*3.1. Rock Physics Modeling and Velocity Dispersion Analyzing*

Here, three rock physics models, the pore fluid dissolution model, the SLS model and the Pride model, are applied for P-wave velocity dispersion calculation, as shown in Figure 2. Here, we consider rocks with micrometric pores, and gas micro-bubbles exist in the pores with bubble radium 1 um. Other parameters used in the models are listed in Table 1.

**Figure 2.** Comparison of velocity dispersion and attenuation calculated by three rock physics models. (**a**) Pore fluid dissolution model, (**b**) Squirt model and (**c**) Pride model. The blue solid line is the P wave velocity, and the red dash line is attenuation.

The corner frequency of the Squirt model is around 105 Hz, and the Pride model's around 10<sup>9</sup> Hz. Compared with the other two models, the pore fluid dissolution model is suitable for description of this rock's seismic frequency band, the corner frequency of which occurs between 0.1 and 100 Hz. The maximum values of the attenuation curves of the three models are similar. The Squirt model and the Pride model predict slightly larger attenuation. For the velocity dispersion, the pore fluid dissolution model and the Pride model share similar velocity range, with lower bound 2880 m/s and upper bound 3230 m/s. Although the lower bound is similar, the Squirt model yields a larger upper bound of 3400 m/s. The blue solid line is the P\_wave velocity, and the red dash line is attenuation. In our model, the mobility of fluid is low due to the low porosity and low permeability, which makes it impossible for the conventional WIFF model to be used. The choice of a suitable rock physics model need to be tested by comparing the attenuation and velocity dispersion curves, and the best one is that which can model the attenuation in the seismic frequency range.

Considering that the constant Q assumption is always accepted for real data application, conventional constant Q theory is then compared for showing the velocity dispersion between logging frequency and seismic frequency. The results of velocity dispersion are shown in Figure 3. The porosity ranges from 0.04 to 0.08, and gas saturation ranges from 0.15% to 0.25%. The SLS model yields almost the same results as the pore fluid dissolution model, while the constant Q model yields a monotonous velocity curve, which contains large difference from that of the pore fluid dissolution model. As shown in Figure 3a–c, as the porosity increases, the velocity range decreases in the pore fluid dissolution model. The upper bound decreases from 3500 m/s to 3000 m/s, and the lower bound decreases from 3300 m/s to 2550 m/s. As shown in Figure 3d–f, as the gas saturation increases, the velocity range shows little difference.

**Figure 3.** Comparison of velocity dispersion calculated by using the pore fluid dissolution model, the SLS model and the constant Q model. (**a**) Porosity 0.04 and gas saturation 0.25%, (**b**) Porosity 0.06 and gas saturation 0.25%, (**c**) Porosity 0.08 and gas saturation 0.25%, (**d**) Porosity 0.08 and gas saturation 0.15%, (**e**) Porosity 0.08 and gas saturation 0.2%, (**f**) Porosity 0.08 and gas saturation 0.25%. The two red solid curves are the results from the pore fluid dissolution model, the dash blue curves are from the SLS model, and the other dash curves (orange curve and cyan curve) are from the constant Q model.

The two red solid curves are the results from the pore fluid dissolution model, where the bubble radius are 4 × 10−<sup>6</sup> and 6 × 10<sup>−</sup>6, respectively. The dash blue curves are from the SLS model. The other dash curves (orange curve and cyan curve) are from the constant Q model, and the Q values are picked from the pore fluid dissolution model at 100 Hz.

The corresponding 1/Q curves are compared in Figure 4. The two curves in each subfigure represent different bubble radii. As porosity increases, the attenuation becomes larger, while the gas saturation increase influences little about the attenuation.

**Figure 4.** Comparison of 1/Q curves from the pore fluid dissolution model and the SLS model. The red solid curve is the pore fluid dissolution model, and the dash blue curve is the SLS mode. (**a**) Porosity 0.04 and gas saturation 0.25%, (**b**) Porosity 0.06 and gas saturation 0.25%, (**c**) Porosity 0.08 and gas saturation 0.25%, (**d**) Porosity 0.08 and gas saturation 0.15%, (**e**) Porosity 0.08 and gas saturation 0.2%, (**f**) Porosity 0.08 and gas saturation 0.25%.
