*3.4. Correlation between DF Microseisms and Ocean Wave Parameters 3.4. Correlation between DF Microseisms and Ocean Wave Parameters*

The time histories of average PSDs in DF1, DF2, and DF3 bands are shown in Figure 4b,d,f, respectively. The curves are stacked according to the latitudes of the stations and the reliefs show the time-dependent variations of PSD levels. The DWFs at the DO, SlDO, and SlSh buoys are closer to the frequency band of event I, and the waves whose DWFs match events II and III are observed in groups SlDO, SlSh, and Sh (for the time history of DWFs at the buoys, see Figure S3 in the Supplementary Materials to this article). The Pearson correlation coefficients (CC) between the time series of ocean wave height and PSD in the three DF bands are calculated for all pairs of ocean buoy and ambient noise station, and the CC values are then averaged in each buoy group for each DF band at each station, as plotted Figure 5. The right most bar in Figure 5 gives the CC values averaged for all stations. The CC values are normalized within the range [−1.0, 1.0], where positive (negative) values represent the same (opposite) trends of ocean wave height and PSD pairs and the absolute value of CC express the level of consistency in these trends. In the DF1 band, better correlations can be found between the DF microseisms at all stations and the ocean wave heights in the continental slope on deep ocean side (SlDO). In the DF2 band, the DF microseisms at most stations correlate well with the ocean wave heights in SlDO, and some with those in the continental slope on the shelf side (SlSh). In the DF3 band, higher CC values can be found in all SlDO, SlSh, and continental shelf (Sh) groups. Near-zero negative CC values for the deep ocean (DO) buoys implies that deep ocean waves do not exert a positive influence on the DF microseisms. The time histories of average PSDs in DF1, DF2, and DF3 bands are shown in Figure 4b,d,f, respectively. The curves are stacked according to the latitudes of the stations and the reliefs show the time-dependent variations of PSD levels. The DWFs at the DO, SlDO, and SlSh buoys are closer to the frequency band of event I, and the waves whose DWFs match events II and III are observed in groups SlDO, SlSh, and Sh (for the time history of DWFs at the buoys, see Figure S3 in the Supplementary Materials to this article). The Pearson correlation coefficients (CC) between the time series of ocean wave height and PSD in the three DF bands are calculated for all pairs of ocean buoy and ambient noise station, and the CC values are then averaged in each buoy group for each DF band at each station, as plotted Figure 5. The right most bar in Figure 5 gives the CC values averaged for all stations. The CC values are normalized within the range [−1.0, 1.0], where positive (negative) values represent the same (opposite) trends of ocean wave height and PSD pairs and the absolute value of CC express the level of consistency in these trends. In the DF1 band, better correlations can be found between the DF microseisms at all stations and the ocean wave heights in the continental slope on deep ocean side (SlDO). In the DF2 band, the DF microseisms at most stations correlate well with the ocean wave heights in SlDO, and some with those in the continental slope on the shelf side (SlSh). In the DF3 band, higher CC values can be found in all SlDO, SlSh, and continental shelf (Sh) groups. Near-zero negative CC values for the deep ocean (DO) buoys implies that deep ocean waves do not exert a positive influence on the DF microseisms.

**Figure 5.** Average Pearson correlation coefficients (CC) between the PSDs in the three DF bands and the ocean wave heights in four groups of ocean buoys. **Figure 5.** Average Pearson correlation coefficients (CC) between the PSDs in the three DF bands and the ocean wave heights in four groups of ocean buoys.

side (SlDO), the continental slope on both deep ocean and continental shelf sides (SlDO and SlSh), and SlSh, respectively. These domains of wave activities are separated by the continental slope, where waves approaching from the deep ocean zone are reflected back creating nonlinear wave–wave interactions. This naturally leads to a hypothesis that the continental slope plays a significant role in

*4.1. Hypothesis on the Significance of Continental Slope for the Origination of DF Microseisms* 

explained in detail in the following.

#### **4. Discussion** 331 and 329. A coincidence can be found between the changes of PSD levels and wave energy on the

#### *4.1. Hypothesis on the Significance of Continental Slope for the Origination of DF Microseisms* continental slope segment between the Georges Bank and Blake Ridge (outlined by the purple dash-dot line), which supports the hypothesis.

The correlation analysis (Figure 5) shows that the DF microseism trends in DF1, DF2, and DF3 bands are most compatible with the ocean wave activities in the continental slope on the deep ocean side (SlDO), the continental slope on both deep ocean and continental shelf sides (SlDO and SlSh), and SlSh, respectively. These domains of wave activities are separated by the continental slope, where waves approaching from the deep ocean zone are reflected back creating nonlinear wave–wave interactions. This naturally leads to a hypothesis that the continental slope plays a significant role in the origination of DF microseisms, and with increasing frequency band, the dominant origination area migrates from SlDO to SlSh in the east coast of the United States. Validity of this hypothesis is explained in detail in the following. As no hurricane development was reported in Northern Atlantic Ocean during the period of recordings analyzed in this study, most DF microseisms identified from these recordings should be generated mainly by the nonlinear interactions of incoming and reflected ocean waves of similar frequencies. These interactions take place at different intensities and directions as determined by ordinary ocean activities and ocean bottom topography. Theoretically strong reflections leading to strong DF energy can occur only if the incoming waves encounter an obstacle perpendicular to their propagation direction, as shown in Figure 7. The area and energy of constructive interaction is much larger when the incoming wave direction is perpendicular (Figure 7b) rather than nearly parallel

shows the differences of the wave energy and PSD levels corresponding to DF2 band between day

*J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 11 of 21

the origination of DF microseisms, and with increasing frequency band, the dominant origination area migrates from SlDO to SlSh in the east coast of the United States. Validity of this hypothesis is

During the time period of event I (Figure 4a), the continental slope is shown to be the boundary of impact from the ocean wave in frequency band of 0.05–0.1 Hz, the increase of wave energy in the deep ocean area south of Georges Bank does not cause an increase of PSD levels at the stations in the north section but the decrease of ocean wave energy on the continental slope do coincide well with the decrease of PSD levels in most stations from day 2014/326 to 327. Comparing events II and III

During the time period of event I (Figure 4a), the continental slope is shown to be the boundary of impact from the ocean wave in frequency band of 0.05–0.1 Hz, the increase of wave energy in the deep ocean area south of Georges Bank does not cause an increase of PSD levels at the stations in the north section but the decrease of ocean wave energy on the continental slope do coincide well with the decrease of PSD levels in most stations from day 2014/326 to 327. Comparing events II and III (Figure 4c,e), the PSD levels are much higher on day 331 than day 329, mainly because of the higher wave energy on the continental slope between Georges Bank and Blake Ridge on day 331. Figure 6 shows the differences of the wave energy and PSD levels corresponding to DF2 band between day 331 and 329. A coincidence can be found between the changes of PSD levels and wave energy on the continental slope segment between the Georges Bank and Blake Ridge (outlined by the purple dash-dot line), which supports the hypothesis. (Figure 7a) to the obstacle. Considering that, in a reflection system, at each point of incidence at any angle, the energy normal to the reflector is the largest (Figure 7b), a station receives the strongest signal when the station and incident point is aligned with the line normal to the reflector (Path A in Figure 7b). Such an alignment should therefore correspond to the great circles (lines connecting the wave origination areas to the stations) intersecting the continental slope nearly at orthogonal angles. In order to test this hypothesis, the intersection angles between the great circles and the strike of the continental slope are defined as shown in Figure 8a and the frequency histograms of s in the three DF bands are generated and shown in Figure 8b. The medians of s in the three DF bands are 72.4°, 74.1°, and 72.5°, respectively, and the largest frequencies of occurrences are within the 81°–90° range, which support the proposed hypothesis.

**Figure 6.** Difference of the ocean wave energy (*E*(*F*/2) in log10(m2/Hz)) and PSD levels between day 329 and 331 (Figure 4c,e, respectively). **Figure 6.** Difference of the ocean wave energy (*E*(*F*/2) in log10(m<sup>2</sup> /Hz)) and PSD levels between day 329 and 331 (Figure 4c,e, respectively).

As no hurricane development was reported in Northern Atlantic Ocean during the period of recordings analyzed in this study, most DF microseisms identified from these recordings should be generated mainly by the nonlinear interactions of incoming and reflected ocean waves of similar frequencies. These interactions take place at different intensities and directions as determined by ordinary ocean activities and ocean bottom topography. Theoretically strong reflections leading to

strong DF energy can occur only if the incoming waves encounter an obstacle perpendicular to their propagation direction, as shown in Figure 7. The area and energy of constructive interaction is much larger when the incoming wave direction is perpendicular (Figure 7b) rather than nearly parallel (Figure 7a) to the obstacle. Considering that, in a reflection system, at each point of incidence at any angle, the energy normal to the reflector is the largest (Figure 7b), a station receives the strongest signal when the station and incident point is aligned with the line normal to the reflector (Path A in Figure 7b). Such an alignment should therefore correspond to the great circles (lines connecting the wave origination areas to the stations) intersecting the continental slope nearly at orthogonal angles. In order to test this hypothesis, the intersection angles δ between the great circles and the strike of the continental slope are defined as shown in Figure 8a and the frequency histograms of δs in the three DF bands are generated and shown in Figure 8b. The medians of δs in the three DF bands are 72.4◦ , 74.1◦ , and 72.5◦ , respectively, and the largest frequencies of occurrences are within the 81◦–90◦ range, which support the proposed hypothesis. *J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 12 of 21

*J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 12 of 21

**Figure 7.** A sketch describing how constructive interactions of ocean waves and their reflections from a barrier (the continental slope or the shoreline) can result in different energies when the angle of incidence is (**a**) large and (**b**) 0°. Note a given station receives the strongest signals along the shortest path A. **Figure 7.** A sketch describing how constructive interactions of ocean waves and their reflections from a barrier (the continental slope or the shoreline) can result in different energies when the angle of incidence is (**a**) large and (**b**) 0◦ . Note a given station receives the strongest signals along the shortest path A. **Figure 7.** A sketch describing how constructive interactions of ocean waves and their reflections from a barrier (the continental slope or the shoreline) can result in different energies when the angle of incidence is (**a**) large and (**b**) 0°. Note a given station receives the strongest signals along the shortest path A.

**Figure 8.** (**a**) Defining the angle (<90°) between a great circle and the continental slope's strike. (**b**) Histogram of the angles s in the three DF bands. **Figure 8.** (**a**) Defining the angle δ (<90◦ ) between a great circle and the continental slope's strike. (**b**) Histogram of the angles δs in the three DF bands.

**Figure 8.** (**a**) Defining the angle (<90°) between a great circle and the continental slope's strike. (**b**) Histogram of the angles s in the three DF bands. As the waves are reflected from the continental slope, the wave energy should be higher in the continental slope and the nearby deep ocean zone than in the distant deep ocean zone and the As the waves are reflected from the continental slope, the wave energy should be higher in the continental slope and the nearby deep ocean zone than in the distant deep ocean zone and the

continental shelf. To examine this notion, the mean and standard deviation of ocean wave energy

were calculated in each of the four buoy groups, 2.19 and 0.44 m in DO, 2.48 and 0.98 m in SlDO, 2.10 and 0.99 m in SlSh, and 1.57 and 0.74 m in Sh. The highest wave energy appears at the SlDO buoys and then DO and SlSh buoys, which coincide well with areas of intersection of the great circle paths (purple dashed ellipses in Figure 4). Similar observations can also be found in [33]. Recalling once more that there was no strong storm in the northern Atlantic Ocean during the microseism

and then DO and SlSh buoys, which coincide well with areas of intersection of the great circle paths (purple dashed ellipses in Figure 4). Similar observations can also be found in [33]. Recalling once more that there was no strong storm in the northern Atlantic Ocean during the microseism

recordings, the identified DF microseisms cannot be explained by ocean storms.

recordings, the identified DF microseisms cannot be explained by ocean storms.

As the waves are reflected from the continental slope, the wave energy should be higher in the

The hypothesis is also supported by several ocean bottom observations in shallow and deep waters divided by the continental slope. For example, the authors of [56] concluded that the excitation at DF peaks require some part of the ocean storm to extend over the shallow water based on coherence studies. Comparing ocean waves recorded in shallow waters (100 m deep) in Tasman Sea and microseisms recorded near the shoreline (30 km away from the ocean buoy) of the North Island of New Zealand, the authors of [57] observed that DF peaks were in the > 0.2 Hz band when there was a local wind in the Tasman Sea but lower than 0.2 Hz when the sea was calm and a swell from Southern Ocean arrived across the continental slope. Another example is presented by [31]. Two pressure spectra were obtained from two seafloor stations in the continental shelf (water depth of 0.6 km) and in the continental shelf edge followed by a steep and deep continental slope (water depth of

The hypothesis is also supported by several ocean bottom observations in shallow and deep waters divided by the continental slope. For example, the authors of [56] concluded that the excitation at DF peaks require some part of the ocean storm to extend over the shallow water based on coherence studies. Comparing ocean waves recorded in shallow waters (100 m deep) in Tasman Sea and microseisms recorded near the shoreline (30 km away from the ocean buoy) of the North Island of New Zealand, the authors of [57] observed that DF peaks were in the > 0.2 Hz band when there was a local wind in the Tasman Sea but lower than 0.2 Hz when the sea was calm and a swell from Southern Ocean arrived across the continental slope. Another example is presented by [31]. Two pressure spectra were obtained from two seafloor stations in the continental shelf (water depth of 0.6 km) and in the continental shelf edge followed by a steep and deep continental slope (water depth of continental shelf. To examine this notion, the mean and standard deviation of ocean wave energy were calculated in each of the four buoy groups, 2.19 and 0.44 m in DO, 2.48 and 0.98 m in SlDO, 2.10 and 0.99 m in SlSh, and 1.57 and 0.74 m in Sh. The highest wave energy appears at the SlDO buoys and then DO and SlSh buoys, which coincide well with areas of intersection of the great circle paths (purple dashed ellipses in Figure 4). Similar observations can also be found in [33]. Recalling once more that there was no strong storm in the northern Atlantic Ocean during the microseism recordings, the identified DF microseisms cannot be explained by ocean storms.

The hypothesis is also supported by several ocean bottom observations in shallow and deep waters divided by the continental slope. For example, the authors of [56] concluded that the excitation at DF peaks require some part of the ocean storm to extend over the shallow water based on coherence studies. Comparing ocean waves recorded in shallow waters (100 m deep) in Tasman Sea and microseisms recorded near the shoreline (30 km away from the ocean buoy) of the North Island of New Zealand, the authors of [57] observed that DF peaks were in the > 0.2 Hz band when there was a local wind in the Tasman Sea but lower than 0.2 Hz when the sea was calm and a swell from Southern Ocean arrived across the continental slope. Another example is presented by [31]. Two pressure spectra were obtained from two seafloor stations in the continental shelf (water depth of 0.6 km) and in the continental shelf edge followed by a steep and deep continental slope (water depth of 1 km), respectively, off the coast of southern California (see topographic profiles in [58]). At the shallower site, a high spectral peak with pressure level of around 10<sup>3</sup> Pa<sup>2</sup> /Hz was observed at around 0.2 Hz when a storm directly passed overhead, whereas no spectral peak could be clearly identified when there was no passing storm. On the deeper site, two high and sharp pressure spectral peaks appeared at 0.14 and 0.3 Hz with pressure levels of 5 <sup>×</sup> <sup>10</sup><sup>3</sup> and 10<sup>4</sup> Pa<sup>2</sup> /Hz, respectively. Differences between the effects of shallow and deep ocean on DF peaks' frequencies and energy levels presented in these studies imply that DF microseism in the continental shelf is driven by local weather, whereas that in the deep ocean is excited by the standing waves [35] generated by the interaction between the distant ocean swell and the waves reflected due to the sudden change of water depth at the continental slope.
