## 5 Conclusions  
Shifted-matrix decomposition is a powerful tool that can simultaneously compress and improve seismic data. This is done by converting the seismic data from a matrix into a set of pairs of singular vectors coupled with shift vectors which require less memory to store the seismic data. Furthermore, reconstructing the seismic data from compression results, creates a denoised version of the original data. Shifted-matrix decomposition  
Figure 15: Standard deviation of shift vector curvature from each of the 20 data files. The results from subsets containing only noise are presented in blue and the results from subsets containing parts of coherent waves are presented in red.  
provides an improvement to some of the existing denoising techniques such as SOSVD by avoiding numerical artifacts in areas with multiple intersecting waves of different slopes. This allows us to apply SMD to complicated field data with a large number of arriving waves and still achieve 80% compression.  
When applied to synthetic data and ocean gathers it was able to boost coherent signal and erase the majority of the noise. In synthetic data with signal-to-noise ratio of 1.9, it was able to increase the ratio to 4.7 in the case of 80% compression and to 12.3 in the case of 95% compression. However, the excellent result achieved with 95% compression in the synthetic data is an artifact of the lack of coherent noise and the small number of coherent waves. Due to noise coherence and more complicated overlap of coherent waves, we recommend applying 80% compression to examples of field data in order to accurately represent the signal of interest. In field data, SMD was able to reduce the noise in areas preceding the signal as well as in areas containing coherent waves. As a results, weak waves that were difficult to notice in the original data, can be seen more clearly in the data reconstructed from SMD results. The only drawbacks are that in some scenarios SMD may fail to boost weaker signals and it is not meant to be applied to seismic data obtained from a small number of receivers.  
There is a good correlation between the physical properties such as elastic wave velocity and the results of the SMD. As an example, the average wave velocity in the medium through which the waves propagate (seawater) was roughly estimated by analyzing the shift vector curvature. In the future, we will use machine learning to build models that infer with high accuracy the properties of the source and the velocity model, directly from the SMD results. Results of SMD can also be used for other analysis, such as signal detection. By analyzing only the first several shift vectors, we can check for the presence of coherent waves. Because it requires such a small amount of data, this technique can be executed very quickly by taking only the initial results of SMD. We recommend using it during microseismic monitoring before fully processing the data with SMD.  
M.B.: conceptualization, methodology, software; E.G., R.L.G., M.E.E.: review and guidance. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Crisman/Berg-Hughes, project number HF.12.19B.  
Not applicable.  
All code used in this paper can be obtained by contacting the author at [EMAIL_ADDRESS] or [EMAIL_ADDRESS].  
We would like to thank [PERSON] and his student [PERSON] for providing us with the field data which played an integral role in the development and testing of the SMD.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} DAS & Distributed acoustic sensing \\ SMD & Shifted-matrix decomposition \\ SVD & Singular value decomposition \\ SOSVD & Structure-oriented singular value decomposition \\ SNR & Signal-to-noise ratio \\ STD & standard deviation \\ PCA & Principal component analysis \\ STA/LTA & short-term average over long-term average \\ \end{tabular}