Summary
Propagation of Love waves due to a point source in an axially symmetric heterogeneous layer lying between two homogeneous half-spaces is studied. The variation of Lamé's parameters and the density in the layer is assumed to be of the type
where α is a constant andz is the distance measured from one of the interfaces into the layer. The vector wave equation is separable in this case and the solution is obtained in terms ofWhittaker's function. Using the asymptotic approximation forWhittaker's function, an approximate solution is obtained to the first power in α. This agrees with the solution obtained directly by neglecting the squares and higher powers of α at each stage.
Similar content being viewed by others
References
Ari-Ben Menahem,Diffraction of Elastic Waves from a Surface Source in a Heterogeneous Medium, Bull. Seism. Soc. Amer.50 (1), 15–33.
S. S. Avila Geraldo andJoseph B. Kellar,The High Frequency Asymptotic Field of a Point Source in an Inhomogeneous Medium, Comm. Pure and Appl. Math.16 (1963), 363–381.
J. F. Hook,Contribution to the Theory of Separability of the Vector Wave Equation of Elasticity for Inhomogeneous Media, J. Acoust. Soc. Amer.34, (1962), 946.
Kehar Singh,Love Waves Propagated in an Axially Symmetric Heterogeneous Layer Lying Between Two Homogeneous Half-Spaces, Pure and Appl. Geophys.68 (1967/III), 236–243.
S. K. Mishra,Propagation of Sound Pulses in a Semi-Infinite Stratified Medium, Proc. Indian Acad. Sci. [sec. A]LIX, 1, 21–48.
Peter Wolfe andRobert M. Lewis,Progressing Waves Radiated from a Moving Point Source in an Inhomogeneous Medium, J. Differential Equations2, 3 (1966), 328–350.
Sarvajit Singh,On the Distribution due to a Point Source in an Inhomogeneous Medium, Pure and Appl. Geophys. (in the press).
L. J. Slater,Confluent Hypergeometric Functions (Cambridge University Press, 1960).
Takaku Koshun,Propagation of Elastic Waves in Spherical Symmetric Inhomogeneous Medium, J. Phys. Soc. Japan16 (1961), 2550–2560.
N. J. Vlaar,The Field from an SH-Point Source in a Continuously Layered Inhomogeneous Medium, Bull. Seism. Soc. Amer.56, 3 (1966), 715–724.
E. T. Whittaker andG. N. Watson,A Course of Modern Analysis, 4th ed. (Cambridge University Press, 1927), 337.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Singh, K. Love waves due to a point source in an axially symmetric heterogeneous layer between two homogeneous halfspaces. PAGEOPH 72, 35–44 (1969). https://doi.org/10.1007/BF00875690
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00875690