MS_TI_parameters
MS_TI_parameters - TI parameters from C.
Returns various parameters describing TI anisotropy given an elasticity matrix (C) and density (rho) in GPa and kg/m^3.
[loveA, loveC, loveL, loveN, loveF, vpv, vsv, eps, gam, del ... vpa, vsa, xi, phi, eta] = MS_TI_parameters(C, rho)
Output: vpa : isotropic Voigt average P-wave velocity, km/s vsa : isotropic Voigt average S-wave velocity, km/s vpv : vertical P-wave velocity, km/s vsv : vertical S-wave velocity, km/s eps, gam, del : dimensionless Thomsen (1986) parameters xi, phi, eta : dimensionless anisotropy parameters (e.g. Panning and Romanowicz, 2006) loveA, loveC, loveL, loveN, loveF : Love's (1927) anisotropy parameters, GPa Notes
Input units should be GPa for the elasticity matrix and kg/m^3 for the density - this gives output parameters in units of km/s for velocity and GPa for elasticity. Choosing a different unit for the elasticity will change the units for the Love parameters and velocities but not the dimensionless parameters. Choosing an arbitrary value for the density will not alter the dimensionless parameters or Love parameters, but the velocities will be meaningless. The values reported for xi, phi and eta do not assume eta=1 or A=C (as assumed by Panning and Romanowicz, 2006). Compare 'Panning' and 'global' modes in MS_TI. References
Thomsen, L. (1986) "Weak elastic anisotropy" Geophysics vol.51 pp.1954-1966
Mark Panning and Barbara Romanowicz (2006) A three-dimensional radially anisotropic model of shear velocity in the whole mantle. Geophysical Journal International v167, 361–379. doi: 10.1111/j.1365-246X.2006.03100.x
Love, A.E.H., (1927). A Treatise on the Theory of Elasticity, Cambridge Univ. Press, Cambridge.
See also: MS_TI, MS_polyaverage