Excitation of normal modes by non-linear interaction of ocean waves

S U M M A R Y Recent development in seismology has shown that seismic noise is a useful source of Earth structure study. Non-linear interaction of ocean waves is considered to be one of the important causes for seismic noise, although source locations and detailed mechanisms are not clear yet. In order to improve our understanding of this mechanism quantitatively, we derive a normal-mode excitation formula due to this effect. Longuet-Higgins’ pressure formula naturally comes out from the vertical forcing term in the excitation coefficient. A novel aspect of our formula is the horizontal forcing term that becomes comparable to the vertical forcing term for frequencies below about 5 mHz (millihertz), especially in shallow oceans. This term is not likely to be important for microseisms because the main frequency range of microseisms is about 0.05– 0.4 Hz but it may make significant contributions to the excitation of the continuous background oscillations (the hum) whose frequency range is 2–7 mHz.