A new fifth parameter for transverse isotropy

Abstract:

Kawakatsu et al. (2015) recently proposed a new parameter, $¥eta_{¥kappa}$
that properly characterizes the incidence angle dependence (relative to the symmetry axis)
 of seismic bodywaves in a transverse isotropy (TI) system. While the commonly used fifth parameter in
 global seismology to describe TI system, $¥eta=F/(A-2L) $, has no simple physical meaning, the newly defined parameter,
¥[
¥eta_{¥kappa} ~=~ ¥frac{F+L}{ (A-L)^{1/2}(C-L)^{1/2} } ,
¥] 
where A, C, F and L denote the Love's elastic constants for TI,
measures the departure from the ``elliptic condition" (Thomsen, 1986)
when $¥eta_{¥kappa}$ not equal to unity, and characterizes nicely the incidence angle dependence of bodywaves.

When existing models of upper mantle radial anisotropy are compared in terms of this new parameter,
PREM shows a distinct property.
Within the anisotropic layer of PREM (a depth range of 24.4-220km), $¥eta_{¥kappa} < 1$
in the top half and $¥eta_{¥kappa} > 1$ in the lower half. If $¥eta_{¥kappa} > 1$,
anisotropy cannot be attributed to the layering of homogeneous layers.
While how well the fifth parameter is constrained from data needs to be carefully examined,
we now have, at least, a parameter that properly characterizes the TI system.
I suggest (hope) this parameter to be used in future surface wave and bodywave studies
of the mantle anisotropy,
rather than the conventional $¥eta$.

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{¥bf Reference:} ¥¥
¥noindent
Kawakatsu, H, J-P Montagner, and T-R A Song, On DLA's $¥eta$,
in The Interdisciplinary Earth: A volume in honor of Don L. Anderson, edited by Foulger et al., GSA, in press (2015).