Modelling the ocean site effect on seismic noise body waves

Secondary microseismic noise is generated by non-linear interactions between ocean waves at the ocean surface. We present here the theory for computing the site effect of the ocean layer upon body waves generated by noise sources distributed along the ocean surface. By defining the wavefield as the superposition of plane waves, we show that the ocean site effect can be described as the constructive interference of multiply reflected P waves in the ocean that are then converted to either P or SV waves at the ocean-crust interface. We observe that the site effect varies strongly with period and ocean depth, although in a different way for body waves than for Rayleigh waves. We also show that the ocean site effect is stronger for P waves than for S waves. We validate our computation by comparing the theoretical noise body wave sources with the sources inferred from beamforming analysis of the three seismogram components recorded by the Southern California Seismic Network. We use rotated traces for the beamforming analysis, and we show that we clearly detect P waves generated by ocean gravity wave interactions along the track of typhoon Ioke (2006 September). We do not detect the corresponding SV waves, and we demonstrate that this is because their amplitude is too weak.