Han, B.; Feng, G. F.; Liu, J. Q. A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation. (English) Zbl 1088.65083 Appl. Math. Comput. 172, No. 1, 406-420 (2006). Summary: An algorithm of the generalized pulse-spectrum technique (GPST) is used for the inverse problems of two-dimensional acoustic wave equation, and a skill of saving computational cost is designed in choosing regularizing parameters. To overcome the defect of the local convergence of the GPST, a widely convergent GPST (WCGPST) is constructed. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the WCGPST. It is found that the WCGPST is not only as robust as the standard GPST but also possessing widely convergent region. Cited in 5 Documents MSC: 65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs 35L05 Wave equation 35R30 Inverse problems for PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 86A22 Inverse problems in geophysics 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs Keywords:Inverse problem of geophysical prospecting; Nonlinear inversion; 2D wave equation inversion; Generalized pulse-spectrum technique; Homotopy method; Numerical examples; Tikhonov regularization; Algorithm; Acoustic wave equation; Convergence PDFBibTeX XMLCite \textit{B. Han} et al., Appl. Math. Comput. 172, No. 1, 406--420 (2006; Zbl 1088.65083) Full Text: DOI References: [1] Wang, S. D.; Liu, J. Q., Chinese J Geophys, 39, 145 (1995) [2] Bleistein, N.; Cohen, J. K., Geophysics, 52, 26 (1987) [3] Bunks, C.; Saleck, F. M., Geophysics, 60, 1457 (1995) [4] Mora, P., Geophys, 52, 1211 (1987) [5] Tsien, D. S.; Chen, Y. M., Computing Methods in Nonlinear Mechanics (1974), University of Texas: University of Texas Austin, p. 935 · Zbl 0309.76059 [6] Chen, Y. M.; Tsien, D. S., J. Comput. Phys., 25, 366 (1977) [7] Tsien, D. S.; Chen, Y. M., Radio Sci., 13, 775 (1978) [8] Chen, Y. M.; Liu, J. Q., J. Comput. Phys., 43, 315 (1981) [9] Hatcher, R. D.; Chen, Y. M., SIAM J. Sci. Stat. Comput., 4, 149 (1983) [10] Chen, Y. M.; Liu, J. Q., J. Comput. Phys., 50, 193 (1983) [11] Liu, J. Q.; Chen, Y. M., SIAM J. Sci. Stat. Comput., 5, 255 (1984) [12] Chen, Y. M.; Liu, J. Q., J. Comput. Phys., 53, 429 (1984) [13] Xie, G. Q.; Chen, Y. M., Appl. Numer. Math., 1, 217 (1985) [14] Chen, Y. M., Geophysics, 50, 1664 (1985) [15] Chen, Y. M.; Xie, G. Q., J. Comput. Phys., 62, 143 (1986) [16] Liu, X. Y.; Chen, Y. M., SIAM J. Sci, Stat. Comput., 8, 436 (1987) [17] Chen, Y. M.; Liu, M. S., J. Comput. Phys., 72, 372 (1987) [18] Chen, Y. M.; Zhang, F. G., Appl. Numer. Math., 6, 431 (1989/90) [19] Zhu, J. P.; Chen, Y. M., Appl. Numer. Math., 10, 159 (1992) [20] Wang, S. D.; Liu, J. Q., Geophysics, 61, 735 (1996) [21] Han, B.; Zhang, M. L., Appl. Math. Comput., 81, 97 (1997) [22] Tiknonov, A. N.; Asrenis, V. Y., Solution of Ill-posed Problem (1977), John Wiley and Sons: John Wiley and Sons New York [23] Ortega, J. M.; Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York · Zbl 0241.65046 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.