3D seismic trace interpolation using noncausal spatial filters

Abstract

Seismic datasets are often spatially undersampled in 3D exploration. Trace interpolation, a well-known solution to this sampling deficiency, is often used to generate unrecorded traces from a spatially undersampled dataset. One interpolation method used routinely for this task is the so-called f?x domain prediction filter interpolation method. This method operates on 2D seismic data to interpolate spatially aliased events. For 3D data, it is possible to extend the method to the f?x?y domain. F?x?y prediction filters operate in the frequency space domain where for each frequency plane a two-dimensional prediction filter is computed. The 2-D filter can be computed by either 1) solving for a quadrant filter and then placing its conjugate flipped version opposite itself, this is called a pseudo-noncausal filter; or 2) solving for all the prediction coefficients in a single operation, this is called a non-causal filter. While pseudo-noncausal filters are commonly used in trace interpolation methods, their non-causal counterparts can offer some significant advantages, namely, they are more centre-loaded, less sensitive to the size of window used in their derivation and better in handling amplitude variation. In this paper we show how the technique of 2-D trace interpolation can be extended to 3-D trace interpolation. In addition, we demonstrate the benefits of using non-causal prediction filters over their pseudo non-causal counterparts through their applications on synthetic and field data.