**5. Conclusions**

This study explored the role and significance of the continental slope in the interactions between the ocean waves and the continental margin as well as the resulting double-frequency (DF) microseisms recorded in ENAM. The primary vibration direction analysis of the ambient noise recordings in the study area shows that these DF microseisms originated in areas of the North Atlantic Ocean, which are generally aligned in the SE direction with the recording stations. The great circles corresponding to these primary vibration directions for different DF peaks intersect at a number of locations enabling delineation of source areas along the continental slope. Correlation analysis between DF microseisms and ocean wave climate by considering the correspondence in their frequency composition and variation in energy levels shows that the DF microseisms in DF1 (0.1–0.2 Hz), DF2 (0.2–0.3 Hz), and DF3 (0.3–0.4 Hz) bands correlate well with the ocean wave activities in the continental slope on the deep ocean side, and in the continental slope on both the deep ocean and shelf sides, and in the continental slope on the shelf side, respectively. These analyses lead to a hypothesis on the frequency dependent interactions of ocean waves with the continental margin and the origination of DF microseisms. The steep continental slope is a key submarine topographic feature which behaves as an obstacle causing reflections of the incoming low frequency (≤ 0.15 Hz) ocean waves and formation of standing waves to generate low frequency (≤ 0.3 Hz) DF microseisms. While the high frequency (≥ 0.15 Hz) ocean waves are reflected at the shallow portion of the continental shelf to excite high frequency (≥ 0.3 Hz) DF microseisms. This hypothesis is also supported by the observations that (1) the great circles corresponding to the primary vibration directions of DF microseisms are mostly normal to the strike of the continental slope; and (2) the ocean wave energy in the continental slope or the nearby deep ocean are higher than in the distant deep ocean and the continental shelf. Additional systematic observations at different parts of the globe will help to determine validity and limits of the proposed hypothesis under all possible climatic and bathymetric conditions.

Understanding the generation mechanisms and locating the source regions of the DF microseisms would improve the reliability of estimating the amplification factor based on ambient noise because the amplification process could be understood by bridging the variations of the input energy levels at the sources and the energy at the site. In addition, DF microseisms recordings at the coastal areas suggests that the sources are not homogeneously distributed. However, surface wave tomography could be carried out only if the noise sources are homogenously distributed. Therefore, locating the source regions could improve the current method of tomography or initiate a new method using non-homogenous ambient noise.

With the frequency dependent interactions between the ocean waves and the continental margin determined, one could further analyze the possible mass wasting on the continental margin caused by the ocean wave energy input and transmission while ocean waves interact with the continental margin.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2077-1312/8/2/134/s1, Figure S1: (a) Map of the USarray transportable array stations and their groups. Vertical power spectral density (PSD) plots in time and frequency domain of (b) coastal stations, (d) Appalachian mountain stations, and (f) south section stations. (c,e,g) Ra outlines and rose diagrams of polarized back azimuth in three DF bands of the stations in the three station groups, Figure S2: Daily WWIII hindcasts of spectral ocean wave height in Northern Atlantic Ocean (color gradient maps), and PSD levels (small circles with scaled sizes) and primary vibration directions (great circles) at all stations in the corresponding DF bands: DF1 in the top two rows, DF2 in the middle two rows, and DF3 in the bottom two rows. The frequency band of ocean wave (half of corresponding DF band) and day are labeled on top of each plot, Figure S3: Time history of double dominant ocean wave frequencies (DWF) and significant ocean wave heights (WH) at the ocean buoys grouped according to their locations, deep ocean (DO), the continental slope on the deep ocean side (SlDO), the continental slope on the shelf side (SlSh), and the continental shelf (Sh) (see Figure 1 for their locations and original names), Figure S4: An example to verify the validity of the great circle projecting to the sources of LPDF microseisms. The great circles at the station T2 on bedrock in Tishomingo, Mississippi project to the sources of DF microseisms induced by hurricane "Sandy" on 27 October 2012 successfully.

**Author Contributions:** Conceptualization, Z.G.; methodology, Z.G.; formal analysis, Z.G.; investigation, Z.G.; writing—original draft preparation, Z.G.; writing—review and editing, A.A., M.X. and Y.H.; funding acquisition, Y.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 51778467.

**Acknowledgments:** The Transportable Array (network TA) data are available on IRIS data management center at http://ds.iris.edu/ds/nodes/dmc/. The ocean buoy data are from the National Data Buoy Center database at http://www.ndbc.gov/ (last accessed Feb. 20, 2019). The WAVEWATCH III®hindcasts of ocean wave energy between 2014/325 and 2014/334 are from https://wwz.ifremer.fr/iowaga/Products. The historical hurricane data in East Pacific Ocean and Atlantic Ocean from National Hurricane Center (NHC) at http://www.nhc.noaa.gov/data/#tcr (last accessed Feb. 20, 2019). The gridded topographic and bathymetric data are downloaded from General Bathymetric Chart of the Oceans (GEBCO) at http://www.gebco.net/data\_and\_products/gridded\_bathymetry\_data/ (last accessed Feb. 20, 2019). We wish to thank Colton Lynner for sharing the shear velocity model in the eastern North American margin.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
