Open AccessComments on the Paper ‘On Variational Principles and Matrix Methods in Elastodynamics’ by B. L. N. Kennett
Author(s) -
Jobert G.,
Jobert N.,
Kennett B. L. N.
Publication year - 1975
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.1975.tb06190.x
Subject(s) - matrix (chemical analysis) , variational principle , homogeneous , simple (philosophy) , series (stratigraphy) , transformation (genetics) , expression (computer science) , extension (predicate logic) , lanczos resampling , construct (python library) , mathematics , calculus (dental) , physics , mathematical analysis , geology , computer science , statistical physics , philosophy , chemistry , epistemology , quantum mechanics , eigenvalues and eigenvectors , gene , programming language , biochemistry , chromatography , dentistry , medicine , paleontology
Summary Kennett has shown how the equations of elastodynamics may be derived from a variational principle (see also Lanczos, Germain) and attempted to extend this method to the ‘Minor Matrix’ system (Gilbert & Backus). Unfortunately such a direct extension is impossible as will be shown below. However in the case of a medium composed of a series of homogeneous layers, it is possible to construct a stationary expression by a simple transformation. Our discussion will be limited to P‐SV or Rayleigh waves in such a medium. References to the equations of Kennett will be denoted, e. g. (K‐ 4. 1).