solve the resulting non-quadratic minimization problem. The total variation stabilization functional permits recovers of non-smooth solution or density functions with sharp edges in contrast with smoothing stabilization functionals commonly used in geophysical inversion algorithms. Comparison of numerical solutions obtained with different stabilization functionals is given. Requests for preprints and reprints to: hugo@math.utah.edu This source can be found at http://www.math.utah.edu/research/