titest.txt

titest(1)                                                            titest(1)



NNAAMMEE
       titest - see if a set of anisotropic elastic constants are transversely
       isotropic

SSYYNNOOPPSSIISS
       ttiitteesstt << eellaassttiicc__ccoonnssttaannttss

       ttiitteesstt expects to read from standard input a fully general  anisotropic
       stiffness  matrix in the form of 6 numbers on each of 6 lines of input.
       It finds the best-fitting transversely isotropic (TI) medium, and  out-
       puts:
       0) the input matrix,
       1) the input elastic constants rotated so that the best-fitting TI axis
       is the Z axis,
       2) the TI approximation to the rotated matrix,
       3) the TI approximation in the original unrotated coordinate system,
       4) the percent difference between the input stiffness  matrix  and  the
       best-fitting  TI approximation, in the original coordinates (normalized
       by dividing each element in the difference matrix by the scalar norm of
       the input stiffness matrix),
       5) the total scalar percent difference from TI, and
       6)  the coordinates of the axis vector, in both cartesian and spherical
       notation.

       Note for the ``total scalar percent difference from TI'', 0  means  the
       medium is exactly TI.  100% is the maximum possible error. This is only
       possible in extreme cases, for example if c16=1 and all the other elas-
       tic  constants  are  0.  Such a case (the medium has no TI component at
       all, and all the error is concentrated in a  single  elastic  constant)
       would also be the only way a 100% error in an individual stiffness con-
       stant could be attained.

       Spherical coordinates are specified using phi and theta:
       phi=0 is the +Z axis
       phi=90 theta=0 is the +X axis
       phi=90 theta=90 is the +Y axis

       For more about what "best-fitting" means for elastic  stiffness  matri-
       ces,  see  the  article  by  Arts,  Helbig, and Rasolofosaon in the SEG
       extended abstracts for 1991, page 1534:  "General  Anisotropic  Elastic
       Tensor in Rocks: Approximation, Invariants, and Particular Directions".

OOPPTTIIOONNSS
       Currently there are no options or arguments.

EEXXAAMMPPLLEESS
       The following stiffness matrix is TI (transversely isotropic), but this
       fact is not obvious because it has been rotated to have a symmetry axis
       pointing in the direction phi=12.345 and theta=67.890 degrees:

       331.325      128.029      112.309     -1.30380     -23.3328     -1.92204
       128.029      339.374      108.716     -9.83459     -4.08399     -1.99410
       112.309      108.716      226.191     0.447454      1.10140      1.74841
       -1.30380     -9.83459     0.447454      56.8929      1.27023     -9.88887
       -23.3328     -4.08399      1.10140      1.27023      59.5035     -3.66209
       -1.92204     -1.99410      1.74841     -9.88887     -3.66209      103.658

       Inputting this matrix into titest finds the TI equivalent  with  the  Z
       axis as the symmetry axis:

        341          129          107            0            0            0
        129          341          107            0            0            0
        107          107          227            0            0            0
        0            0            0              54           0            0
        0            0            0              0            54           0
        0            0            0              0            0            106


AAUUTTHHOORR
       This program was written by Joe Dellinger at the Amoco Tulsa Technology
       Center during February 1997.

SSEEEE AALLSSOO
       oorrtthhootteesstt(l)



                                  18 Feb 1997                        titest(1)