Abstract
In [1] we considered the problem of finding a function ρ(x) from the eigenvalue s = s(p) of an equation y″ + [pρ(x) − s] y = 0. The methods employed in [1] allow us to consider a more general equation [A(x)y′]′+ [pB(x) − sC(x)] y = 0. This in turn makes it possible to study some questions of uniqueness in the inverse problem for Love waves, i.e., determination of the characteristics of the medium from the phase or group velocity.
Translated from Vychislitel’naya Seismologiya, No. 4, pp. 78–94, Moscow, Nauka (1968).
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Literature Cited
Gerver, M. L., and D. A. Kazhdan (1967), “On finding the function ρ(x) from the eigenvalue s = s(p) of the equation y″ + [pρ(x) − s] y = 0,” Matern. Sb., 73:115.
Vil’kovich, E. V., A. L. Levshin, and M. G. Neigauz (1966), “Love waves in a vertically inhomogeneous medium (allowance for sphericity, parameter variations, and absorption),” Computational Seismology, No. 2, Moscow, Nauka, pp. 130–149 [English translation in: Seismic Love Waves, New York, Consultants Bureau (1967)].
Gerver, M. L., and V. M. Markushevich (1965), “Study of ambiguity in determining seismicwave propagation velocity from travel-time curves,” Dokl. Akad. Nauk SSSR, Vol. 163, No. 6.
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Markushevich, V. M. (1950), Theory of Analytic Functions, Moscow and Leningrad, Gostekhizdat.
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Gerver, M.L., Kazhdan, D.A. (1972). Finding a Velocity Profile from a Love Wave Dispersion Curve: Problems of Uniqueness. In: Keilis-Borok, V.I., Flinn, E.A. (eds) Computational Seismology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8815-9_20
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DOI: https://doi.org/10.1007/978-1-4684-8815-9_20
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