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Application of the theory of eigenfunctions to the calculations of surface wave velocities
Author(s) -
KeilisBorok V. I.,
Neigauz M. G.,
Shkadinskaya G. V.
Publication year - 1965
Publication title -
reviews of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.087
H-Index - 156
eISSN - 1944-9208
pISSN - 8755-1209
DOI - 10.1029/rg003i001p00105
Subject(s) - eigenfunction , eigenvalues and eigenvectors , differential equation , rayleigh wave , mathematical analysis , physics , surface wave , transformation (genetics) , computation , wave equation , surface (topology) , love wave , mathematics , wave propagation , longitudinal wave , mechanical wave , geometry , quantum mechanics , optics , chemistry , biochemistry , algorithm , gene
Surface wave phase velocities for an inhomogeneous medium are usually given as eigenvalues of the wave equation. This is a differential equation (Love waves) or pair of differential equations (Rayleigh waves) of the second order. By means of a change of variable the problem is reducible to finding the zeros of a first‐order differential equation or pair of differential equations of first order. The solution can be obtained in any order of surface waves, and the eigenfunctions can be obtained as well by means of this transformation. The solution is thus amenable to computation.