Seismic data interpolation beyond aliasing using regularized nonstationary autoregression

Abma decimated-trace interpolation tests

A benchmark example created by Raymond Abma (personal communication) shows a simple curved event (Figure 2a). The challenge in this example is to account for both nonstationarity and aliasing. Figure 2b shows the interpolated result using Claerbout's stationary $t$ -$x$ PEF, which was estimated and applied in one big window, with each PEF coefficient $B_n$ constant at every data location. Note that the $t$ -$x$ PEF method can recover the aliasing trace only in the dominant slope range. The trace-interpolating result using regularized nonstationary autoregression is shown in Figure 2c. The adaptive PEF has 20 (time) $\times$ 3 (space) coefficients for each sample and a 20-sample (time) $\times$ 3-sample (space) smoothing radius. The proposed method eliminates all nonstationary aliasing and improves the continuity of the curved event.

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Figure 2. Curve model (a), trace interpolation with stationary PEF (b), and trace interpolation with adaptive PEF (c).

Abma and Kabir (2005) present a comparison of several algorithms used for trace interpolation. We chose the most challenging benchmark Marmousi example from Abma and Kabir to illustrate the performance of RNA interpolation. Figure 3a shows a zero-offset section of the Marmousi model, in which curved events violate the assumptions common for most trace-interpolating methods. Figure 3b shows that our method produces reasonable results for both curved and weak events and does not introduce any undesirable noise. The adaptive PEF parameters correspond to 7 (time) $\times$ 5 (space) coefficients for each sample and a 40-sample (time) $\times$ 30-sample (space) smoothing radius.

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Figure 3. Marmousi model (a) and trace interpolation with regularized nonstationary autoregression (b).

Seismic data interpolation beyond aliasing using regularized nonstationary autoregression