**1. Introduction**

Ambient noise (or seismic noise) has been widely used to estimate the seismic site effect parameters (e.g., predominant frequency *f* <sup>0</sup>, sediment thickness, amplification factor, etc.) of a site [1–5] and to characterize both deep (down to the mantle of the Earth) and shallow (within the depth of geological engineering activities) subsurface structures [6–15] for its advantages as a fast, effective, and reliable tool. However, the accuracies and reliabilities of the applications listed above would be strongly affected by the spatial and temporal variations of the ambient noise sources. One example is given in [16] who estimated the amplification factors in Northern Mississippi of United States applying the horizontal-to-vertical spectral ratio (HVSR, or Nakamura) method based on long term ambient noise recordings. As the *f* <sup>0</sup>s in their study region lie in the frequency band of ocean waves induced double-frequency (DF) microseisms (0.1–0.5 Hz), the estimated amplification factors (HVSR values at *f* <sup>0</sup>) fluctuate with time and are strongly correlated with the energy of the DF microseisms as well as the ocean wave height. Many other studies suggest that if the noise sources are not homogeneously distributed, the cross-correlation function cannot be reconstructed causing big errors in subsurface tomography or even failure of subsurface tomography [17–22]. In addition, the ambient noise with frequency greater than 0.1 Hz would be used in shallow subsurface tomography. From this point of view, exploring the source locations, the spatial and temporal characteristics and the generation mechanisms of the ambient noise with frequency greater than 0.1 Hz, especially the DF microseisms, would significantly improve the application of the ambient noise in site effect evaluation and shallow subsurface tomography.

In the spectrum of ambient noise recorded globally, the DF microseisms (or secondary microseisms) manifest themselves as one or more energy peaks in the frequency band of 0.1–0.5 Hz which is roughly twice of ocean waves' frequencies. It is widely accepted that DF microseisms are generated by the nonlinear interaction between ocean waves propagating in opposite directions with similar frequencies (e.g., [23–31]).

Recent studies suggest that two different circumstances may be responsible for generating opposing ocean waves that trigger DF microseisms. The first group considers wave–wave interactions in the open-ocean during strong storms [27,32–34]. However, DF microseisms can be observed worldwide even when there are no strong storms locally or globally. This is explained by the second group of studies who emphasize the role of interactions between the incident and reflected ocean waves at the continental margin [22,35–39]. For example, the authors of [40] observed that Rayleigh waves in a microseism recording at an ocean bottom seismometer in the Pacific Ocean were approaching from California coast during a super-typhoon rather than the location of the typhoon and concluded that the microseisms were generated by interactions of typhoon-induced waves toward and their reflections from the coastal line. In a different set of studies based on correlation analyses between the ocean storms developed close to shorelines and the ambient noise recorded on coastal seafloor or costal land, it was recognized that the long- and short-period DF microseisms (LPDF, 0.1–0.2 Hz and SPDF, 0.2–0.5 Hz, respectively) were excited by swells from distant and local waves, respectively [25,30,31,41,42]. However, regarding the locations where the interactions (reflection) occur, there exist a debate in terms of the water depth (deep or coastal). In [43] the authors summarized the debate and compared theoretical and observed DF characteristics for each case considering the ocean wave frequency composition and velocities. It appears that the relationship between DF microseisms and ocean waves is not yet directly investigated as a function of water depth across the continental margin.

In this study, the continental slope, as a boundary between shallow (continental shelf) and deep (open ocean) water, is explored for its interactions with the ocean waves as well as its role and significance in the generation of DF microseisms. To reach this goal, a total of 10-days (2014/325–334) of ambient noise recordings the WAVEWATCH III® (WWIII) hindcasts of ocean wave energy in Atlantic Ocean, and ocean wave climate parameters are utilized and analyzed.
