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We begin by recalling some notation needed in the remainder of the paper.
For transversely isotropic media with vertical symmetry axis,
the relationship between components of stress and strain
(where *u*_{j} is the
*j*th component of the displacement vector) is given by

| |
(1) |

where *a* = *b* + 2*m* (*e.g.*, Musgrave, 1970; Auld, 1973),
with *i*,*j*,*k*,*l* obviously each ranging from 1 to 3 in Cartesian coordinates.
The matrix describes isotropic media in the special case when
, , and .

The Thomsen (1986) parameters , , and are related
to these stiffnesses by

| |
(2) |

| |
(3) |

| |
(4) |

For P-wave propagation in the earth near the vertical, the important
anisotropy parameter is . For SV-wave propagation near the
vertical, the combination plays essentially the
same role as does for P-waves. For SH-waves, the pertinent
anisotropy parameter is . All three of the Thomsen parameters
vanish for an isotropic medium.
It is also useful to note for later reference that

| |
(5) |

In TI media, *c* and *l* are the velocities normal to the layering.
Then, , , and measure the deviations from
these normal velocities at other angles. We present the relevant
details of the phase velocity analysis later in the paper.

** Next:** Gassmann results for isotropic
** Up:** NOTATION AND SOME PRIOR
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Stanford Exploration Project

10/16/2003