# Computational Vibro-Acoustic Time Reversal for Source and Novelty Localization
## 5 Examples
### Source Localization Example
#### 5.1.1 Comparison of SNRs with and without Structures  
As mentioned above, we introduce structures in the domain (two beams in our case) and in this vibro-acoustic problem we are prompted to investigate whether the presence of the structures improves the SNR. By considering only the 24 boundary receivers/emitters, the recorded signals at the forward step were sent back, and for different simulation times, we calculated the SNRs for the two following cases. In the first case, there were not any structures in the domain, while in the second case, two beams (see Figure 3), were introduced. Shown in Figure 5 are the SNRs for both cases with their respective simulation duration. The longest duration of 84k time steps corresponds to a travel distance of 187 \(L\), where \(L\) is the horizontal length of the domain. We notice that the presence of the beams improves the quality of focusing considerably, as expressed by the SNR values. This was an expected behaviour, since it has been observed that in random or general complex media the time reversal presents better refocusing properties [23].  
It is worth mentioning that the presence of beams in the acoustic domain might be significant in the overall system's response. In this context, we have tried to send back in the acoustic domain, during the backward time reversal step, the data recorded in the vibro-acoustic environment. As it was expected, the results were not acceptable. For example, in two experiments with simulation durations corresponding to 125 \(L\) & 187 \(L\) travel distances, at the expected source focusing times, the highest pressure values were not found at the source location. Considering this, we emphasize the importance of taking into account the presence of structural components into an acoustic domain and their interaction.  
Figure 4: The Ricker pulse used in the numerical experiments and its spectrum.  
Figure 3: The domain with two beams immersed in the fluid and 48 receivers/emitters in total.  
**Remark 1**.: _This numerical example highlights the importance of the structural component. Indeed, we observe that when a structure is present, the complexity of the medium increases and this results in effectively improving the SNR. We also observe that the backward step does not focus on the source location when the structure is not taken into account. This last point raises some interesting questions regarding the accuracy with which the structure should be modeled. Further investigations in this direction will be the object of future work._  
**Remark 2**.: _We observe in Figure 5 that the SNR decreases as a function of time. One may think that this is due to the accumulated numerical phase error. However, although the error indeed accumulates as the time of the experiment increases, our numerical simulations suggest that this does not affect either the refocusing location or the SNR. In fact, it is well known that time-reversal focusing is very robust. Even one bit time reversal (i.e., when signals are digitized over one bit) has good focusing properties, as demonstrated in [24]. The decrease in SNR with time is attributed to the presence of ghosts, as explained in [3]._