Seismic data interpolation beyond aliasing using regularized nonstationary autoregression

Seismic data are often inadequately or irregularly sampled along spatial axes. Irregular sampling can produce artifacts in seismic imaging results. We present a new approach to interpolate aliased seismic data based on adaptive predictionerror filtering (PEF) and regularized nonstationary autoregression. Instead of cutting data into overlapping windows (patching), a popular method for handling nonstationarity, we obtain smoothly nonstationary PEF coefficients by solving a global regularized least-squares problem. We employ shaping regularization to control the smoothness of adaptive PEFs. Finding the interpolated traces can be treated as another linear least-squares problem, which solves for data values rather than filter coefficients. Compared with existing methods, the advantages of the proposed method include an intuitive selection of regularization parameters and fast iteration convergence. Benchmark synthetic and field data examples show that the proposed technique can successfully reconstruct data with decimated or missing traces. INTRODUCTION The regular and fine sampling along the time axis is common, whereas good spatial sampling is often more expensive or prohibitive and therefore is the main bottleneck for seismic resolution. Too large a spatial sampling interval may lead to aliasing problems that adversely affect the resolution of subsurface images. An alternative to expensive dense spatial sampling is interpolation of seismic traces. One important approach to trace interpolation is prediction interpolating methods (Spitz, 1991), which use low-frequency non-aliased data to extract antialiasing prediction-error filters (PEFs) and then interpolates high frequencies beyond aliasing. Claerbout (1992) extends Spitz’s method using PEFs in the t-x domain. Porsani (1999) proposes a half-step PEF scheme that makes the interpolation process more efficient. Huard et al. (1996) and Wang (2002) extend f -x trace interpolation to higher spatial dimensions. Gulunay (2003) introduces an algorithm similar to f -x prediction filtering, which has an elegant representation in the f -k domain. Curry (2006) uses multidimensional nonstationary PEFs to interpolate diffracted multiples. Naghizadeh and Sacchi (2009) propose an adaptive f -x interpolation using exponentially weighted