*4.2. Types of Continental Margin*

In this study, two types of continental margins are identified as exemplified by the transects A-A0 and B-B0 (profile locations are marked in Figure 1) in Figure 9a,b, respectively. Both types have wide (≈100 km) and shallow (<0.2 km) shelves. Along the first type (A-A<sup>0</sup> ), a high (≈2.5 km) and steep slope sharply changes the profile followed by a long gentle slope (continental rise). In the second type (B-B0 ), the shelf transition into the slope via a wide and gently dipping plateau (Blake Plateau) followed by a shorter (≈1.5 km) and gentler slope (than the first type), then a wide undulating plateau (continental rise) ending with a relatively steep slope.

These differences between the continental margin profiles appear to modify the mechanism of DF microseism generation as suggested by the consistently high spatial densities in the area covering the Blake Ridge and northern Blake Plateau in all three DF bands (Figure 3). A more gradual transition from the shelf and a shorter continental slope are the most prominent features that can support generation of a relatively stable energy level in these areas. Concavity of the continental slope at the edge of the Blake Plateau potentially causes strong reflections resulting in higher DF energy. In contrast, the continental slope at Cape Hatteras has a convex outline that could cause a diffraction pattern, consequently a lower spatial density in this area as shown in the map of the DF1 band in Figure 3. As the DF3 microseisms are generated in the continental shelf, the rough shoreline at Cape Hatteras may be the reason for higher density observed in the DF3 band in Figure 3.

*J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 14 of 21

**Figure 9.** Topographic profiles of the continental margin along (**a**) A-A' and (**b**) B-B' (marked in Figure 1) based on General Bathymetric Chart of the Oceans (GEBCO, 2014). The shear velocity profile and contours in (**a**) are reproduced on [15]. The geophysical interface between sediments and bedrock is estimated (black dotted line) by horizontal-to-vertical spectral ratio (HVSR) method and was extended seaward by inference (black dashed line) to connect with the 2.2 km/s shear velocity contour. A transitional zone (TZ) with the largest shear velocity gradient is identified and outlined by the two pink dashed lines in (**a**). The shear velocity models inside the white box outlined in Figure 1 are generated for elevations (Elv.) of −5.2 km (**c**) and −15.2 km (**d**) based on [15]. **Figure 9.** Topographic profiles of the continental margin along (**a**) A-A0 and (**b**) B-B0 (marked in Figure 1) based on General Bathymetric Chart of the Oceans (GEBCO, 2014). The shear velocity profile and contours in (**a**) are reproduced on [15]. The geophysical interface between sediments and bedrock is estimated (black dotted line) by horizontal-to-vertical spectral ratio (HVSR) method and was extended seaward by inference (black dashed line) to connect with the 2.2 km/s shear velocity contour. A transitional zone (TZ) with the largest shear velocity gradient is identified and outlined by the two pink dashed lines in (**a**). The shear velocity models inside the white box outlined in Figure 1 are generated for elevations (Elv.) of −5.2 km (**c**) and −15.2 km (**d**) based on [15].

Recent studies also support the hypothesis about the role of the continental slope and show that submarine ridges act similarly to cause reflection of the waves. In [59], by comparing the seasonal variation of DF microseisms and ocean activities, the authors concluded that the DF microseism in the 0.1–0.2 Hz band on the King George Island (on Antarctic Peninsula) originates from a region of Drake Passage instead of the continental shelf around Antarctic Peninsula even though it is several times wider than that around Cape Hatteras. The ocean at Drake Passage is at least 3 km deep and is delimited by the continental slope of Antarctic Peninsula and an underwater ridge roughly normal to the slope. The authors of [33] showed that the excitation locations of both P- and S-wave microseisms observed by a seismometer array in Japan are distributed along the eastern continental slope of Greenland and Reykjanes Ridge extended from Iceland into the deep ocean. An ocean bottom straight blocked by relief features [34,59] promotes formation of ocean wave reflection at the continental slope. Recent studies also support the hypothesis about the role of the continental slope and show that submarine ridges act similarly to cause reflection of the waves. In [59], by comparing the seasonal variation of DF microseisms and ocean activities, the authors concluded that the DF microseism in the 0.1–0.2 Hz band on the King George Island (on Antarctic Peninsula) originates from a region of Drake Passage instead of the continental shelf around Antarctic Peninsula even though it is several times wider than that around Cape Hatteras. The ocean at Drake Passage is at least 3 km deep and is delimited by the continental slope of Antarctic Peninsula and an underwater ridge roughly normal to the slope. The authors of [33] showed that the excitation locations of both P- and S-wave microseisms observed by a seismometer array in Japan are distributed along the eastern continental slope of Greenland and Reykjanes Ridge extended from Iceland into the deep ocean. An ocean bottom straight blocked by relief features [34,59] promotes formation of ocean wave reflection at the continental slope.

The hypothesis may appear to fail the test based on the observations in [37], who compared the DF spectra (around 0.15 Hz) at three seismometer stations in the coastal region of Oregon and California with the ocean wave climate parameters' spectra (see their Figure 17). Based on an excellent correlation between DF peak and wave spectra, they concluded that the DF microseism is generated by the wave activities near the shoreline. Significantly different widths of the continental shelves, being much narrower on the western continental margin of North America, and the location of the ocean buoys being on the edge of such a narrow continental shelf (see their Figure 15) can explain the apparent failure. Together with the low frequency (< 0.2 Hz) of their DF peak, it can be argued that The hypothesis may appear to fail the test based on the observations in [37], who compared the DF spectra (around 0.15 Hz) at three seismometer stations in the coastal region of Oregon and California with the ocean wave climate parameters' spectra (see their Figure 17). Based on an excellent correlation between DF peak and wave spectra, they concluded that the DF microseism is generated by the wave activities near the shoreline. Significantly different widths of the continental shelves, being much narrower on the western continental margin of North America, and the location of the ocean buoys being on the edge of such a narrow continental shelf (see their Figure 15) can explain the apparent failure. Together with the low frequency (< 0.2 Hz) of their DF peak, it can be argued that the

DF microseism observed by [60] was also a result of the reflections from the nearby continental slope as put forward in the proposed hypothesis. the DF microseism observed by [60] was also a result of the reflections from the nearby continental slope as put forward in the proposed hypothesis.

*J. Mar. Sci. Eng.* **2020**, *8*, x FOR PEER REVIEW 15 of 21

#### *4.3. Rayleigh Wave Refraction 4.3. Rayleigh Wave Refraction*

As mentioned in "Data acquisition and processing" section, the Ra and polarization analysis methods to estimate the primary vibration direction are based on an assumption that DF microseisms propagate dominantly as fundamental mode Rayleigh waves. To verify this assumption, Figure 10 was generated to show the probability distributions of the phase differences between the two orthogonal horizontal components (ϕ*HH*) and between the vertical and horizontal components in the primary vibration direction (ϕ*VH*) in the three DF bands. The facts that ϕ*HH* is dominant in 0◦ and ϕ*VH* is mainly in 65◦–80◦ and −65◦–−80◦ reveal that the energy is propagating as Rayleigh waves dominantly [61], which coincides well with the observation in [55]. As mentioned in "Data acquisition and processing" section, the Ra and polarization analysis methods to estimate the primary vibration direction are based on an assumption that DF microseisms propagate dominantly as fundamental mode Rayleigh waves. To verify this assumption, Figure 10 was generated to show the probability distributions of the phase differences between the two orthogonal horizontal components () and between the vertical and horizontal components in the primary vibration direction () in the three DF bands. The facts that is dominant in 0° and is mainly in 65°–80° and −65°–−80° reveal that the energy is propagating as Rayleigh waves dominantly [61], which coincides well with the observation in [55].

**Figure 10.** Probability distribution of the phase difference between (**a**) the two horizontal components () and (**b**) the vertical and horizontal component in the primary vibration direction (). **Figure 10.** Probability distribution of the phase difference between (**a**) the two horizontal components (ϕ*HH*) and (**b**) the vertical and horizontal component in the primary vibration direction (ϕ*VH*).

#### 4.3.1. Refraction at the Water–Solid Earth Interface 4.3.1. Refraction at the Water–Solid Earth Interface

4.3.2. Refraction within the Solid Earth

As explained by [61], when the energy in the DF band is generated from wave–wave interaction in the ocean, it propagates as "pseudo-Rayleigh waves" (p*R*g) in water column and turns to free surface Rayleigh waves (FSRW) when it reaches solid earth. In the water column, due to phase speed difference, the p*R*g exists in different forms: dominantly elastic p*R*g in shallow water with phase speed roughly equal to that of FSRW, and acoustic p*R*g in deep water with phase speed of about 60% of FSRW. Definitions of shallow and deep waters vary with the wave frequencies. According to the analysis in this study, the energy in LPDF (DF1) band is generated around the continental slope where the water depth is generally smaller than 3000 m (Figure 1), especially on the Blake Plateau (≤ 1000 m) and the edge of the Blake Ridge (≈3000 m). According to Figure 14 in [61], with the increase of frequency from 0.1 to 0.2 Hz, the depth in the water column of elastic p*R*g dominance decrease from 3000 to 1500 m, under which the elastic p*R*g transfer to fundamental acoustic p*R*g. Thus, a phase-speed difference might exist at the water–solid earth interface deeper than 1500 m, i.e., areas except the Blake Plateau, however, the DF energy would still propagate vertically in the water column and transfer to solid earth. Even though there is significant energy loss at the interface, the spherical spreading of the DF energy in the solid earth will not change. Therefore, the phase speed difference on the water–solid earth interface is not likely to affect the determination of the source location by great circle. For high-frequency (0.2–0.5 Hz) DF band, the hypothesis put forward in this manuscript claims that the energy is generated in the continental slope and continental shelf where the water depth is smaller than 200 m. The same figure in [61] shows that the energy in this band should also propagate as elastic p*R*g and directly transition to FSRW on the continental shelf. As there is no significant phase speed difference between elastic p*R*g and FSRW, Rayleigh wave refraction at the surface of solid earth is not likely to be significant. As explained by [61], when the energy in the DF band is generated from wave–wave interaction in the ocean, it propagates as "pseudo-Rayleigh waves" (p*R*g) in water column and turns to free surface Rayleigh waves (FSRW) when it reaches solid earth. In the water column, due to phase speed difference, the p*R*g exists in different forms: dominantly elastic p*R*g in shallow water with phase speed roughly equal to that of FSRW, and acoustic p*R*g in deep water with phase speed of about 60% of FSRW. Definitions of shallow and deep waters vary with the wave frequencies. According to the analysis in this study, the energy in LPDF (DF1) band is generated around the continental slope where the water depth is generally smaller than 3000 m (Figure 1), especially on the Blake Plateau (≤ 1000 m) and the edge of the Blake Ridge (≈3000 m). According to Figure 14 in [61], with the increase of frequency from 0.1 to 0.2 Hz, the depth in the water column of elastic p*R*g dominance decrease from 3000 to 1500 m, under which the elastic p*R*g transfer to fundamental acoustic p*R*g. Thus, a phase-speed difference might exist at the water–solid earth interface deeper than 1500 m, i.e., areas except the Blake Plateau, however, the DF energy would still propagate vertically in the water column and transfer to solid earth. Even though there is significant energy loss at the interface, the spherical spreading of the DF energy in the solid earth will not change. Therefore, the phase speed difference on the water–solid earth interface is not likely to affect the determination of the source location by great circle. For high-frequency (0.2–0.5 Hz) DF band, the hypothesis put forward in this manuscript claims that the energy is generated in the continental slope and continental shelf where the water depth is smaller than 200 m. The same figure in [61] shows that the energy in this band should also propagate as elastic p*R*g and directly transition to FSRW on the continental shelf. As there is no significant phase speed difference between elastic p*R*g and FSRW, Rayleigh wave refraction at the surface of solid earth is not likely to be significant.

TZ.
