Seismic data interpolation without iteration using $t$ -$x$ -$y$ streaming prediction filter with varying smoothness

2D aliasing decimated-trace interpolation test

A benchmark example from Claerbout (2009) showed a strongly aliased gather. The number of space samples was set to 30. We used the two-step approach based on the $t$ -$x$ SPF to insert three additional traces between each of the adjointing input traces. We designed the SPF using 19 (time) $\times$ 11 (space) coefficients for each sample. The four scale parameters were 0.3 ($\xi_t$ ), 0.2 ($\xi_x$ ), 0.12 ($\delta_t$ ), and 0.12 ($\delta_x$ ). The proposed method effectively removed the spatial aliasing artifacts (Figure 5b). The SPF compared well with the plane-wave destruction (PWD) (Fomel, 2002) and adaptive PEF (Liu and Fomel, 2011), and showed higher efficiency in computational speed. The adaptive PEF methods were based on scale invariance for regular trace interpolation by interlacing the filter coefficients with zeros, however, the SPF methods cannot use the scale invariance because SPF is a local algorithm, which reconstructs decimated traces similar to missing traces. The CPU times, for single 2.10 GHZ CPU, were 1.18 s for the $t$ -$x$ SPF, 43.91 s for the PWD, and 10.71 s for the adaptive PEF.

jaliasp,add1
Figure 5. (a) Aliased synthetic model and (b) trace interpolation with the 2D $t$ -$x$ SPF. The interpolated data has four times more traces than the original model.

Seismic data interpolation without iteration using $t$ -$x$ -$y$ streaming prediction filter with varying smoothness