Open AccessLove Waves in a Heterogeneous Medium
Author(s) -
Hudson J. A.
Publication year - 1962
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1962.tb02976.x
Subject(s) - rigidity (electromagnetism) , wavelength , love wave , piecewise , mathematics , mechanics , geometry , mechanical wave , physics , geology , longitudinal wave , optics , mathematical analysis , wave propagation , quantum mechanics
Summary In this paper we investigate the existence of Love waves in a layer of finite depth, with the upper surface free from stress and the lower boundary rigidly fixed. The density and rigidity of the medium vary in any way with depth. Sturm‐Liouville theory indicates the form of variation of the wavelength of the waves with period, and also the variation of group velocity with period. The same theory shows the effect on the periods of the Love waves of a change in the rigidity or density in some range of depth, and the effect of a change in total depth of the layer. Love waves are found to exist for any variation in density, such that it is integrable as a function of depth, and any variation in rigidity such that it is a piecewise, continuous function of depth. The periods of waves of given wavelength, as might be expected, are reduced if the rigidity is increased or the density decreased in some range of depth. Finally, we show that this last result holds when the depth of the layer becomes infinite.