# Application of Riemannian Seismic Ray Path Tracing in Salt Dome Prospecting
## 5 Discussion
### Assessment of the Ray Tracing in the Previous Geophysical Setups
#### 5.1.4 Geodesics through a Salt Dome  
It is important to remark that the model in Equation (24) is not symmetric as it intensely depends on both variables, \((x,z)\). Although this is not observable in the density plots of Figures 4 and 5, the effects of asymmetry are evident in the behaviour of seismic rays in such figures. It should noted that the results of refraction and reflection are shown separately (in Figures 4 and 5, respectively) for the sake of clarity.  
The experiments shown in Figure 4 demonstrate the well-known effect that the high-speed contrast between the salt dome and the surroundings impedes seismic rays from penetrating the salt dome, hindering surveys below the salt body. Consequently with the results of Section 4.2, in Figure 4b where the source of seismic rays is located above the salt body, only almost vertical (refracted) rays penetrate the salt dome, crossing it and continuing to travel through the subsoil.  
If the (refraction) experiment is performed by locating the source in the right corner of the seismic section (see Figure 4c), as the rays impinge with large angles (with respect to the vertical), they are all unable to penetrate the salt dome, being instead reflected and thus received at ground level.  
On the other side, if the experiment is performed by locating the source in the other (left) corner, the asymmetry of the synthetic model arises. In this setup (Figure 4a), while the incident rays at large angles (with respect to the vertical) typically reflect at the top of the salt dome, there are (more vertical) rays that travel below the dome and are curved by the higher P-wave speed at the low part of the model, returning to its upper part. These latter rays impinge with the base of the salt body, some being reflected and some (the most vertical ones) refracted, crossing the dome and finally arriving at ground level with higher arrival times but closer to the source, complicating the interpretation of the seismic section.  
As for the portion of the energy of each ray which is reflected (not refracted), the overall results for the same three experiments can be observed in Figure 5. The experiment where the source was located in the middle part above the salt dome is shown in Figure 5b; it can be observed that in this case, all the rays that impinge in the top part of the salt body cross it effectively, and continue travelling far below the salt dome in a notably vertical fashion, which does not return back to ground level.  
As for both experiments with the source located at the left and right corners of the section (Figures 5a and 5c, respectively), it can be observed that the fraction of energy of the incident rays enters the salt dome and stays enclosed within it in several internal reflections until finally (and probably very weakly) exiting the dome at the opposite part of the body. Nevertheless, in the case of Figure 5c and due to the asymmetry of the synthetic model, some rays emerge from the left side of the salt dome and are directed to the surface, which would be confused with rays coming from the refraction experiment, hindering the interpretation of the results.  
As an overall conclusion for the experiments performed in Section 4.4, neither refracted nor reflected rays in any of the performed experiments are able to provide information about the base of the salt dome nor below which can be retrievable at the surface level. Thus, this formalism is consistent with traditional seismic surveys which always find it difficult to illuminate these regions. In this sense, Figures 4 and 5 provide a more visual (physically and geometrically) insight into the outcome of seismic rays in the presence of bodies with high P-wave speed contrasts, like salt domes.