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Bulletin of the Seismological Society of America; August 1969; v. 59; no. 4; p. 1667-1693
© 1969 Seismological Society of America
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Universal dispersion tables

III. Free oscillation variational parameters

DON L. ANDERSON and ROBERT L. KOVACH

SEISMOLOGICAL LABORATORY CALIFORNIA INSTITUTE OF TECHNOLOGY, PASADENA, CALIFORNIA 91109
DIVISION OF GEOLOGICAL SCIENCES
DEPARTMENT OF GEOPHYSICS STANFORD UNIVERSITY, STANFORD, CALIFORNIA

Abstract

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 oSo 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.




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