** Next:** Application to tomography
** Up:** 12: OPERATOR OF INTEGRAL
** Previous:** Geometry of the main

Our task is to describe the profile of the main discontinuity of the field

| |
(126) |

along the line .I remind you that
Applying the operator we obtain the field
Then we fix a line in the plane :
which we shall call a pseudoray. For each point *M*^{'} belonging to the
pseudoray, we apply the expansion of the difference
into Taylor's series in a neighborhood of the point
:
where and
The above equations are absolutely the same as those that we have already done
for the *KO*. As a result, we will receive a very similar formula
describing the field *U*(*M*^{'}):
| |
(127) |

where .
But here we have some important differences that we have to take into account:
Formula (127) describes the profile of the discontinuity along the
pseudoray but not along a line . There is a formalism that connects
different profiles of discontinuity. I shall omit this consideration and give
you only the final result under :

| |
(128) |

where .I consider this formula to be the main result of the developing theory.

** Next:** Application to tomography
** Up:** 12: OPERATOR OF INTEGRAL
** Previous:** Geometry of the main
Stanford Exploration Project

1/13/1998