Open AccessMode‐sum to ray‐sum transformation in a spherical and an aspherical earth
Author(s) -
Zhao L.,
Dahlen F. A.
Publication year - 1996
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.1996.tb05299.x
Subject(s) - inner core , born approximation , physics , scattering , normal mode , outer core , mathematical analysis , seismic wave , geometry , classical mechanics , computational physics , geophysics , optics , mathematics , quantum mechanics , vibration
SUMMARY We complete our series of studies on the duality between relatively high‐frequency normal modes and seismic body waves by explicitly converting the normal‐mode summation expressing the elastic response of a spherically symmetric earth model into a body‐wave summation. The procedures in this conversion are discussed in detail for a crust‐stripped version of model 1066A with a solid mantle, a fluid outer core and a solid inner core. The resulting body‐wave responses, the Green tensors representing the various body waves, are in agreement with the well‐documented results obtained using geometrical ray theory. The results derived for the spherically symmetric earth model are then used to obtain the first‐order body‐wave Green tensors in a laterally heterogeneous earth model based upon the Born approximation. The first‐order effect of the coupling between normal‐mode multiplets is shown to be equivalent to the single scattering of seismic body waves by the lateral heterogeneity, as expected from numerous previous studies. We present compact expressions for the scattering matrix and the body‐wave Frechet kernels. A few numerical examples of the Frechet kernels for monochromatic body waves are also provided.