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Bulletin of the Seismological Society of America; February 1968; v. 58; no. 1; p. 103-131
© 1968 Seismological Society of America
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Approximate solutions to the inverse normal mode problem

FREEMAN GILBERT and GEORGE E. BACKUS

INSTITUTE OF GEOPHYSICS AND PLANETARY PHYSICS UNIVERSITY OF CALIFORNIA,, SAN DIEGO

Abstract

Observed normal mode periods in the range 1.388 min to 53.90 min are compared to two approximate solutions to the inverse normal mode problem. Each solution fits the observed periods with an r.m.s. relative error less than 3.1 x 10–3 and a maximum relative error less than 1.29 x 10–2. Each solution fits the observed mantle surface wave periods with a maximum relative error less than 3.9 x 10–3, a phase velocity error of 0.016 km/sec. The two solutions have S velocity distributions in the upper mantle that have a mean relative difference of 1.5 x 10–2 and a maximum relative difference of 2.8 x 10–2. The mantle surface wave periods of the two solutions have a maximum relative difference of 8.5 x 10–4, a phase velocity difference of 0.004 km/sec. The structural details of the two solutions are significantly different in the upper mantle. Two additional solutions are presented for mantle surface wave modes in the period range 1.388 min to 6.044 min. The spectrum of each solution fits the data with a maximum relative error less than 2.2 x 10–3, a phase velocity error of 0.009 km/sec. The spectra of the two solutions have a maximum relative difference of 4.0 x 10–4, a phase velocity difference of 0.002 km/sec. Both solutions have a zone of low-shear velocity with a minimum at a depth of 86 km. Other features of the two solutions are dissimilar.




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