INTRODUCTION

Interpolation has become of more importance 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) Van Dedem and Verschuur (2005). Examples of current 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 (), DMO-based methods Biondi and Vlad (2001), and the focal transform (), which requires an input focal operator instead of velocity.

In this paper, I describe a hybrid approach that combines both non-stationary prediction-error filters 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 a surface-consistent cross-correlation of a multiple model with the input data. 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).

The data used in this example is from 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. I estimate a PEF on the original data (with the missing offsets) and can produce an ideal reconstruction. Estimating a PEF on the pseudo-primaries, which are generated without the near offset data, gives promising results, which can be quality-controlled with the output of the convolution of the pseudo-primary-derived PEF with the recorded data.