Seismic data interpolation beyond aliasing using regularized nonstationary autoregression |

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).

jaliasp,dealias,jamiss
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.
Figure 1. |
---|

Seismic data interpolation beyond aliasing using regularized nonstationary autoregression |

2013-07-26