A statistical analysis of the generation of microseisms

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.

[1]  J. Oliver.  A worldwide storm of microseisms with periods of about 27 seconds , 1962 .

[2]  Simplified method of determining refraction coefficients for sea waves , 1960 .

[3]  M. Longuet-Higgins.  On the transformation of a continuous spectrum by refraction , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  Carl Eckart,et al.  Hydrodynamics of oceans and atmospheres , 1960 .

[5]  W. M. Ewing,et al.  Elastic Waves in Layered Media , 2015 .

[6]  R. Phinney.  Leaking modes in the crustal waveguide: 1. The oceanic PL wave , 1961 .

[7]  Charles Henry Brian Priestley,et al.  Turbulent Transfer in the Lower Atmosphere , 1959 .

[8]  F. Gilbert,et al.  Experimental investigation of PL modes in a single layer , 1962 .

[9]  M. Ewing,et al.  Microseisms in the 11- to 18-second period range , 1957 .

[10]  O. Phillips.  On the generation of waves by turbulent wind , 1957, Journal of Fluid Mechanics.

[11]  K. Hasselmann.  On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility , 1963, Journal of Fluid Mechanics.

[12]  W. Munk,et al.  Comparative spectra of microseisms and swell , 1963 .

[13]  M. Longuet-Higgins.  A theory of the origin of microseisms , 1950, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[14]  J. H. Rosenbaum,et al.  The long‐time response of a layered elastic medium to explosive sound , 1960 .

[15]  Hans A. Panofsky,et al.  One-Dimensional Spectra of Atmospheric Turbulence in the Lowest 100 Metres , 1959 .

[16]  N. A. Haskell.  The Dispersion of Surface Waves on Multilayered Media , 1953 .

[17]  K. Hasselmann.  On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory , 1962, Journal of Fluid Mechanics.

[18]  J. E. Moyal.  The spectra of turbulence in a compressible fluid; eddy turbulence and random noise , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[19]  M. Lighthill.  On sound generated aerodynamically II. Turbulence as a source of sound , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  E. Deacon.  Aerodynamic roughness of the sea , 1962 .

[21]  J. Oliver,et al.  Leaking modes and the PL phase , 1959 .

[22]  M. Lighthill.  On sound generated aerodynamically I. General theory , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  M. Miche.  Mouvements ondulatoires de la mer en profondeur constante ou décroissante , 1944 .

[24]  I. Proudman,et al.  The generation of noise by isotropic turbulence , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[25]  G. Batchelor,et al.  The theory of homogeneous turbulence , 1954 .