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Published August 1, 1969 | Published
Journal Article Open

Universal dispersion tables III. Free oscillation variational parameters


The effect of a small change in any parameter of a realistic Earth model on the periods of free oscillation is computed for both spheroidal and torsional modes. The normalized partial derivatives, or variational parameters, are given as a function of order number and depth in the Earth. For a given mode it can immediately be seen which parameters and which regions of the Earth are controlling the period of free oscillation. Except for _oS_o and its overtones the low-order free oscillations are relatively insensitive to properties of the core. The shear velocity of the mantle is the dominant parameter controlling the periods of free oscillation and density can be determined from free oscillation data only if the shear velocity is known very accurately. Once the velocity structure is well known free oscillation data can be used to modify the average density of the upper mantle. The mass and moment of inertia are then the main constraints on how the mass must be redistributed in the lower mantle and core.

Additional Information

© 1969 Seismological Society of America. Manuscript received February 13, 1969. This research was supported by the Advanced Research Projects Agency and was monitored by the Air Force Office of Scientific Research under contracts AF 49(638)-1337 (CIT) and AF 49(638)-1687 (SU). Support was also provided by NASA grant NGL 05-020-232 to Stanford University. The authors wish to acknowledge the assistance of Martin Smith, Tom Jordan, Laszlo Leaches and Shirley Fisher in the preparation of the manuscript.

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