MS_TI

MS_TI - generate elastic constants for a vertically transverse isotropic
         medium from specified parameter sets. Symmetry is in the 3-axis.
[C]=MS_TI( list_of_parameters , parameter_set_string )
where parameter_set_string defines the set which precede it:

thomsen (default)

[C]=MS_TI(vp,vs,rh,eps,gam,del) -or-
[C]=MS_TI(vp,vs,rh,eps,gam,del,'thomsen')
Inputs:
    rh  : Density (kg/m2)
    vp  : km/s (vertical)
    vs  : km/s (vertical)
    eps, gam, del : Dimensionless
Output:
     C : Stiffness tensor (6x6 notation, GPa)
Given Thomsen (1986) parameters for a weakly anisotropic VTI medium,
return the elasticity matrix

panning

[C]=MS_TI(vp,vs,rh,xi,phi,eta,'panning')
Inputs:
    rh  : Density (kg/m2)
    vp  : km/s (isotropic average)
    vs  : km/s (isotropic average)
    xi, phi, eta : Dimensionless anisotropy parameters
Output:
     C : Stiffness tensor (6x6 notation, GPa)
Calculates the elastic tensor for a VTI medium from average Vp and Vs,
and anisotropic parameters xi, phi and eta (see, e.g., Panning and
Romanowicz, 2006). Derivation only valid if eta = 1 and phi = 1.

global

[C]=MS_TI(vp,vs,rh,xi,phi,eta,'global')
Inputs:
    rh  : Density (kg/m2)
    vp  : km/s (Voigt isotropic average)
    vs  : km/s (Voigt isotropic average)
    xi, phi, eta : Dimensionless anisotropy parameters
Output:
     C : Stiffness tensor (6x6 notation, GPa)
Calculates the elastic tensor for a VTI medium from the Voigt average
Vp and Vs and anisotropic parameters xi, phi and eta (see, e.g., Babuska
and Cara, 1991)

love

[C]=MS_TI(A,C,L,N,F,'love')
Inputs:
     A,C,L,N,F : Love parameters (GPa)
Output:
     C : Stiffness tensor (6x6 notation, GPa)
Calculates the elastic tensor for a VTI medium from Love (1927) parameters.

anderson

[C]=MS_TI(Vpv, Vph, Vp45, Vsv, Vsh, rho, 'anderson')
Inputs:
     Vpv    : Velocity of P-wave along 3-axis
     Vph    : Velocity of P-wave normal to 3-axis
     Vp45   : Velocity of P-wave at 45 degrees to 3-axis
     Vsv    : Velocity of S-wave along 3-axis (or normal to 3-axis
              polarised normal to 1-2 plane)
     Vsh    : Velocity of S-wave normal 3-axis polarised
              parallel to 1-2 plane
     rho    : Density
Output:
     C : Stiffness tensor (6x6 notation, GPa)
Calculates the elastic tensor for a VTI medium from Anderson's (1961)
parameters. Velocities in km/s, density in kg/m^3.

References

Anderson, D. L. (1961) "Elastic wave propagation in layered
    anisotropic media" Journal of Geophysical Research 66:2953 - 2963
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
Babuska, V. and Cara, M. (1991). Seismic Anisotropy in the Earth. Kluwer
   Academic, Boston.
Love, A.E.H., (1927). A Treatise on the Theory of Elasticity,
   Cambridge Univ. Press, Cambridge.
See also: MS_iso, MS_elasticDB