References
- Anagaw, A.Y., and M.D. Sacchi. 2014. Comparison of multifrequency selection strategies for simultaneous-source full-waveform inversion. Geophysics 79, no. 5: R165–R181. doi:10.1190/GEO2013-0263.1.
- Berenger, J.P. 1994. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics 114, no. 2: 185–200. doi:10.1006/jcph.1994.1159.
- Boonyasiriwat, C., P. Valasek, P. Routh, W.P. Cao, G.T. Schuster, and B. Macy. 2009. An efficient multiscale method for time-domain waveform tomography. Geophysics 74, no. 6: WCC59–WCC68. doi:10.1190/1.3151869.
- Broyden, C. G. 1970. The convergence of a class of double-rank minimization algorithms. Journal of the Institute of Mathematics and Its Applications 6: 76–90. doi: 10.1093/imamat/6.1.76
- Bube, K.P., and T. Nemeth. 2007. Fast line searches for the robust solution of linear systems in the hybrid and Huber norms. Geophysics 72, no. 2: A13–A17. doi:10.1190/1.2431639.
- Bunks, C., F.M. Saleck, S. Zaleski, and G. Chavent. 1995. Multiscale seismic waveform inversion. Geophysics 60, no. 5: 1457–1473. doi:10.1190/1.1443880.
- Dos Santos, A.W.G., and R.C. Pestana. 2015. Time-domain multiscale full-waveform inversion using the rapid expansion method and efficient step-length estimation. Geophysics 80, no. 4: R203–R216. doi:10.1190/GEO2014-0338.1.
- Fletcher, R. 1970. A new approach to variable metric algorithms. Computer Journal 13: 317–322. doi: 10.1093/comjnl/13.3.317
- Goldfarb, D. 1970. A family of variable metric updates derived by variational means. Mathematics of Computation 24: 23–26. doi: 10.1090/S0025-5718-1970-0258249-6
- Guasch, L., Burgess, T., and Warner M. 2015. Optimised adaptive waveform inversion- Improved convergence via conjugate gradients and superior step-length calculation. 77th Annual International Meeting, EAGE, Expanded Abstracts.doi: 10.3997/2214-4609.201413207
- Hager, W.W., and H.C. Zhang. 2006. A survey of nonlinear conjugate gradient methods. Pacific Journal of Optimization 2: 35–58.
- Hu, W.Y., A. Abubakar, and T.M. Habashy. 2009. Simultaneous multifrequency inversion of full-waveform seismic data. Geophysics 74, no. 2: R1–R14. doi:10.1190/1.3073002.
- Lailly, P. 1983. The seismic inverse problem as a sequence of before stack migrations. SIAM Conference on Inverse Scattering, Theory and Applications, Expanded Abstracts, 206–220.
- Liu, D.C., and J. Nocedal. 1989. On the limited memory BFGS method for large scale optimization. Mathematical Programming 45, no. 1-3: 503–528. doi:10.1007/BF01589116.
- Liu, X.J., Y.K. Liu, H.Y. Lu, H. Hu, and M. Khan. 2017a. Prestack correlative least-squares reverse time migration. Geophysics 82, no. 2: S159–S172. doi:10.1190/geo2016-0416.1.
- Liu, X.J., Y.K. Liu, X.G. Huang, and P. Li. 2016a. Least-squares reverse-time migration with cost-effective computation and memory storage. Journal of Applied Geophysics 129: 200–208. doi:10.1016/j.jappgeo.2016.03.009.
- Liu, Y.S., J.W. Teng, T. Xu, J. Badal, Q.Y. Liu, and B. Zhou. 2017b. Effects of conjugate gradient methods and step-length formulas on the multiscale full waveform inversion in time domain: numerical experiments. Pure and Applied Geophysics 174: 1983–2006. doi:10.1007/s00024-017-1512-3.
- Liu, Y.S., J.W. Teng, T. Xu, Z.M. Bai, H.Q. Lan, and J. Badal. 2016b. An efficient step-length formula for correlative least-squares reverse time migration. Geophysics 81, no. 4: S221–S238. doi:10.1190/GEO2015-0529.1.
- Ma, X.N., Z.Y. Li, B.L. Gu, P. Ke, and G.H. Liang. 2015. Comparisons and analysis of several optimization finite-differencing schemes in 2D acoustic frequency-domain numerical modeling. Progress in Geophysics 30, no. 2: 0878–0888. [in Chinese]. doi:10.6038/pg20150254.
- Ma, X.N., Z.Y. Li, S.H. Xu, P. Ke, and G.H. Liang. 2017. Comparison of frequency-band selection strategies for 2D time-domain acoustic waveform inversion. Journal of Seismic Exploration 26: 499–519.
- Marfurt, K.J. 1984. Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations. Geophysics 49, no. 5: 533–549. doi:10.1190/1.1441689.
- Métivier, L., and R. Brossier. 2016. The SEISCOPE optimization toolbox: A large-scale nonlinear optimization library based on reverse communication. Geophysics 81, no. 2: F11–F25. doi:10.1190/GEO2015-0031.1.
- Mora, P. 1987. Nonlinear two-dimensional elastic inversion of multioffset seismic data. Geophysics 52, no. 9: 1211–1228. doi:10.1190/1.1442384.
- Nocedal, J., and Wright, S. J., 1999, Numerical optimization, Berlin: Springer.
- Operto, S., J. Virieux, and F. Sourbier. 2007. Documentation of FWT2D program (version 4.8): Frequency domain full-waveform modeling/inversion of wide-aperture seismic data for imaging 2D acoustic media: Technical report 007 – SEISCOPE project.
- Pan, W.Y., K.A. Innanen, G.F. Margrave, and D.P. Cao. 2015. Efficient pseudo-Gauss-Newton full-waveform inversion in the domain. Geophysics 80, no. 5: R225–R238. doi:10.1190/GEO2014-0224.1.
- Pica, A., J.P. Diet, and A. Tarantola. 1990. Nonlinear inversion of seismic reflection data in a laterally invariant medium. Geophysics 55, no. 3: 284–292. doi:10.1190/1.1442836.
- 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, no. 2: 495–503. doi:10.1111/j.1365-246X.2006.02978.x.
- Pratt, R.G., and M.H. Worthington. 1990. Inverse theory applied to multi-source cross-hole tomography. part I: acoustic wave-equation method. Geophysical Prospecting 38, no. 3: 287–310. doi:10.1111/j.1365-2478.1990.tb01846.x.
- Pratt, R.G., C. Shin, and G.J. Hicks. 1998. Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion. Geophysical Journal International 133, no. 2: 341–362. doi:10.1046/j.1365-246X.1998.00498.x.
- Shanno, D. F. 1970. Conditioning of quasi-Newton methods for function minimization. Mathematics of Computation 24: 647–656. doi: 10.1090/S0025-5718-1970-0274029-X
- Shin, C., and Y.H. Cha. 2008. Waveform inversion in the Laplace domain. Geophysical Journal International 173, no. 3: 922–931. doi:10.1111/j.1365-246X.2008.03768.x.
- Shin, C., and Y.H. Cha. 2009. Waveform inversion in the Laplace-Fourier domain. Geophysical Journal International 177, no. 3: 1067–1079. doi:10.1111/j.1365-246X.2009.04102.x.
- Tape, C., Q.Y. Liu, and J. Tromp. 2007. Finite-frequency tomography using adjoint methods-Methodology and examples using membrane surface waves. Geophysical Journal International 168, no. 3: 1105–1129. doi:10.1111/j.1365-246X.2006.03191.x.
- Tarantola, A. 1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics 49, no. 8: 1259–1266. doi:10.1190/1.1441754.
- Tarantola, A. 1986. A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics 51, no. 10: 1893–1903. doi:10.1190/1.1442046.
- Vigh, D., E.W. Starr, and J. Kapoor. 2009. Developing earth models with full waveform inversion. The Leading Edge 28, no. 4: 432–435. doi:10.1190/1.3112760.
- Virieux, J., and S. Operto. 2009. An overview of full-waveform inversion in exploration geophysics. Geophysics 74, no. 6: WCC1–WCC26. doi:10.1190/1.3238367.
- Wolfe, P. 1969. Convergence conditions for ascent methods. SIAM Review 11, no. 2: 226–235. doi:10.1137/1011036.
- Xu, K., and G.A. McMechan. 2014. 2D frequency-domain elastic full-waveform inversion using time-domain modeling and a multistep-length gradient approach. Geophysics 79, no. 2: R41–R53. doi:10.1190/geo2013-0134.1.
- Zhang, H.C., and W.W. Hager. 2004. A nonmonotone line search technique and its application to unconstrained optimization. SIAM Journal on Optimization 14, no. 4: 1043–1056. doi:10.1137/S1052623403428208.
- Zhou, B., L. Gao, and Y.H. Dai. 2006. Gradient methods with adaptive step-sizes. Computational Optimization and Applications 35, no. 1: 69–86. doi:10.1007/s10589-006-6446-0.