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In principle,
missing traces can be determined to simplify -space.
Consider a wave field *P*
composed of several linear events in (*t*,*x*)-space.
A **contour** plot of energy in -space
would show energy concentrations along lines of various ,much like Figure 18.
Let the energy density be .Along contours of constant *E*,
we should also see .The **gradient vector**
()is perpendicular to the contours.
Thus the dot product of the vector with the gradient
should vanish.
I propose to solve the **regression** that the dot product
of the vector with the
gradient of the log energy be zero,
or, formally,
| |
(14) |

The variables in the regression are the values of the missing traces.
Obviously, the numerator and the denominator should be smoothed
in small windows in the -plane.
This makes conceptual sense but
does not fit well with the idea of small windows
in (*t*,*x*)-space.
It should be good for some interesting discussions, though.
For example, in Figure 18,
what will happen where event lines cross?
Is this formulation adequate there?
Also, how should the Nyquist limitation on total bandwidth be expressed?

** Next:** TOMOGRAPHY AND OTHER APPLICATIONS
** Up:** A FULLY TWO-DIMENSIONAL PE
** Previous:** The hope method
Stanford Exploration Project

10/21/1998