*3.1. Power Spectral Density (PSD)*

Figure 2a shows the vertical *PSD*(*t*,*f*) plots at the stations selected to cover a wide latitude range (40◦N–34◦N) (see Figure 1 for locations of the stations). The remaining stations were divided into three groups according to their locations (for their groups, see Figure S1a in the Supplementary Materials to this article) and their *PSD*(*t*, *f*) plots are shown in Figure S1b,d,f. In the recording time period of this study, DF peaks are mainly in the frequency band of 0.15–0.3 Hz at the selected example stations, however, may cover a much wider frequency band at the stations close to the coastline (see Figure S1b in the Supplementary Materials to this article). At all stations, three DF microseism events are identified and labeled with I, II, and III which will be described in Section 3.3. *J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 6 of 21

**Figure 2.** (**a**) Power spectral density (PSD) plots in time-frequency domain of the vertical components at the selected stations. The dashed lines at 0.2 and 0.3 Hz mark the boundaries of the three frequencies ranges. Three relatively strong double-frequency (DF) microseism events are identified and labeled as I, II, and III. (**b**) Polar plots of average () values (blue) combined with rose diagrams of back azimuths (calculated by the polarization analysis) (purple) at the three DF bands at the selected stations in the whole recording period. On each plot, the text labels refer to the recording station (e.g., N61A), probability of back azimuth (in purple, e.g., 10%) and the scale of the solid outer circle in multiples of the () value (in blue, e.g., *Ra* = 2). The same plots for the remaining stations are shown in Figure S1 in the Supplementary Materials. **Figure 2.** (**a**) Power spectral density (PSD) plots in time-frequency domain of the vertical components at the selected stations. The dashed lines at 0.2 and 0.3 Hz mark the boundaries of the three frequencies ranges. Three relatively strong double-frequency (DF) microseism events are identified and labeled as I, II, and III. (**b**) Polar plots of average *Ra*(ϕ) values (blue) combined with rose diagrams of back azimuths (calculated by the polarization analysis) (purple) at the three DF bands at the selected stations in the whole recording period. On each plot, the text labels refer to the recording station (e.g., N61A), probability of back azimuth (in purple, e.g., 10%) and the scale of the solid outer circle in multiples of the *Ra*(ϕ) value (in blue, e.g., *Ra* = 2). The same plots for the remaining stations are shown in Figure S1 in the Supplementary Materials.

#### *3.2. Primary Vibration Directions at DF Peaks 3.2. Primary Vibration Directions at DF Peaks*

Figure 2b presents the polar plots of average radial-to-transverse spectral ratios *Ra*(*φ*) (blue outline) and rose diagrams of back azimuths calculated by the polarization analysis (purple) in DF1, DF2, and DF3 bands for the selected stations over the entire recording period of 10 d. The same plots for the remaining stations are given in Figures S1c, S1e, and S1g in the Supplementary Materials. The longer axis of each () outline is identified indicating the average primary vibration direction in Figure 2b presents the polar plots of average radial-to-transverse spectral ratios *Ra*(ϕ) (blue outline) and rose diagrams of back azimuths calculated by the polarization analysis (purple) in DF1, DF2, and DF3 bands for the selected stations over the entire recording period of 10 d. The same plots for the remaining stations are given in Figure S1c,e,g in the Supplementary Materials. The longer axis

to be in 110°–150°, which is perfectly consistent with the results in the same area in [55].

of each *Ra*(ϕ) outline is identified indicating the average primary vibration direction in 10 days (ϕ*m*10), which closely coincide with the major polarized direction.

The ϕ*m*1s was calculated as well for all stations, and rose diagrams of them in 10 days were generated for the three DF bands in Figure 3. The main back-azimuth in the three DF bands are shown to be in 110◦–150◦ , which is perfectly consistent with the results in the same area in [55]. *J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 7 of 21

**Figure 3.** The normalized spatial density (color gradient maps) of the great circles corresponding to the daily primary vibration directions (ଵ) and the vertical PSDs averaged for the entire recording period (scaled circles) in the three DF bands. The yellow lines contour the density of 0.5. The rose diagram shows the probability distribution of all ଵs. **Figure 3.** The normalized spatial density (color gradient maps) of the great circles corresponding to the daily primary vibration directions (ϕ*m*1) and the vertical PSDs averaged for the entire recording period (scaled circles) in the three DF bands. The yellow lines contour the density of 0.5. The rose diagram shows the probability distribution of all ϕ*m*1s.

The spatial density of ଵs was calculated, normalized, and plotted as a color gradient map for each DF band in Figure 3, as well as the contours at a density of 0.5 and the ocean bathymetries. Comparing the three maps, it can be observed that the areas of high spatial density, e.g., the areas sketched by the density contours of 0.5, shrink towards the continental shelf with increase of frequency, and the spatial density in the area between Blake Ridge and Cape Hatteras is high in all three DF bands. The spatial density of ϕ*m*1s was calculated, normalized, and plotted as a color gradient map for each DF band in Figure 3, as well as the contours at a density of 0.5 and the ocean bathymetries. Comparing the three maps, it can be observed that the areas of high spatial density, e.g., the areas sketched by the density contours of 0.5, shrink towards the continental shelf with increase of frequency, and the spatial density in the area between Blake Ridge and Cape Hatteras is high in all three DF bands.

### *3.3. Excitation of the Three Relatively Strong DF Microseism Events 3.3. Excitation of the Three Relatively Strong DF Microseism Events*

First, the spectral WWIII hindcasts of ocean wave energy (*E*(*F*/2) in log10(m2/Hz)) in North Atlantic Ocean (see Figure S2 in the Supplementary Materials to this article) were used to explore the temporal and spatial relationships in each frequency band of the energy levels between PSDs and wave energy. This result demonstrates that (1) the primary vibration directions do not point to the areas of high wave energy in open ocean, and (2) variations of ocean wave activities in open ocean of the North Atlantic Ocean have limited influence on the DF microseisms observed in the east coast of the United States. First, the spectral WWIII hindcasts of ocean wave energy (*E*(*F*/2) in log10(m<sup>2</sup> /Hz)) in North Atlantic Ocean (see Figure S2 in the Supplementary Materials to this article) were used to explore the temporal and spatial relationships in each frequency band of the energy levels between PSDs and wave energy. This result demonstrates that (1) the primary vibration directions do not point to the areas of high wave energy in open ocean, and (2) variations of ocean wave activities in open ocean of the North Atlantic Ocean have limited influence on the DF microseisms observed in the east coast of the United States.

Based on the spatial density of great circles of ଵs presented in Figure 3, it can be inferred that the excitations of DF microseisms appear to be associated with the ocean waves in different areas of the continental margin of the western North Atlantic Ocean. Therefore, the excitation mechanisms of the three DF microseism events identified in Figure 2 are explored below with reference to the area of the continental margin as outlined in Figure 4. Based on the spatial density of great circles of ϕ*m*1s presented in Figure 3, it can be inferred that the excitations of DF microseisms appear to be associated with the ocean waves in different areas of the continental margin of the western North Atlantic Ocean. Therefore, the excitation mechanisms of the three DF microseism events identified in Figure 2 are explored below with reference to the area of the continental margin as outlined in Figure 4.

3.3.1. Event I

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

**Figure 4.** (**a**,**c**,**e**) Daily WAVEWATCH III hindcasts of ocean wave spectra (*E*(*F*/2) in log10 (m2/Hz)) in Northern Atlantic Ocean (color gradient maps), PSD levels (small circles with scaled sizes), and primary vibration directions (segments of great circles) at all stations corresponding to the three events (I, II, and III) identified in Figure 2. The purple circles/ellipses delimit the intersections of the great circles; (**b**,**d**,**f**) Time history of average PSDs in three frequency bands. In each plot, the curves are stacked by the latitudes of the stations and the relief of each curve shows the change of PSD level. The starting time of the three events are picked and connected to form the red lines, the arrows of which show the impact sequence. **Figure 4.** (**a**,**c**,**e**) Daily WAVEWATCH III hindcasts of ocean wave spectra (*E*(*F*/2) in log10 (m<sup>2</sup> /Hz)) in Northern Atlantic Ocean (color gradient maps), PSD levels (small circles with scaled sizes), and primary vibration directions (segments of great circles) at all stations corresponding to the three events (I, II, and III) identified in Figure 2. The purple circles/ellipses delimit the intersections of the great circles; (**b**,**d**,**f**) Time history of average PSDs in three frequency bands. In each plot, the curves are stacked by the latitudes of the stations and the relief of each curve shows the change of PSD level. The starting time of the three events are picked and connected to form the red lines, the arrows of which show the impact sequence.

Figure 4a,c,e shows the WWIII hindcasts of *E*(*F*/2) in the western Northern Atlantic Ocean (color gradient maps) within the half frequency band of events I, II, and III identified in Figure 2. In the corresponding days and frequency bands of the events, the PSD levels and the primary vibration directions are demonstrated by the small circles with scaled sizes and segments of great circles passing though the corresponding stations. The bathymetries of the western Northern Atlantic Ocean are plotted as well in order to examine the importance of the continental slope in generation of DF microseisms. In Figure 4b,d,f, the arrival times of each event are picked on the PSD-time plots of all stations, and the connection of them form the red lines indicating the sequence of energy impact on stations. In order to facilitate the description of the spatial variations of PSD levels and primary vibration directions, the area where stations are placed are divided into two sections, north and south of Cape Hatteras. Figure 4a,c,e shows the WWIII hindcasts of *E*(*F*/2) in the western Northern Atlantic Ocean (color gradient maps) within the half frequency band of events I, II, and III identified in Figure 2. In the corresponding days and frequency bands of the events, the PSD levels and the primary vibration directions are demonstrated by the small circles with scaled sizes and segments of great circles passing though the corresponding stations. The bathymetries of the western Northern Atlantic Ocean are plotted as well in order to examine the importance of the continental slope in generation of DF microseisms. In Figure 4b,d,f, the arrival times of each event are picked on the PSD-time plots of all stations, and the connection of them form the red lines indicating the sequence of energy impact on stations. In order to facilitate the description of the spatial variations of PSD levels and primary vibration directions, the area where stations are placed are divided into two sections, north and south of Cape Hatteras.
