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Here we see how the interpolation beyond aliasing was done.
interpolation ! beyond aliasing
The first ``statement of wishes'' is that the observational data should result from a linear interpolation of the uniformly sampled
model space ; that is,
.Expressing this as a change gives the fitting goal
in terms of the model change,
.The second wish is really an assertion
that a good way to find missing parts of a function
(the model space)
is to solve for the function and its PEF at the same time.
We are merging the fitting goal
() for irregularly sampled data with the fitting goal
(42) for finding the prediction-error filter.

| |
(48) |

| (49) |

Writing this out in full for 3 data points
and 6 model values on a uniform mesh
and a PEF of 3 terms,
we have
| |
(50) |

where *r*_{m} is the convolution of the filter *a*_{t} and the model *m*_{t},
where *r*_{d} is the data misfit ,and where was defined in equation (11).
fitting goal ! nonlinear
Before you begin to use this nonlinear fitting goal,
you need some starting guesses for and .The guess is satisfactory (as explained later).
For the first guess of the filter, I suggest you load it up with
as I did for the examples here.

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Stanford Exploration Project

4/27/2004