INTRODUCTION

Interpolation has become more important recently, largely due to increased reliance on algorithms that require dense and regular data sampling, such as wave-equation migration and 3D surface-related multiple elimination (SRME) Dedem and Verschuur (2005). Examples of current interpolation methods include Fourier Duijndam and Schonewille (1999); Liu and Sacchi (2004); Xu et al. (2005), Radon transform Trad (2003), and prediction-error filter (PEF) based methods Spitz (1991). Other methods that rely on the underlying physics (and typically also a velocity model) include migration/demigration Pica et al. (2005), DMO-based methods Biondi and Vlad (2001), and the focal transform Berkhout et al. (2004), which requires an input focal operator instead of velocity.

In this paper, I further examine a hybrid approach that combines both non-stationary PEFs Crawley (2000) and pseudo-primaries generated from surface-related multiples Shan and Guitton (2004) in order to interpolate missing near offsets. I generate pseudo-primaries by auto-correlation of the input data, which gives a similar result to the cross-correlation of the input data with a multiple model described in a previous paper Curry (2006). Once the pseudo-primaries have been generated, I estimate a non-stationary PEF on the pseudo-primaries by solving a least-squares problem. I then solve a second least-squares problem where the newly found PEF is used to interpolate the missing data Claerbout (1999). This is done in both the t-x and f-x domains.

The data used in this example is the Sigsbee2B synthetic dataset where the first 2000 feet of offset were removed. Near-offset data is typically missing from marine data, and large near-offset gaps can exist when undershooting obstacles such as drilling platforms. Estimating a PEF on the pseudo-primaries, which are generated without the near offset data, gives promising results using t-x filters but f-x filters do not eliminate the crosstalk.