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What I have described above represents my first iteration.
It can be called a
``**linear-estimation** method."
Next we will try a
``**nonlinear-estimation** method"
and see that it works better.
If we think of minimizing the *relative* error in the residual,
then in linear estimation
we used the wrong divisor--that is, we used
the squared data *v*^{2} where we should have used
the squared residual .Using the wrong divisor is roughly justified
when the crosstalk is small
because then
*v*^{2} and are about the same.
Also, at the outset the residual was unknown,
so we had no apparent alternative to *v*^{2},
at least until we found .Having found the residual, we can now use it in a second iteration.
A second iteration causes to change a bit,
so we can try again.
I found that,
using the same data as in Figure 1,
the sequence of iterations converged in about two iterations.

**reswait
**

Figure 2
Comparison of weighting methods.
Left shows crosstalk as badly removed by uniformly weighted
least squares.
Middle shows crosstalk removed by deriving a weighting
function from the input *data*.
Right shows crosstalk removed by deriving a weighting
function from the fitting *residual*.
Press button for movie over iterations.

Figure 2 shows the results of the various weighting methods.
Mathematical equations summarizing the bottom row of this figure are:

| |
(9) |

| (10) |

| (11) |

For the top row of the figure,
these equations also apply,
but and should be swapped.

** Next:** Clarity of nonlinear picture
** Up:** Solution by weighting functions
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Stanford Exploration Project

10/21/1998