Efficient calculation of jacobian and adjoint vector products in the wave propagational inverse problem using automatic differentiation

Journal of Computational Physics

Volumn 157, Issue 1, 2000, Pages 234-255

  Coleman, Thomas F ^a   Santosa, Fadil ^b   Venna, Arun ^c  

^a Department of Computer Science and School of Operations Research and Information Engineering   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c Department of Obstetrics Gynecology   (United States)

Author keywords

Adjoints; Automatic differentiation; Finite difference computation; Hyperbolic pdes; Inverse problems seismic inversion; Jacobian and adjoint products; Stencils; Wave propagation

Indexed keywords

DIFFERENTIAL EQUATIONS; GEOPHYSICAL PROSPECTING; MEDICAL IMAGING; MEDICAL PROBLEMS; WAVE PROPAGATION;

ADJOINTS; AUTOMATIC DIFFERENTIATIONS; FINITE DIFFERENCE COMPUTATION; HYPERBOLIC PDES; INVERSE PROBLEM SEISMIC INVERSION; JACOBIAN AND ADJOINT PRODUCT; JACOBIANS; SEISMIC INVERSION; STENCIL;

INVERSE PROBLEMS;

EID: 0040016695     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6373     Document Type: Article

References (16)

1. G. Chavent, F. Clement, and S. Gomez, Waveform inversion by MBTT formulation, in Mathematical and Numerical Aspects of Wave Propagation, edited by Cohen, et al. (SIAM, Philadephia, 1995), p. 713.
2. T. Coleman and A. Verma, The efficient computation of sparse Jacobian matrices using automatic differentiation, SIAM J. Sci. Comput. 19, 1210 (1998).
3. T. Coleman and A. Verma, Structure and efficient Hessian calculation, in Advances in Nonlinear Programming, edited by Yuan (Kluwer Academic, Boston, 1996).
4. T. Coleman and A. Verma, Structure and efficient Jacobian calculation, in Computational Differentiation: Techniques, Applications, and Tools, edited by Berz et al. (SIAM, Philadelphia, 1996), p. 149.
5. T. Coleman, F. Santosa, and A. Verma, Semi-automatic differentiation, in Proceedings of Optimal Design and Control Workshop, VPI, 1997.
6. B. Enquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31, 629 (1977).
7. R. Giering, Tangent Linear and Adjoint Model Compiler (User Manual, TAMC Version 4.7, 1997).
8. A. Griewank, Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation, Optim. Methods Software 1, 35 (1992).
9. A. Griewank, Some bounds on the complexity of gradients, Jacobians, and Hessians, in Complexity in Nonlinear Optimization, edited by Pardalos (World Scientific, Singapore, 1993).
10. A. Griewank, D. Juedes, and J. Utke, ADOL-C, a package for the automatic differentiation of algorithms written in C/C++, ACM Trans. Math. Software 22, 131 (1996).
11. T. Mast, A. Nachman, and R. Waag, Focussing and imaging using eigenfunctions of the scattering operator, J. Acous. Soc. Am., in press.
12. F. Santosa and W. Symes, An Analysis of Least-Squares Velocity Inversion (Society of Exploration Geophysicists, Tulsa, 1989).
13. F. Santosa and W. Symes, Computation of the Hessian for least-squares solutions of inverse problems of reflection seismology, Inverse Problem 4, 211 (1988).
14. W. Symes, A differential semblance criterion for inversion of multioffset seismic reflection data, J. Geophys. Res. 98, 2061 (1993).
15. W. Symes and C. Zhang, A Finite Difference Time Stepping Class, Rice University TRIP Report, 1997.
16. A. Tarantola, Inverse Problem Theory (Elsevier, Amsterdam, 1987).