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![]() | Interpolation of near offsets using multiples and prediction-error filters | ![]() |
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Interpolation can be phrased in two steps, where a nonstationary prediction-error filter is first estimated from fully-sampled training data and is then used to interpolate missing data. The training data required by this method should have the same local autocorrelation as that of the desired output interpolated data. Pseudo-primaries, having roughly the same dip as the missing data, serve as training data for a PEF. Some of the problems with the pseudo-primary data, such as the different phase and amplitude, do not influence the PEF.
To estimate a nonstationary PEF, we solve,
Once this filter has been estimated from the pseudo-primary data, the
filter is used in a second least-squares problem. In this problem, we
estimate an interpolated output, , composed of missing data,
, and known data,
, that, when convolved with the nonstationary
PEF, produces a minimized output,
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![]() | Interpolation of near offsets using multiples and prediction-error filters | ![]() |
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