We generate a synthetic 3-D dataset using the formula
First, a white noise trace is generated and passed through a low-pass filter. Then, according to the position of the trace on the n2 by n3 plane, we shift the trace by tshift. As a special case, if we set a=0 and b=0, we will get a dataset consisting of many horizontal reflections, as shown in Figure 9. Otherwise, we will generate a series of dipping reflections, as shown in Figure 10 (a=1, b=1). Finally, we mix three datasets of different dipping reflections together and get a new dataset, as shown in Figure 11. The size of this cube is n1=256, n2=128, and n3=128.
This dataset mainly consists of coherent component. Therefore, the result from horizontal reflections is nearly perfect. However, with the increase of dipping angle, the extent of coherency decreases and the compression ratio also decreases from several thousand to less than two hundred. This verifies our analysis in last section, i.e., steep dipping reflections are more difficult to compress. This is why we prefer to compress the dataset after NMO correction.
One interesting thing is, the result of the mixing case is better than the case of dipping reflections (difference of SNR is 1.17dB). This is because some high-frequency, high-wavenumber coherent noise is introduced into the dataset after compression. In the mixing case, the coherent noise cancels each other. Therefore the influence is not so serious. As shown in Figure 12 and 13, it is very easy to notice the high-frequency, high-wavenumber coherent component in the f-k domain. In the real seismic dataset, there exist reflections with many different dipping angles. This coherent noise usually will not cause big problem.