Open AccessNormal‐mode representations of multiple‐ray reflections in a spherical earth
Author(s) -
Nolet Guust,
Kennett Brian
Publication year - 1978
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.1978.tb03739.x
Subject(s) - isotropy , mode (computer interface) , duality (order theory) , phase (matter) , representation (politics) , physics , earth (classical element) , mathematical analysis , earth model , order (exchange) , classical mechanics , mathematics , geometry , computational physics , optics , geophysics , computer science , quantum mechanics , mathematical physics , pure mathematics , finance , politics , law , political science , operating system , economics
Summary. In a spherically symmetric, isotropic earth model the duality between seismic rays and modes can be established completely by application of the principle of stationary phase to the summed normal‐mode representation of the time signal. The requirement of stationary phase must be applied not only on the sum over the angular order but also over the radial‐order summation. This approach is illustrated by using asymptotic approximations to the equations for toroidal oscillations. In this way the travel‐time formulae for rays from a surface source in a sufficiently smooth earth model are easily derived, and the distribution of modes between the different rays can be found. The result may be used as a selection criterion to reduce the number of modes that must be summed to construct synthetic seismograms at a certain distance and within a certain time window.