Introduction

A common problem with seismic data is the presence of coherent noise, such as multiple reflections. When these multiples are generated by cross-line structure, the lack of sampling along this axis becomes painfully obvious. One example of such noise is out-of-plane diffracted multiples. Methods to remove these multiples, such as 3D surface-related multiple elimination (SRME) Van Dedem and Verschuur (2005) require a much greater density of sampling as well as recording aperture. This is particularly true in the cross-line.

A synthetic data set provided by ExxonMobil illustrates an extreme example of out-of-plane diffracted multiples coupled with a modern high-density acquisition. The underlying geology is very simple, excluding a large number of point diffractors which create diffracted multiples that obscure the region of interest. These multiples could be removed by the application of 3D SRME, provided that the input wavefield is adequately sampled, making this synthetic data tailor-made for testing interpolation methods.

Many different interpolation methods exist, including Fourier-based methods Duijndam and Schonewille (1999); Liu and Sacchi (2004); Xu et al. (2005), radon-based methods Trad (2003), imaging-operator based methods Biondi and Vlad (2001) as well as prediction-error filter based methods Spitz (1991). Non-stationary prediction-error based methods Crawley (2000) are used throughout this paper to interpolate missing data.

Most tests for interpolation are limited to an increase in source sampling by a factor of two, which corresponds to interpolating missing shots in a flip-flop shooting configuration by using information from the surrounding shots in the same sail line. In addition to missing shots, additional cross-line offsets are needed in the form of additional receiver cables. Both extra shots as well as extra receiver cables are created, using multi-dimensional non-stationary prediction-error filters. The number of dimensions in the filters is varied for both cases, and it is shown that the receiver cable interpolation benefits much more from a higher-dimensional filter than the shot interpolation does. This is in part due to the small number of points sampled in the cross-line.

While this method appears to work well for both in-line shot interpolation as well as cross-line receiver interpolation, still more data needs to be created. The cross-line receivers need to be extrapolated and extra sail lines also need to be interpolated. The measure of the success of these methods needs to be gauged by the end result of the 3D SRME.