Open AccessA parabolic approximation for surface waves
Author(s) -
Hudson J. A.
Publication year - 1981
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.1981.tb06952.x
Subject(s) - surface wave , rayleigh wave , wavelength , love wave , surface (topology) , amplitude , mechanical wave , boussinesq approximation (buoyancy) , position (finance) , wave propagation , mathematical analysis , internal wave , rayleigh scattering , physics , mathematics , classical mechanics , longitudinal wave , geometry , optics , mechanics , natural convection , convection , finance , rayleigh number , economics
Summary. A parabolic approximation to the equation of motion of elastic waves as a sum of surface modes and discovering a parabolic approximation be applied directly to surface waves. The approximation depends on the material properties varying slowly within a wavelength, whereas surface waves may travel in a surface wave guide whose depth is of the same order of magnitude as a wavelength. This difficulty is overcome by representing the waves as a sum of surface modes and discovering a parabolic approximation for the amplitudes as a function of position on the surface. The theory is applicable to the propagation of Love or Rayleigh waves in a structure which is vertically stratified in an arbitrary way, but varies slowly in any horizontal direction.