Abstract
The Schur algorithm is an inverse scattering algorithm which computes the reflectivity function using the relation between incident and reflected waves on a medium. The use of the inverse scattering algorithm is fast and stable due to orthogonality. We show results of a number of experiments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Schur, “Ueber Potenzreihen, die im Innern des Einheitskreises beschränkt sind”, J. für die Reine und Angewandte Mathematik, vol. 147, Berlin 1917, pp. 205–232.
P. Dewilde, Vieira A.C. and Kailath T., “On a generalized Szegö-Levinson Realization Algorithm for Optimal Linear Predictors Based on a Network Synthesis Approach”, IEEE CAS-25, no. 9, 1978, pp. 663 – 675.
M.G. Krein, “The continuous analogues of theorems on polynomials orthogonal on the unit circle”, Dokl. Akad. Nauk. SSSR, vol. 104, 1955, pp. 437 – 440.
I. Widya, “Continuous-time stochastic modelling with lossless structures ”, Ph. D. thesis Delft Univ. of Technology, Department of EE, reportno. 12, 1982.
J.F. Claerbout, “Fundamentals of Geophysical Data Processing ”, McGraw-Hill, 1976.
B. Ursin, “Review of elastic and electromagnetic wave propagation in horizontally layered media ”, Geophysics, vol. 18, no. 8, 1983, pp. 1063 – 1082.
J. Ware and K. Aki, “Continuous and Discrete Invers-Scattering Problems in Stratified Elastic Medium, Part I: Plane Waves at Normal Incidence”, J. Acoust. Soc. Am., vol 45, 1969, pp. 911–921.
P. Dewilde, J. Fokkema and I. Widya, “Inverse Scattering and Linear Prediction, the Time-continuous case ”, in Stochastic Systems: The Mathematics of Filtering and Identification and Applications, edited by M. Hazewinkel and J. Willems, D. Reidel Publ. Co., 1981, pp. 351 – 382.
T. Kailath, L. Ljung and M. Morf, “Generalized Krein-Levinson equations for efficient Calculation of Fredholm Resolvents of Non-displacement Kernels”, Topics in Functional Analysis, edited by I. Gohberg and M. Kac, Academic Press. N.Y. 1978, 169 –184.
F.R. Gantmacher, “The Theory of Matrices”, N.Y. Chelsea, 1959.
A.E. Yagle, and B.C. Levy, “Application of the Schur algorithm to the inverse problem for a layered acoustic medium”, J. Acoust. Soc. Am., vol. 76, no. 1, 1984, pp. 301 – 308.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Plenum Press, New York
About this chapter
Cite this chapter
Widya, I. (1985). Numerical Performance of the Schur Algorithm in Seismic Inversion and Continuous-Time Prediction Problems. In: Berkhout, A.J., Ridder, J., van der Wal, L.F. (eds) Acoustical Imaging. Acoustical Imaging, vol 14. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2523-9_24
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2523-9_24
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9524-2
Online ISBN: 978-1-4613-2523-9
eBook Packages: Springer Book Archive