A statistical analysis of the generation of microseisms

Abstract

Theories of the origin of microseisms have in the past generally been expressed in terms of the Green functions of the elastic systems considered. An alternative approach based on spectral transfer functions and the local energy‐balance equation of the seismic field is proposed. The method enables a rigorous analysis of the statistical aspects of the problem, which could be treated only approximately and under restrictive conditions in terms of the far‐field representations used previously. Three suggested origins of microseisms are considered: (1) the action of ocean waves on coasts, originally proposed by Wiechert; (2) atmospheric pressure fluctuations, as suggested by Gherzi, Scholte, and others; and (3) nonlinear interactions between ocean waves as proposed by Longuet‐Higgins. In all cases appreciable microseisms are generated only by Fourier components of the random exciting fields that have the same phase velocities as free modes of the elastic system. The effect of pressure fluctuations associated with turbulence in the atmosphere is found to be negligible. The theory for Wiechert's and Longuet‐Higgins' mechanisms is in good agreement with recent measurements by Haubrich et al.