Isotropic tomography fits circles (*t ^{2}* = (

Horizontal or near horizontal rays are
typical of a cross-well geometry. These
rays sample a portion of the slowness
surface close to the horizontal and for this reason
the estimated *S*_{x} corresponds to the real horizontal slowness.
On the contrary, *S*_{z} is not sampled by
cross-well geometries. The inversion gives
the vertical slowness of the best fitting ellipse (*S*_{znmo}) which
coincides with the real vertical slowness only if the wave type
considered is *SH*. However, we can generally expect *S*_{znmo}
to be closer than *S*
to the real vertical slowness.
This will
be illustrated later with field data by comparing *S*, *S*_{x} and *S*_{znmo}
with sonic logs.

Vertical or near vertical rays are typical of a VSP-like geometry.
From this type of geometry we can get *S*_{xnmo} and *S*_{z}. These two
slownesses plus *S*_{x} and *S*_{znmo} obtained from cross-well geometries
can be used to estimate the real slowness surface of the medium using the following approximate expression (Muir, 1990):

This expression is called the double elliptic approximation. Dellinger and Muir (1991) demonstrate that this approximation accurately fits general transversely isotropic media.

In the cross-well geometry examples that follow,
the estimated vertical slowness
will be referred to as *S*_{z} rather than *S*_{znmo}.

12/18/1997