A unified theory of microseisms and hum

Interacting ocean surface waves force water column pressure fluctuations with spectral peaks at the same frequencies of primary microseisms (PM), double-frequency microseisms (DF), and seismic hum. Prior treatment of nonlinear ocean wave interactions has focused on the DF pressure fluctuations which, in the presence of opposing waves, do not decay with depth and hence are dominant in deep waters. For an arbitrary 2-D surface wave spectrum we integrate over all pairings of wave vectors, directions, and frequencies to obtain a full-spectrum perturbation expansion including the first-and second-order pressure waves. First-order pressure waves generate a peak at PM frequencies and second-order pressure waves generated by obliquely interacting surface waves generate pressure fluctuations at DF and hum frequencies. These pressure fluctuations decay with depth but interact with the seabed in shallow water. As their generation does not require precise wave states, they are likely ubiquitous in shallow water.