*3.3. Velocity Dispersion Correction on Synthetic Seismic Data*

The upscaled velocities from the SLS model, the constant Q model and the Backus averaging method are all applied to the synthetic seismic data for velocity dispersion correction. The synthetic seismic data are generated by convolution of the reflection coefficient with the minimum phase wavelet. The original velocity used is that in the logging band. The amplitude of the data is not changed, as different velocity is used, only the phase. Firstly, the Backus averaging method is applied as shown in Figure 7. For

windows with three different sizes, the synthetic data show little variation from the real data. The event at around 0.7 s arrives earlier that of the real data.

**Figure 6.** Velocity variation from the pore fluid dissolution model and the constant Q model. The orange area is the velocity range of the constant Q model. The cyan area is the velocity range of the pore fluid dissolution model. (**a**) Porosity ranges from 0.04 to 0.08, gas saturation is 0.25%, (**b**) porosity is 0.08, gas saturation ranges from 0.15% to 0.25%.

**Figure 7.** Comparison of synthetic seismic data by using upscaled velocity from three different sizes of sample window using the Backus averaging method.

Then, the constant Q model is applied for the velocity dispersion correction. The results are shown in Figure 8. For the maximum velocity of the constant Q model, the synthetic data are similar to the real data. For the minimum velocity, as the values are smaller than those of logging velocity, the synthetic data stretch obviously, especially for the data after 0.4 s.

**Figure 8.** Comparison of synthetic seismic data by using upscaled velocity from the maximum and minimum velocity of constant Q model in Figure 6a.

The SLS model is then applied and shown in Figure 9. As the velocity shows much smaller values in Figure 6a, the synthetic data show much more stretch than both the constant Q model and the Backus averaging method. The stretch can be seen starting from 0.2 s, and it becomes larger at 0.4 s. The stretch is largest at 0.9 s. The whole length of the data is 1.2 s.

**Figure 9.** Comparison of synthetic seismic data by using upscaled velocity from the maximum and minimum velocity of the SLS model in Figure 6a.
