# Computational Vibro-Acoustic Time Reversal for Source and Novelty Localization
## 5 Examples
### Source Localization Example
#### 5.1.2 Using Signals Recorded on the Beams Only  
Here, we present the results, in cases where signals recorded only on the beams were time reversed and emitted back to the domain from the emitters on the beams. The magnitudes of these signals are much smaller than those recorded at the boundaries (or inside the domain), so certain amplification would be necessary if we wish to combine the beam signals with those recorded in the fluid domain. In the last column of Table 1 SNRs are reported for a simulation time of 28 k time steps (\(\approx\)62 L), and for several combinations of emitters on the beams. First, only one or two emitters are activated on each beam, then one from one beam and one from the other, then two and two, etc. Our observations regarding these experiments are the following: When there is only one emitter (on either beam) the SNR varies from 1.08 to 1.67. With two emitters on the same beam, the SNR lies between 1.55 and 1.64, while with one emitter on each beam the SNR increases and is between 1.83 and 2.29, and with two emitters on each beam the SNR is around 2.28, which is remarkable since when all emitters are active, the SNR value is 2.50. Moreover, since for another simulation duration of 8 k time steps, where we have either emitters 1 and 5 on beam 1 or emitters 1 and 7 on beam 2 we obtain SNRs, 1.61 and 1.51, respectively, we conclude that a large recording/emitting time is not necessarily needed in order to obtain a good SNR value.  
Figure 5: SNRs vs simulation time for when beams are and are not present inside the domain.  
When the domain is excited by all 12 (=5 + 7) emitters on the two beams, the SNR versus simulation duration is shown in Figure 5(a). The maximum simulation duration of 28 ms corresponds to 84 k time steps or equivalently 187.7 \(L\) distance traveled. We notice that the SNR stabilizes fairly quickly around the value of 2.49. A graph of the absolute pressure for a simulation duration of 9.333 ms corresponding to the last row of Table 1, is shown in Figure 5(b).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Emitters on Beam 1** & **Emitters on Beam 2** & **SNR** \\ \hline
1 & & 1.08 \\
1,2 & & 1.12 \\
1,5 & & 1.64 \\  & 1 & 1.67 \\  & 1,7 & 1.55 \\
1 & 1 & 1.83 \\
5 & 7 & 2.83 \\
3 & 4 & 2.29 \\
1,5 & 1,7 & 2.28 \\
1,2,3,4,5 & & 1.88 \\  & 1,2,3,4,5,6,7 & 2.31 \\
1,2,3,4,5 & 1,2,3,4,5,6,7 & 2.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The SNR for some combinations of emitters on Beam 1 and Beam 2 and for total number of 28 k time steps.  
Figure 6: The SNR vs simulation duration when all emitters on the beams are active (corresponding to the last row of Table 1).  
**Remark 3**.: _In this numerical example, we see that focusing on the source can be obtained even when recorders only on the structural component are available. The SNR in this case is lower than when receivers in the acoustic part are also used. The quality of the refocusing, as seen in Figure 6b, indicates that the source can be localized. The refocusing spot size depends on the pulse used. Since the width of the pulse is known, this information can be used to estimate the width of the peak. We should note, however, that this method does not allow for a precise estimation of the support of the source or the defect. It allows for the detection and localization by providing an estimate of where the source or the defect is located._