Abstract
A method is proposed for the determination of the dispersion equation of Love waves propagating in a homogeneous layer lying over a laterally inhomogeneous half-space. The proposed method can be made to work only when the lateral inhomogeneities in the lower half-space are finite in nature so that their Fourier transforms are available. As an illustration the dispersion equation of Love waves is obtained for one of such media in which the shear-wave velocity and the rigidity in the lower half-space either increases or decreases along the direction of propagation of waves according as the parameter of heterogeneity is positive or negative.
Similar content being viewed by others
References
Anderson, D. L. (1967),Latest information from seismic observations, in the Earth's mantle. (Edited by T. F. Gaskell, Academic Press, London, p. 355–420.
Babich, V. M. andMolotkov, I. A. (1966),The propagation of Love waves in an elastic half-space which is inhomogeneous in the direction of two coordinates. Izvest. Akad. Nauk SSSR, Phys. Solid Earth,6, 364–366.
Bhattacharya, S. N. (1970),Love wave dispersion in a laterally heterogeneous layer lying over a homogeneous semi-infinite medium, Geophys. J. R. Astronom. Soc.,19, 361–366.
Boore, D. M. (1970),Love waves in non-uniform guides: finite difference calculations, J. Geophys. Res.,75 (8), 1512–1527.
Carslaw, H. S. andJaeger, J. C. (1953),Operational Methods in Applied Mathematics, Oxford Univ. Press, p. 355.
Chatterjee, S. N. (1972),The dispersion of Love waves in a laterally and in a vertically heterogeneous layer lying over a homogeneous half-space, Bull. Seismol. Soc. Am.62, 805–813.
De, T. K. (1968),Love waves in non-homogeneous media, Bull. del. Ac. Pl. Sc.6, 249–252.
De, T. K. (1980),A note on the approximate determination of the dispersion of Love waves in a laterally non-homogeneous layer lying over a homogeneous half-space, Pure Appl. Geophys.18, 1170–1178.
Gjevik, B. (1974),Ray tracing for seismic surface waves, Geophys. J. R. Astronom. Soc.39, 29–39.
Gregersen, S. (1976),Surface waves in isotropic laterally inhomogeneous media, Pure Appl. Geophys.,114, 821–832.
Kennett, B. L. N. (1974),Seismic waves in a laterally inhomogeneous media, Geophys. J. R. Astronom. Soc.27, 301–325.
Mikhlin, S. G. (1957),Integral Equations, Pergamon Press, p. 10.
Negi, J. G. andSingh, V. P. (1973a),Dispersion of Love waves in non-uniform channels lying over a homogeneous half-space, Pure Appl. Geophys.104, 484–494.
Negi, J. G. andSingh, V. P. (1973b),Love waves dispersion analysis for the crustal structure of laterally inhomogeneous Himalayas, Bull. Seismol. Soc. Am.63, 1163–1172.
Singh, V. P. (1974),Love waves dispersion in a transversely isotropic and laterally inhomogeneous crustal layer, Bull. Seismol. Soc. Am.67, 331–343.
Singh, B. M., Singh, S. J., Chopra, S. D. andGogna, M. L. (1976),On Love waves in laterally and vertically heterogeneous layered media, Geophys. J. R. Astronom. Soc.45, 357–370.
Sneddon, I. N. (1951),Fourier Transforms, McGraw-Hill, p. 23.
Woodhouse, J. H. (1974),Surface waves in a laterally varying layered structure, Geophys. J. R. Astronom. Soc.37, 461–490.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
De, T.K. On love wave dispersion in a homogeneous layer lying over a laterally heterogeneous half-space. PAGEOPH 123, 43–58 (1985). https://doi.org/10.1007/BF00877048
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00877048