Open AccessA phase‐front method — I. Narrow‐frequency‐band SH ‐waves
Author(s) -
Haines A. J.
Publication year - 1983
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.1983.tb02833.x
Subject(s) - curvilinear coordinates , diffraction , mathematical analysis , wavelength , phase (matter) , physics , wave propagation , displacement (psychology) , parabolic cylindrical coordinates , wave equation , displacement field , coordinate system , frequency domain , classical mechanics , mathematics , optics , geometry , parabolic partial differential equation , finite element method , partial differential equation , quantum mechanics , psychology , parabolic cylinder function , psychotherapist , thermodynamics
Summary A new approach to modelling the propagation of short‐period seismic waves through heterogeneous media is introduced by presenting the theory for narrow‐frequency‐band SH ‐waves. It is based on a parabolic approximation which is derived by, first, choosing a curvilinear space coordinate so that the phase fronts of the displacement field more or less coincide with the surfaces on which the coordinate is constant, and then making assumptions about the sizes of terms in the equation of motion. The resulting equation, which is only valid for disturbances whose wavelengths are small compared with the scale‐lengths of variations in material properties, resembles the equations for ray theory. The parabolic approximation, however, allows for diffraction where the diffracted energy propagates near the original direction of propagation. Unlike other parabolic approximations, it is formulated in the time rather than the frequency domain, and can be used close to a source. An example is given below to show that it can be applied in a wide variety of situations.