Open AccessObservations on seismic wave equation and reflection coefficient symmetries in stratified media
Author(s) -
Thomson C.,
Clarke T.,
Garmany J.
Publication year - 1986
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.1986.tb03853.x
Subject(s) - symmetry (geometry) , homogeneous space , reflection (computer programming) , seismic wave , spacetime symmetries , notation , physics , eigenvalues and eigenvectors , wave equation , lossy compression , matrix (chemical analysis) , anisotropy , reflection coefficient , mathematical analysis , theoretical physics , classical mechanics , mathematics , geometry , geophysics , quantum mechanics , optics , computer science , chemistry , programming language , quantum field theory in curved spacetime , arithmetic , statistics , chromatography , quantum gravity , quantum
Summary. The equations describing seismic waves in a stratified earth have a number of symmetry properties, one of which has recently been used by Garmany to derive a simple expression for the inverse of the matrix of eigenvectors appearing in the solution of the equations. We review these symmetries of the wave equation in several notations to demonstrate that the property used by Garmany is distinct from the usual symmetries found in the seismological literature. Like the others, the new symmetry has implications for the reflection and transmission properties of a medium. These implications are briefly reviewed in order to show how the new symmetry is placed relative to the others. A limited discussion of the physical origins of the symmetries is given and, though the overall picture is incomplete, it is noted that the new symmetry yields conservation of energy for reflection/transmission at a single interface in all types of media (anisotropic, lossy, etc.).