On the microseisms associated with coastal sea waves

Abstract

We present a model that concerns microseisms in the period range between 7 and 9 s. In this modelling we have incorporated the effects of incident and reflected sea waves along the shoreline. A relationship between the phenomena of wave reflection along the shoreline and microseisms is suggested by this study. In addition, the far‐field microseismic energy computed from this model is considerably larger than our two previous calculations (Darbyshire & Okeke 1969; Okeke 1972) and, interestingly, closer to that obtained from recent measurements (Trevorrow et al. 1989). A possible explanation is that the present model incorporates the activity of the wave train approaching the shoreline from a wide range of directions. Thus, it is a generalization of the normal incident theory originally proposed by Darbyshire & Okeke (1969) and employed in our two previous calculations (Darbyshire & Okeke 1969; Okeke 1972). This model also estimates the distance from the shoreline over which the approaching shallow water waves are expected to acquire measurable bottom pressure and confirms that this distance is proportional to the wave period (Fig. 3). 3 The ratio of the energy spectrum of microseisms and sea waves as a function of wave period. (a) Observed values Darbyshire & Okeke (1969); (b) theoretical calculations Darbyshire & Okeke (1969); (c) theoretical calculations Okeke (1972); (d) theoretical calculations (this paper); (e) variation of shelf width with wave period. Furthermore, by assuming that the elastic parameters in the far field are functions of the vertical coordinate only, the depth dependence of frequency bandwidth and the associated spectral energy peak are calculated. The results depict reasonably well the possible effects of structural layering below the Earth’s surface in the locality.

Seafloor topography, ocean infragravity waves, and background Love and Rayleigh waves

“…At frequencies above 20 mHz, we have suggested that topographic coupling in shallow seas plays a role. This shallow process might be somehow related to the microseisms activity at the primary frequencies between 50 and 100 mHz, which is known to be strongly correlated with the activities of oceanic swells [ Okeke and Asor , 2000; Stehly et al , 2006]. The suggested mechanisms in this frequency range include propagation of oceanic swells along the coastal slope that produces the vertical pressure force to emit Rayleigh waves in all the directions [ Darbyshire and Okeke , 1969] and the horizontal frictional force to emit Love waves in the direction parallel to the coastal line [ Friedrich et al , 1998].…”

Background Love and Rayleigh waves simultaneously generated at the Pacific Ocean floors

“…Their temporal variations coincide approximately with those of the mean amplitudes of Love and Rayleigh waves around 0.0125 Hz. Such coincidence suggests that low‐frequency background Love and Rayleigh waves may have a common origin with the microseisms which are known to be strongly correlated with the activities of oceanic infragravity waves [ Okeke and Asor , 2000; Darbyshire and Okeke , 1969].…”

Some dynamical characteristics of microseism time-series

“…the features listed in Section 2. Also, this model is minimalist in the sense that it contains the minimum number of parameters needed to explain observations, although not excluding other external contributions, such as coastal sea waves (Okeke & Asor 2000) or resonances generated by the geometry of coastal Fjords (Friedrich et al 1998). As a novelty this model reveals that the main peak corresponds to the fundamental harmonic of the potential; that is, it represents a medium property, and when the frequency f 2 is close to the resonant frequency f r , a competitive process is triggered which results in an enhancement of the resonant (secondary) peak.…”