oa 3D seismic trace interpolation using noncausal spatial filters

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 noncausal prediction filters over their pseudo non-causal counterparts through their applications on synthetic and field data.