First-break traveltime tomography with the double-square-root eikonal equation

Bibliography

Alkhalifah, T., 2011, Prestack traveltime approximations: 81st Annnual International Meeting, SEG, Expanded Abstracts, 3017-3021.

Belonosova, A. V., and A. S. Alekseev, 1974, About one formulation of the inverse kinematic problem of seismics for a two-dimensional continuously heterogeneous medium: Some methods and algorithms for interpretation of geophysical data (in Russian), Nauka, 137-154.

Bergman, B., A. Tryggvason, and C. Juhlin, 2004, High-resolution seismic traveltime tomography incorporating static corrections applied to a till-covered bedrock environment: Geophysics, 69, 1082-1090.

Bertsekas, D., 1982, Enlarging the region of convergence of Newton's method for constrained optimization: Journal of Optimization Theory and Applications, 36, 221-251.

Brenders, A. J., and R. G. Pratt, 2007, Efficient waveform tomography for lithospheric imaging: implications for realistic, two-dimensional acquisition geometries and low-frequency data: Geophysical Journal International, 168, 152-170.

Chacon, A., and A. Vladimirsky, 2012a, Fast two-scale methods for Eikonal equations: SIAM Journal on Scientific Computing, 33, no. 3, A547-A578.

----, 2012b, A parallel two-scale methods for Eikonal equations: submitted to SIAM Journal on Scientific Computing.

Chapman, C., 2002, Fundamentals of seismic wave propagation: Cambridge University Press.

Cox, M., 1999, Static corrections for seismic reflection surveys: Society of Exploration Geophysics.

Dessa, J. X., S. Operto, A. Nakanishi, G. Pascal, K. Uhira, and Y. Kaneda, 2004, Deep seismic imaging of the eastern Nankai Trough, Japan, from multifold ocean bottom seismometer data by combined traveltime tomography and prestack depth migration: Journal of Geophysical Research, 109, B02111.

Detrixhe, M., C. Min, and F. Gibou, 2013, A parallel fast sweeping method for the eikonal equation: Journal of Computational Physics, 237, 46-55.

Dijkstra, E. W., 1959, A note on two problems in connexion with graphs: Numerische Mathematik, 1, 269-271.

Duchkov, A., and M. V. de Hoop, 2010, Extended isochron ray in prestack depth (map) migration: Geophysics, 75, no. 4, S139-S150.

Engl, H. W., M. Hanke, and A. Neubauer, 1996, Regularization of inverse problems: Kluwer Academic Publishers.

Franklin, J. B., and J. M. Harris, 2001, A high-order fast marching scheme for the linearized eikonal equation: Journal of Computational Acoustics, 9, 1095-1109.

Hestenes, M. R., and E. Stiefel, 1952, Method of conjugate gradients for solving linear systems: Journal of Research of the National Bureau of Standards, 49, 409-436.

Iversen, E., 2004, The isochron ray in seismic modeling and imaging: Geophysics, 69, 1053-1070.

Jeong, W., and R. T. Whitaker, 2008, A fast iterative method for eikonal equations: SIAM Journal on Scientific Computing, 30, 2512-2534.

Kim, S., 2001, An $O (N)$ level set method for eikonal equations: SIAM Journal on Scientific Computing, 22, 2178-2193.

Kuhn, H. W., and A. W. Tucker, 1951, Nonlinear programming: Proceedings of 2nd Berkeley Symposium, 481-492.

Lelièvre, P. G., C. G. Farquharson, and C. A. Hurich, 2011, Inversion of first-arrival seismic traveltimes without rays, implemented on unstructured grids: Geophysical Journal International, 185, 749-763.

Leung, S., and J. Qian, 2006, An adjoint state method for three-dimensional transmission traveltime tomography using first arrivals: Communications in Mathematical Sciences, 4, 249-266.

Li, S., S. Fomel, and A. Vladimirsky, 2011, Improving wave-equation fidelity of Gaussian beams by solving the complex eikonal equation: 71st Annnual International Meeting, SEG, Expanded Abstracts, 3829-3834.

Marsden, D., 1993, Static corrections--a review: The Leading Edge, 12, 43-49.

Noble, M., P. Thierry, C. Taillandier, and H. Calandra, 2010, High-performance 3D first-arrival traveltime tomography: The Leading Edge, 29, 86-93.

Osypov, K., 2000, Robust refraction tomography: 70th Annnual International Meeting, SEG, Expanded Abstracts, 2032-2035.

Paige, C. C., and M. A. Saunders, 1982, LSQR: an algorithm for sparse linear equations and sparse least squares: ACM Transactions on Mathematical Software, 8, 43-71.

Pei, D., 2009, Three-dimensional traveltime tomography via LSQR with regularization: 79th Annnual International Meeting, SEG, Expanded Abstracts, 4004-4008.

Plessix, R. E., 2006, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications: Geophysical Journal International, 167, 495-503.

Popovici, A. M., and J. Sethian, 2002, 3-D imaging using higher order fast marching traveltimes: Geophysics, 67, 604-609.

Rickett, J., and S. Fomel, 1999, A second-order fast marching eikonal solver: Stanford Exploration Project Report, 100, 287-292.

Sethian, J. A., 1999, Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision and material sciences: Cambridge University Press.

Sheng, J., A. Leeds, M. Buddensiek, and G. T. Schuster, 2006, Early arrival waveform tomography on near-surface refraction data: Geophysics, 71, no. 4, U47-U57.

Simmons, J. L., and N. Bernitsas, 1994, Nonlinear inversion of first-arrival times: 64th Annnual International Meeting, SEG, Expanded Abstracts, 992-995.

Stefani, J. P., 1993, Possibilities and limitations of turning ray tomography--a synthetics study: 63rd Annnual International Meeting, SEG, Expanded Abstracts, 610-612.

Taillandier, C., M. Noble, H. Chauris, and H. Calandra, 2009, First-arrival traveltime tomography based on the adjoint-state method: Geophysics, 74, no. 6, WCB57-WCB66.

Tikhonov, A. N., 1963, Solution of incorrectly formulated problems and the regularization method: Soviet Mathematics Doklady, 1035-1038.

Virieux, J., and S. Operto, 2009, An overview of full-waveform inversion in exploration geophysics: Geophysics, 74, no. 6, WCC1-WCC26.

Vladimirsky, A., and C. Zheng, 2013, A fast implicit method for time-dependent Hamilton-Jacobi PDEs: submitted to SIAM Journal on Scientific Computing.

Weber, O., Y. Devir, A. Bronstein, M. Bronstein, and R. Kimmel, 2008, Parallel algorithms for the approximation of distance maps on parametric surfaces: ACM Transactions on Graphics, 27, no. 4, 104.

Yatziv, L., A. Bartesaghi, and G. Sapiro, 2006, A fast $O (N)$ implementation of the fast marching algorithm: Journal of Computational Physics, 212, 393-399.

Zelt, C. A., and P. J. Barton, 1998, 3D seismic refraction tomography: A comparison of two methods applied to data from the Faeroe Basin: Journal of Geophysical Research, 103, 7187-7210.

Zhao, H., 2005, A fast sweeping method for eikonal equations: Mathematics of Computation, 74, 603-627.

----, 2007, Parallel implementations of the fast sweeping method: Journal of Computational Mathematics, 25, 421-429.

Zhu, T., S. Cheadle, A. Petrella, and S. Gray, 2000, First-arrival tomography: method and application: 70th Annnual International Meeting, SEG, Expanded Abstracts, 2028-2031.

Zhu, X., D. P. Sixta, and B. G. Angstman, 1992, Tomostatics: turning-ray tomography + static corrections: The Leading Edge, 11, 15-23.