Open AccessAsymptotic normal modes of the Earth—III. Fréchet kernel and group velocity
Author(s) -
Zhao L.,
Dahlen F. A.
Publication year - 1995
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1995.tb03555.x
Subject(s) - classification of discontinuities , eigenfunction , mathematical analysis , mathematics , group (periodic table) , group velocity , kernel (algebra) , inner core , boundary value problem , geometry , geology , geophysics , physics , pure mathematics , eigenvalues and eigenvectors , quantum mechanics , optics
SUMMARY A comprehensive study of the Fréchet kernels and group velocities of the Earth's normal modes is conducted based upon the asymptotic eigenfrequency and eigenfunction analyses that we developed previously. Two different approaches, which employ the eigenfunctions or eigenfrequency equations, yield asymptotically equivalent results for the Fréchet kernels and group velocities. The latter approach is considerably simpler, since the need to specify the normal‐mode eigenfunctions as well as their radial derivatives is removed, so that the Fréchet kernels and group velocities can be obtained from knowledge of the asymptotic eigenfrequencies only. The asymptotic analyses are discussed for all possible ray parameter regimes and ray‐path combinations within a crustless version of the earth model 1066A with two discontinuities: a core‐mantle boundary and an inner core boundary. The exact and asymptotic numerical results for the Fréchet kernels and group velocities are compared for such a model. The comparison shows that the asymptotic Fréchet kernels and group velocities are very accurate. The accuracy is better for toroidal modes and relatively high‐frequency spheroidal modes.