Extending the t-x prediction to three dimensions is a simple matter of defining the 3-dimensional convolution and its adjoint, that is, its conjugate transpose. Instead of dividing the input into 2-dimensional windows, the input volume is broken into 3-dimensional sub-volumes. Each of these sub-volumes is used in a separate least-squares problem for calculating a 3-dimensional filter, which is a straightforward extension of the calculation of a 2-dimensional t-x filter. Figure shows the configuration of the 3-dimensional filter I used. This configuration is a modification of the more general 3-dimensional filter shown in Claerbout 1992a, page 198. While the 3-dimensional filter might be made symmetrical in space by constraining the filter coefficients across the central element to be equalGulunay et al. (1993), I simply applied the filter in multiple directions and averaged the results.

Figure 4

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