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**Tomography**
is the reconstruction of a function from line integrals
through the function.
Tomography has become a routine part of medicine,
and an experimental part of earth sciences.
For illustration, a simple arrangement is well-to-well tomography.
A sound source can be placed at any depth in one well
and receivers placed at any depth in another well.
At the sender well, we have sender depths *s*,
and at the receiver well, we have receiver depths *g*.
Our data is a table *t*(*s*,*g*) of traveltimes from *s* to *g*.
The idea is to try to map the area between the wells.
We divide the area between wells into cells in (*x*,*z*)-space.
The map could be one of material velocities or one of absorptivity.
The traveltime of a ray increases by adding the *slownesses*
of cells traversed by the ray.
Our model is a table *s*(*x*,*z*) of slownesses in the plane between wells.
(Alternately, the logarithm of the amplitude of the ray is a summation
of absorptivities of the cells traversed.)
The pseudocode is

`
do `*s* = range of sender locations
do *g* = range of receiver locations
*z* = *z*(*s*) # depth of sender.
(s,g) # ray take-off angle.
do *x* = range from senders to receivers.
# ray tracing
if modeling
else tomography

In the pseudocode above, we assumed that the rays were straight lines.
The problem remains one of linear operators even if the rays curve,
making ray tracing more complicated.
If the solution *s*(*x*,*z*) is used to modify the ray tracing
then the problem becomes nonlinear,
requiring the complexities of nonlinear optimization theory.

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** Up:** Adjoint operators
** Previous:** VELOCITY SPECTRA
Stanford Exploration Project

10/21/1998