Abstract
The dispersion relation for Love waves in a layer on a half-space is modified by introducing the wave number and its square instead of the phase velocity. The implicit function theorem is then used to derive the analytical formulae for the group velocity and for the phase- and group-velocity partial derivatives with respect to the parameters of the medium. The formulae are compared with those obtained by Novotný (1971) where the traditional formulation of the dispersion relation was used.
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References
Bullen K.E., 1965: An Introduction to the Theory of Seismology (Third edition), Cambridge University Press, Cambridge.
Harkrider D.G., 1968: The Perturbation of Love Wave Spectra. Bull. Seism. Soc. Am., 58, 861–880.
Holub K. and Novotný O., 1997: Interpretation of the Dispersion Curves of Short-period Rayleigh Waves Observed in the West Carpathians. Acta Montana IRSM AS CR, 104, Series A, No. 11, 49–58.
Jeffreys H., 1961: Small Corrections in the Theory of Surface Waves. Geophys. J. R. astr. Soc., 6, 115–117.
Jin D.J., 1987: Long-period Surface-wave Phase-velocity Partial Derivatives with Respect to Earth Parameters. The Texas Journal of Science, 39, 299–312.
Love A.E.H., 1911: Some Problems of Geodynamics, Cambridge University Press, Cambridge, (Republication by Dover Publications, New York, 1967).
Kosloff D., 1975: A Perturbation Scheme for Obtaining Partial Derivatives of Love-wave Group-velocity Dispersion. Bull. Seism. Soc. Am. 65, 1753–1760.
Meissner E., 1926: Elastische-Oberflächen-Querwellen. Verhandl. Intern. Kongr. Tech. Mech., Zürich, 3–11.
Novotný O., 1970: Partial Derivatives of Dispersion Curves of Love Waves in a Layered Medium. Studia geoph. et geod., 14, 36–50.
Novotný O., 1971: Partial Derivatives of Dispersion Curves of Love Waves in a Single-layered Medium. Studia geoph. et geod., 15, 24–35.
Novotný O., 1976: Methods of Computing the Partial Derivatives of Dispersion Curves. PAGEOPH, 114, 765–774.
Novotný O., 1998: A Method for Analytical Computation of the Group Velocity of Surface Waves. PAGEOPH (submitted).
Novotný O., Burlako L.V. and Proskuryakova T.A., 1996: Modifications of the Dispersion Relations for Surface Waves in a Layer on a Half-space. Studia geoph. et geod., 40, 167–177.
Rodi W.L., Glover P., Li T.M.C. and Alexander S.S., 1975: A Fast, Accurate Method for Computing Group-velocity Partial Derivatives for Rayleigh and Love Waves. Bull. Seism. Soc. Am., 65, 1105–1114.
Savarensky E.F., 1975: Seismic Waves, Mir Publishers, Moscow.
Schwab F.A. and Knopoff L., 1972: Fast Surface Wave and Free Mode Computations. In: B.A. Bolt (Ed.), Methods in Computational Physics, Vol.11, Academic Press, New York and London, 87–180.
Takeuchi H. and Saito M., 1972: Seismic Surface Waves. In: B.A. Bolt (Ed.), Methods in Computational Physics, Vol.11, Academic Press, New York and London, 217–295.
Urban L., Cichowicz A. and Vaccari F., 1993: Computation of Analytical Partial Derivatives of Phase and Group Velocities for Rayleigh Waves with Respect to Structural Parameters. Studia geoph. et geod., 37, 14–36.
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Novotný, O. A Fast Method of Computing Group-Velocity Partial Derivatives for Love Waves Propagating in a Layer on a Half-Space. Studia Geophysica et Geodaetica 43, 78–86 (1999). https://doi.org/10.1023/A:1023314225947
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DOI: https://doi.org/10.1023/A:1023314225947