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A widely convergent generalized pulse-spectrum technique for the inversion of two-dimensional acoustic wave equation. (English) Zbl 1088.65083

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.

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
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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) · Zbl 0365.76079
[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) · Zbl 0469.65086
[9] Hatcher, R. D.; Chen, Y. M., SIAM J. Sci. Stat. Comput., 4, 149 (1983) · Zbl 0513.65070
[10] Chen, Y. M.; Liu, J. Q., J. Comput. Phys., 50, 193 (1983) · Zbl 0515.65088
[11] Liu, J. Q.; Chen, Y. M., SIAM J. Sci. Stat. Comput., 5, 255 (1984) · Zbl 0565.65074
[12] Chen, Y. M.; Liu, J. Q., J. Comput. Phys., 53, 429 (1984) · Zbl 0531.65068
[13] Xie, G. Q.; Chen, Y. M., Appl. Numer. Math., 1, 217 (1985) · Zbl 0566.65092
[14] Chen, Y. M., Geophysics, 50, 1664 (1985)
[15] Chen, Y. M.; Xie, G. Q., J. Comput. Phys., 62, 143 (1986) · Zbl 0574.73035
[16] Liu, X. Y.; Chen, Y. M., SIAM J. Sci, Stat. Comput., 8, 436 (1987) · Zbl 0618.65122
[17] Chen, Y. M.; Liu, M. S., J. Comput. Phys., 72, 372 (1987) · Zbl 0634.65119
[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) · Zbl 0749.76082
[20] Wang, S. D.; Liu, J. Q., Geophysics, 61, 735 (1996)
[21] Han, B.; Zhang, M. L., Appl. Math. Comput., 81, 97 (1997) · Zbl 0884.65096
[22] Tiknonov, A. N.; Asrenis, V. Y., Solution of Ill-posed Problem (1977), John Wiley and Sons: John Wiley and Sons New York · Zbl 0354.65028
[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
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