Figure shows two crossing events and their amplitude spectra. The steeply dipping event is aliased in space. The shaping filter used to reconstruct the HF from the LF is shown in Figure . This filter is convolved with the cubed LF data on the interpolated traces to create the final interpolated section (Figure ). The prominent alias visible in Figure has been removed. However, the interpolation breaks down where the two events cross. The break-down is seen as oscillations and distortions near the crossing point in the time domain and as horizontal lines of noise in the amplitude spectrum.
This distortion is due to the fact that the shaping filter is aliased in space. Where the events are far apart, the shaping filter is very smooth. Near the point where the events cross, the shaping filter gets more complicated and varies rapidly in the spatial direction (Figure ). The filter is calculated where both the HF and LF are known and then interpolated to the trace locations where the HF is unknown. Since the filter is aliased near crossing events, distortions arise in the interpolation. In the previous examples nearest neighbor interpolation was used to interpolate the shaping filter.
Figure 2 Shaping filter used to reconstruct the high-frequency data from the cubed low-frequency data. Notice the oscillations in the filter where the events cross.
The interpolation may be improved by median filtering the shaping filter. The result of this interpolation is presented in Figure . The result is much more satisfying but the amplitude at the crossover may be a little too high and there is still some noise visible in the frequency domain.