A three-dimensional inverse gravimetry problem for ice with snow caps

Inverse Problems and Imaging

Volumn 7, Issue 2, 2013, Pages 523-544

  Isakov, Victor ^a   Leung, Shingyu ^b,c   Qian, Jianliang ^b,c  

^a WICHITA STATE UNIVERSITY   (United States)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Alternating minimization; Green function; Inverse gravimetry; Level set method; Weighted essentially non oscillatory schemes

Indexed keywords

EID: 84878050730     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2013.7.523     Document Type: Article

References (26)

1. M. Bertalmio, L.-T. Cheng, S. Osher and G. Sapiro, Variational problems and partial differ- ential equations on implicit surfaces, J. Comput. Phys., 174 (2001), 759-780.
2. J. Brandman, A level-set method for computing the eigenvalues of elliptic operators defined on compact hypersurfaces, J. Sci. Comput., 37 (2008), 282-315.
3. M. Burger, A level set method for inverse problems, Inverse Problems, 17 (2001), 1327-1356.
4. M. Burger and S. Osher, A survey on level set methods for inverse problems and optimal design, European J. Appl. Math., 16 (2005), 263-301.
5. T. Cecil, S. J. Osher and J. Qian, Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimension, J. Comput. Phys., 213 (2006), 458-473.
6. O. Dorn and D. Lesselier, Level set methods for inverse scattering, Inverse Problems, 22 (2006), R67-R131.
7. A. Elcrat, V. Isakov, E. Kropf and D. Stewart, A stability analysis of the harmonic continuation, Inverse Problems, 28 (2012), 075016.
8. N. Halko, P. G. Martinsson, Y. Shkolnisky and M Tygert, An algorithm for the principal component analysis of large data sets, SIAM J. Sci. Comput., 33 (2010), 2580-2594.
9. S. Hou, K. Solna and H.-K. Zhao, Imaging of location and geometry for extended targets using the response matrix, J. Comput. Phys., 199 (2004), 317-388.
10. V. Isakov, "Inverse Source Problems," AMS, Providence, 1990.
11. V. Isakov, S. Leung and J. Qian, A fast local level set method for inverse gravimetry, Commun. Comput. Phys., 10 (2011), 1044-1070.
12. M. Keldysh, On the solubility and stability of the Dirichlet's problem, Uspekhi Matem. Nauk., 8 (1940), 171-231.
13. S. Leung, Eulerian approach for computing the finite time Lyapunov exponent, J. Comput. Phys., 230 (2011), 3500-3524.
14. A. Litman, D. Lesselier and F. Santosa, Reconstruction of a 2-D binary obstacle by controlled evolution of a level-set, Inverse Problems, 14 (1998), 685-706.
15. C. B. Macdonald and S. J. Ruuth, The implicit closest point method for the numerical solution of partial differential equations on surfaces, SIAM J. Sci. Comput., 31 (2009), 4330-4350.
16. C. Miranda, "Partial Differential Equations of Elliptic Type," Springer-Verlag, New York- Berlin, 1970.
17. P. Novikov, Sur le probleme inverse du potential, Dokl. Akad. Nauk SSSR, 18 (1938), 165-168.
18. S. J. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49.
19. A. I. Prilepko, D. G. Orlovskii and I. A. Vasin, "Methods for Solving Inverse Problems in Mathematical Physics," Marcel Dekker, New York, 2000.
20. J. Qian, L.-T. Cheng and S. J. Osher, A level set based Eulerian approach for anisotropic wave propagations, Wave Motion, 37 (2003), 365-379.
21. J. Qian and S. Leung, A level set method for paraxial multivalued traveltimes, J. Comput. Phys., 197 (2004), 711-736.
22. J. Qian and S. Leung, A local level set method for paraxial multivalued geometric optics, SIAM J. Sci. Comp., 28 (2006), 206-223.
23. F. Santosa, A level-set approach for inverse problems involving obstacles, Control, Optimizat. Calculus Variat., 1 (1996), 17-33.
24. K. van den Doel, U. Ascher and A. Leitao, Multiple level sets for piecewise constant surface reconstruction in highly ill-posed problems, J. Sci. Comput., 43 (2010), 44-66.
25. J. Xu and H. K. Zhao, An Eulerian formulation for solving partial differential equations along a moving interface, J. Sci. Comput., 19 (2003), 573-594.
26. H.-K. Zhao, T. Chan, B. Merriman and S. J. Osher, A variational level set approach for multiphase motion, J. Comput. Phys., 127 (1996), 179-195.