Mitigating Artifacts in Projection Onto Convex Sets Interpolation
- Aaron Stanton (University of Alberta) | Mauricio Sacchi (University of Alberta) | Raymond Abma (BP) | Jaime Stein (Geotrace Technologies Inc.)
- Document ID
- Society of Exploration Geophysicists
- 2015 SEG Annual Meeting, 18-23 October, New Orleans, Louisiana
- Publication Date
- Document Type
- Conference Paper
- 2015. Society of Exploration Geophysicists
- reconstruction, interpolation, processing, seismic, signal processing
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- 15 since 2007
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Ringing artifacts are often observed above the water-bottom when applying POCS interpolation to marine datasets. The ringing is the result of hard thresholding creating sharp cutoffs in the frequency-wavenumber domain. Moreover, it is likely that the artifacts persist below the water-bottom but are masked by adjacent reflections. Modifying the type of thresholding used can mitigate artifacts, but often at the expense of introducing amplitude bias in the interpolated traces. We investigate several thresholding schemes and provide a generalized thresholding function that allows the style of thresholding to be controlled by a single parameter. We find that soft thresholding combined with a debiasing step provides improved results over hard thresholding in both marine and land datasets.
Projection Onto Convex Sets (POCS) is an iterative optimization technique that has found broad application in seismic data processing including interpolation (Abma and Kabir, 2006; Stein et al., 2010), noise attenuation (Gao et al., 2013), and de-blending of simultaneous source data (Abma and Ross, 2013). It is an effective interpolation strategy that often out performs other methods in the presence of low SNR (Stanton et al., 2012).
Interpolation of marine data using POCS often results in a ringing effect above the water-bottom, an effect that is particularly noticeable in areas with large gaps between observed traces. We found that these artifacts are created by the application of the hard thresholding operator to the data in the frequency wavenumber domain. Soft thresholding can mitigate these artifacts, but this often leads to amplitude bias in the interpolated traces. Peyr (2010) detail a number of alternative thresholding strategies that offer a trade-off between these issues.
We investigate several thresholding strategies in POCS interpolation and arrive at a a generalized thresholding function that allows the style of thresholding to be controlled by a single parameter. Should the thresholding introduce amplitude bias for interpolated traces, we provide a simple amplitude compensation step using the median RMS amplitude of original traces. Synthetic and real data examples demonstrate the effectiveness of soft thresholding plus a debiasing step.
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