# Subsea Methane Hydrates: Origin and Monitoring the Impacts of Global Warming
## 3 Seismic Absorption
### Numerical Experiments on Modeling Seismic Waves in Viscoelastic Media  
To evaluate how the Q-factor variability affects the seismic waves, we performed a series of numerical experiments, changing Q in the target set of layers. To achieve this, we used an elastic model that describes the behavior of the velocities and Q-factors of P- and S-waves obtained in the area marked with a red square in Figure 1 (see detailed descriptions in the works [4; 26; 38]).  
The distribution of P-wave velocities used in the simulation is seen in Figure 4. Unfortunately, we do not know the distribution of the S-wave velocities on the same vertical profile, and thus we adopted a fairly common practice of assuming it to be equal to the speed of P-waves divided by \(\sqrt{3}\).  
Drilling data proved that the layer at a depth of 200 m contains gas hydrate deposits. In the initial frozen state, gas hydrates are indistinguishable in their mechanical parameters from an ideally elastic medium; however, the temperature rises, followed by the increase in fluid saturation of the medium, which leads to an increase in absorption--that is, a decrease in quality factors. It is this property of thawing gas hydrates that appears to be a prognostic sign of an approaching catastrophic methane release.  
To evaluate how much Q-factor disturbances affect seismic wave fields, we performed a series of numerical experiments simulating a seismic wave field caused by a point source. In each experiment, we changed the quality factor in the layer at a depth of 200 m (see Figure 4), since it was in this layer that gas hydrates were found by drilling. For simulation, we used the previously developed finite difference schemes on the basis of the \(\tau\)-method, staggered grids and the software created on its basis (see [39] for more detail).  
We used a Ricker pulse with a dominant frequency of 25 Hz as a probing signal radiating by sources located on the free surface. In total, we performed three experiments with different quality factors within the target layer at a depth of 200 m. Figure 5 presents the vertical components of the wave field at a distance of 500 m from the source at a point located in the middle of the target layer. Let us note that the first arrivals presented here correspond to a P-wave, which has a predominantly horizontal polarization inside the target layer.  
* Seismic trace for elastic medium with no attenuation--this case corresponds to the black line. The first arrival times exactly fit those predicted by ray theory for both P- and S-waves.
* The red line corresponds to the same elastic model and the same geometry of the relative position of the source and receiver; however, in the target layer, the quality factor is 20. There are three main differences from the case of a ideal elastic medium: 1. Increase in phase speed. 2. Amplitude reduction.  
Figure 4: P-wave velocities along one of the vertical wells in the study area.  
3. \"Spreading\" of the signal, which indicates a decrease in the dominant frequency.
4. The blue curve sets the seismic trace for a Q factor of 10. The three differences noted above only become stronger.  
For each of the obtained synthetic wave fields, we also estimated their global variability as the quality factor changes. The relative changes of these wave fields reached 10-13%.  
Thus, based on the numerical experiments performed, we can conclude that the variability of the quality factor even in such a narrow layer introduces significant changes in the seismic wave fields. This allows us to hope for a reliable Q-factor reconstruction and, consequently, for the effective implementation of seismic monitoring of the process of thawing of gas hydrates.