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

Theory

Data interpolation can be cast as an inverse problem where the interpolated data can have minimum energy after specified filtering (Claerbout, 1992). A PEF can capture the inverse spectra of the data, thus a variety of PEFs have been used to find the missing data. Unlike the relationship between frequency-space PF and PEF, time-space PF has different coefficients from the corresponding PEF that involves causal time prediction coefficients along the column of the predicted data. The PEF creates the residual and the PF result is the data itself. Time-space PF only preserves spatial predictability in seismic data, therefore, it may provide more reasonable interpolation results than time-space PEF, especially in field non-white noise environments. Data interpolation is commonly implemented as a two-step approach, which includes unknown PF estimation from the known data and missing data reconstruction from the calculated PF. Most adaptive PFs and PEFs based on iterative or recursive approaches are capable of handling the nonstationarity of seismic data, but iterations lead to high computation time and large storage requirements for variable coefficients. In this study, we propose a non-iterative, fast, adaptive PF that acts in the time-space domain.

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