== MS_phasevels

 MS_PHASEVELS - Wave velocities in anisotropic media.

 // Part of MSAT - The Matlab Seismic Anisotropy Toolkit //

 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 (m/s)
       'vs2' = slow shear-wave velocity (m/s)
       'vp'  = P-wave velocity (m/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.
 
 Reference: Mainprice D. (1990). An efficient
            FORTRAN program to calculate seismic anisotropy from
            the lattice preferred orientation of minerals.
            Computers & Gesosciences, vol16, pp385-393.
