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![]() | Seismic data interpolation beyond aliasing using regularized nonstationary autoregression | ![]() |
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A common constraint for interpolating missing seismic traces is to
ensure that the interpolated data, after specified filtering, have
minimum energy (Claerbout, 1992). Filtering is equivalent to
spectral multiplication. Therefore, specified filtering is a way of
prescribing a spectrum for the interpolated data. A sensible choice is
a spectrum of the recorded data, which can be captured by finding the
data's PEF (Crawley, 2000; Spitz, 1991). The PEF, also known
as the autoregression filter, plays the role of the
`inverse-covariance matrix' in statistical estimation theory. A signal
is regressed on itself in the estimation of PEF. The PEF can be
implemented in either
-
(time-space) or
-
(frequency-space) domain. Time-space PEFs are less likely to create
spurious events in the presence of noise than
-
PEFs
(Crawley, 2000; Abma, 1995). When data interpolation is cast as an
inverse problem, a PEF can be used to find missing data. This involves
a two-step approach. In the first step, a PEF is
estimated by minimizing the output of convolution of known
data with an unknown PEF. In the second step, the
missing data is found by minimizing the convolution of the recently
calculated PEF with the unknown model, which is constrained where the
data are known (Curry, 2004).
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![]() | Seismic data interpolation beyond aliasing using regularized nonstationary autoregression | ![]() |
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