## 4 Discussion
The experiment in this subsection proves that there is a strong correlation between the shift vector and relative arrival times of the wave at different receivers. We were able to use that correlation to estimate the velocity of the waves without relying on any information about the medium through which the waves were traveling. We believe that there is also a strong correlation between the column vector and the waveform, as well as between the row vector and the relative amplitudes of the waveform at different receivers. However, proving these correlations will require further testing. In this example, SMD was applied to seismic data from a controlled source. In such cases we can always be certain that there are coherent waves present. However, we are planning a wide range of applications for SMD. During microseismic monitoring, often recorded by DAS, we might want to analyze coherent waves that are not coming from controlled sources. Therefore, when applying SMD to data from microseismic monitoring we do not know in advance whether the data contains signals of interest. For that reason, we developed a method for recognising coherent signal in noisy data, that also relies solely on the results from SMD. We created a method that can differentiate between noisy data and data containing signal, by measuring the curvature in the first several shift vectors. Applying SMD to noisy data without coherent waves returns a set of completely unrelated shift vectors. On the other hand, applying SMD to data containing coherent waves, usually coming from the same source, returns a set of shift vectors most of which have similar curvatures. Therefore, the method differentiates between noisy data and data containing coherent waves, by calculating the standard deviation among the curvatures from the first 10 extracted shift vectors. To test this method, we applied SMD separately to two subsets of data from each of the 20 previously mentioned data files. The first subset contains only the recordings of noise, and the second subset contains recordings of both the coherent waves and the preceding noise (Figure 14). For each subset, we use expression (20) to estimate the curvatures of the first 10 extracted shift vectors and then we compute the standard deviation of the 10 curvature values. The results are presented in Figure 15, in which the standard deviation for each subset without coherent waves is presented in blue, and the standard deviation for each subset containing coherent waves is presented in red. Due to shift vector curvature having random values when SMD results represent noise, the standard deviation among shift vector curvatures should be greater for the data subsets which contain only noise. As can be seen in Figure 15, the standard deviation among shift vectors is consistently lower for subsets containing coherent waves, which are presented in red. This confirms that we can differentiate between data containing only noise and data containing signal, by using our described method. It is important to emphasize that this signal detection method does not contain any information regarding the amplitude of the waves. It is entirely dependent on the curvature of the recorded shift vectors, which is a unique property. This means that this method, while accurate, can also be used to complement other signal detection methods, all of which rely on other properties in seismic data (such as STA/LTA for example, which relies on the amplitudes of the waves). Furthermore, this signal detection method only requires the first 10 shift vectors, which can be acquired very quickly compared to the to the processing time of the SMD. Therefore, when applying SMD to data obtained during seismic monitoring, we suggest first running a quick version of SMD that only extracts the first 10 shift vectors  
Figure 14: Two subsets from a marine field data file. The first subset contains only noise, and the second subset contains both a part of the coherent waves and some of the preceding noise. in order to run signal detection.