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![]() | Seismic data interpolation beyond aliasing using regularized nonstationary autoregression | ![]() |
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We start with a strongly aliased synthetic example from
Claerbout (2009). The sparse spatial sampling makes the gather
severely aliased, especially at the far offset positions
(Figure 1a). For comparison, we used
PWD (Fomel, 2002) to interpolate the traces
(Figure 1b). Interpolation with PWD
depends on dip estimation. In this example, the true dip is
non-negative everywhere and is easily distinguished from the aliased
one. Therefore, the PWD method recovers the interpolated traces
well. However, in the more general case, an additional interpretation
may be required to determine which of the dip components is
contaminated by aliasing. According to the theory described in the
previous section, the PEF-based methods use the lower (less aliased)
frequencies to estimate PEF coefficients, and then interpolate the
decimated traces (high-frequency information) by minimizing the
convolution of the scale-invariant PEF with the unknown model, which
is constrained where the data is known. We designed adaptive PEFs
using 10 (time)
2 (space) coefficients for each sample and a
50-sample (time)
2-sample (space) smoothing radius and then
applied them so as to interpolate the aliased trace. The nonstationary
autoregression algorithm effectively removes all spatial aliasing
artifacts (Figure 1c). The proposed
method compares well with the PWD method. The CPU times, for single
2.66GHz CPU used in this example, are 20 seconds for adaptive PEF
estimation (step 1) and 2 seconds for data interpolation (step 2).
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jaliasp,dealias,jamiss
Figure 1. Aliased synthetic data (a), trace interpolation with plane-wave destruction (b), and trace interpolation with regularized nonstationary autoregression (c). Three additional traces were inserted between each of the neighboring input traces. |
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![]() | Seismic data interpolation beyond aliasing using regularized nonstationary autoregression | ![]() |
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