MS_PHASEVELS - Wave velocities in anisotropic media.

Calculate the phase velocity details for an elsticity matrix.

[ pol, avs, vs1, vs2, vp, ...] = MS_phasevels( C, rh, inc, azi )

Usage:
    [ pol, avs, vs1, vs2, vp ] = MS_phasevels( C, rh, inc, azi )
        Calculate phase velocities from elasticity matrix C (in GPa) and
        density rh (in kg/m^3) for a propogation direction defined by
        an inclination and azimuth (both in degrees, see below). Output
        details are given below.

[ pol, avs, vs1, vs2, vp, SF, SS ] = MS_phasevels( C, rh, inc, azi )
    Additionally output fast and slow S-wave polarisation in vector
    form.

Notes:
    Azi is defined as the angle in degrees from the +ve 1-axis in x1-x2
    plane with +ve being clockwise when looking at origin from the
    3-axis. Inc is defined as the angle in degrees from the x1-x2 plane
    towards x3 with zero being in the x1-x2 plane. Inc and azi may be
    scalars, or vectors of the same size. Outputs are:

'pol' = angle in plane normal to raypath of FSW
       (deg, zero is x3 direction, +ve c'wise looking along
       raypath at origin)
'avs' = shear-wave anisotropy
'vs1' = fast shear-wave velocity (km/s)
'vs2' = slow shear-wave velocity (km/s)
'vp'  = P-wave velocity (km/s)

and all are vectors of length equal to the input inc and azi vectors.
In the case of no S-wave splitting (vs1 and vs2 are equal to within
eps^1/2) pol is set to NaN. Optional outputs SF and SS are arrays of
size (length(inc),3), with each row corresponding to a polarisation
vector. This implementation is based on EMATRIX6 by D. Mainprice.
Re-coded in MATLAB by James Wookey but now avoids transforming
from the 6x6 elasticity matrix into the 3x3x3x3 tensor form using the
method outlined in Winterstein (1990).

Reference: Mainprice D. (1990). An efficient
           FORTRAN program to calculate seismic anisotropy from
           the lattice preferred orientation of minerals.
           Computers & Gesosciences, vol16, pp385-393.
           Winterstein D. F. (1990). Velocity anisotropy terminology
           for geophysicists. Geophysics, vol 55, pp1070-1088.