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Published April 15, 1967 | Published
Journal Article Open

Study of the Energy of the Free Oscillations of the Earth


The energies of the radial, torsional, and spheroidal free oscillations for a Gutenberg model earth were studied. Each mode of oscillation has a characteristic radial distribution of elastic and kinetic energy that fixes the parts of the earth that contribute most heavily in determining a particular resonant frequency. An examination of the partitioning of energy among compressional, shear, and gravitational energy as a function of mode number and depth immediately explains the persistence of the purely radial mode compared with the other normal modes of the earth. Only the first few spheroidal modes are sensitive to the density of the inner core; they are particularly sensitive to the density of the outer part of the core. The low-order spheroidal modes also exhibit a rapid rise of potential energy near the base of the mantle; this rise will permit improved estimates of the velocity to be obtained in this region, which is difficult to examine with body waves. The tabulated results allow estimates to be made of the previously neglected energy contained in the free oscillations excited by large earthquakes. An estimate of the energy in the low-order spheroidal oscillations excited by the great Alaskan shock suggests a value of 10^(23) ergs over the period range from 450 to 830 sec, implying that the energy density increases toward high frequencies if the total energy in the earthquake was of the order of 10^(24)–10^(25) ergs.

Additional Information

© 1967 American Geophysical Union. Manuscript Received: 16 SEP 1966. Contribution 1379, Division of Geological Sciences, California Institute of Technology. This research was partially supported by the Advanced Research Projects Agency and was monitored by the Air Force Office of Scientific Research under contracts AF 49(638)-1687 (SU) and AF 49(638)-1337 (CIT).

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