Modelling secondary microseismic noise by normal mode summation

Secondary microseisms recorded by seismic stations are generated in the ocean by the interaction of ocean gravity waves. We present here the theory for modelling secondary microseismic noise by normal mode summation. We show that the noise sources can be modelled by vertical forces and how to derive them from a realistic ocean wave model. We then show how to compute bathymetry excitation effect in a realistic earth model by using normal modes and a comparison with Longuet-Higgins approach. The strongest excitation areas in the oceans depends on the bathymetry and period and are different for each seismic mode. Seismic noise is then modelled by normal mode summation considering varying bathymetry. We derive an attenuation model that enables to fit well the vertical component spectra whatever the station location. We show that the fundamental mode of Rayleigh waves is the dominant signal in seismic noise. There is a discrepancy between real and synthetic spectra on the horizontal components that enables to estimate the amount of Love waves for which a different source mechanism is needed. Finally, we investigate noise generated in all the oceans around Africa and show that most of noise recorded in Algeria (TAM station) is generated in the Northern Atlantic and that there is a seasonal variability of the contribution of each ocean and sea.