titest.mn

.TH titest 1 "18 Feb 1997"
.SH NAME
titest \- see if a set of anisotropic elastic constants are
transversely isotropic
.SH SYNOPSIS
.BI "titest < elastic_constants
.PP
.B titest
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 outputs:
.br
0) the input matrix,
.br
1) the input elastic constants rotated so that the
best-fitting TI axis is the Z axis,
.br
2) the TI approximation to the rotated matrix,
.br
3) the TI approximation in the original unrotated coordinate system,
.br
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),
.br
5) the total scalar percent difference from TI, and
.br
6) the coordinates of the axis vector, in both cartesian and spherical
notation.
.LP
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 elastic 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 constant could be
attained.
.LP
Spherical coordinates are specified using phi and theta:
.br
phi=0 is the +Z axis
.br
phi=90 theta=0 is the +X axis
.br
phi=90 theta=90 is the +Y axis
.LP
For more about what "best-fitting" means for elastic stiffness matrices, 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".
.SH OPTIONS
Currently there are no options or arguments.
.SH EXAMPLES
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:
.PP
.nf
 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
.fi
.PP
Inputting this matrix into titest finds the TI equivalent with the Z
axis as the symmetry axis:
.PP
.nf
 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 
.fi
.PP
.SH AUTHOR
This program was written by Joe Dellinger at the Amoco Tulsa Technology Center
during February 1997.
This version is copyright (c) 2005 by the Society
of Exploration Geophysicists. For more information,
see http://software.seg.org/2005/0001. You must read and accept the
terms of usage in disclaimer.txt before use.
.SH SEE ALSO
.BR orthotest (l)