## 3 Results
### Field Data  
Finally, the SMD algorithm is tested on field data, collected between January and March 2016 during the CREST expedition, MGL1601, aboard the R/V Marcus G. Langseth. Pressure waves are generated by a tuned array of 36 air guns, towed at a depth of 6 m. The resulting acoustic waves are recorded using a 12,587.5 m hydrophone streamer, towed at the depth of 8 to 12 m, and carrying 1008 receivers. The receivers are spaced by 12.5 m, each of them recording pressure once every 4 ms. The maximum offset between two adjacent columns is a little greater than two rows, so we round it up to three rows. Further information regarding data acquisition can be found in [21]. Seismic data are also available at the NSF-sponsored Academic Seismic Portal hosted by the University of Texas Institute for Geophysics and can be accessed at [[https://www.marine-geo.org/tools/search/Files.php?data_set_uid=23597](https://www.marine-geo.org/tools/search/Files.php?data_set_uid=23597)]([https://www.marine-geo.org/tools/search/Files.php?data_set_uid=23597](https://www.marine-geo.org/tools/search/Files.php?data_set_uid=23597)) (retrieved on 31 March 2021). Unfortunately, when being applied to real seismic data such as in Figures 12 and 13 SMD with 95% compression cannot reconstruct the arriving waves properly. Due to multiple reflections and dispersion, the number of coherent waves is much larger in marine seismic gathers than in synthetic data. Furthermore, the noise has high coherence such that it can closely resemble wave arrivals. Using SMD with 80% compression ensures that the arriving waves will be properly reconstructed while also ensuring the noise is drastically reduced. Figure 12: (**a**) The original data from ocean seismic gathers with strong reflections. (**b**) The data reconstructed after applying 80% compression with SMD to the original data. Areas highlighted in red are enlarged 3 times along \(x\)-axis and 6 times along \(y\)-axis. The first data set (Figure 12) contains strong reflections arriving far after the direct wave which can be seen at early times on the few receivers close to the source. In this test, SMD was able to identify prominent waveform-related features while almost completely ignoring noise-dominated sections of data. The Figure 12 highlights in red an enlarged portion of the data (3 times along \(x\)-axis and 6 times along \(y\)-axis) in which we can see the first arriving reflections. In the original data (Figure 12a), at the lower half of the enlarged window we can also see the preceding noise. However, once the data is processed with SMD (Figure 12b) the preceding noise is no longer present. A principal drawback of SMD is that in some scenarios it will also ignore weaker incoming waves, and fail to differentiate them from noise. The second data set (Figure 13) is from a different shot-gather in which we can observe weak reflections arriving closely after the much stronger direct wave. In Figure 13 the reflections are circled with purple lines, direct wave with green lines, and the preceding  
Figure 13: (**a**) The original data from ocean seismic gathers with weak reflections. (**b**) The data reconstructed after applying 80% compression with SMD to the original data. Areas highlighted in red are enlarged (2 times along the \(x\)- and \(y\)-axes). The reflected waves are circled with purple lines, direct wave with green lines, and the preceding noise with black lines. noise with black lines. Red lines are used to highlight and enlarge (2 times along the \(x\)- and \(y\)-axes) an example of noise interfering with the reflected waves. The reflections are hard to differentiate from the more noticeable direct waves and because of their small amplitude, they are noticeably distorted by noise. In this test, SMD identified and properly reconstructed both direct waves and reflected waves, while reducing noise in all parts of the data. The preceding noise (circled in black) is noticeably weaker in the data reconstructed from SMD results (Figure 13b) than in the original data (Figure 13a).