Validity of the great circular average approximation for inversion of normal mode measurements

Abstract

Synthetic seismograms based upon first-order perturbation theory are analysed to test the validity of assumptions which form the basis of current velocity inversion procedures. It is found that the lowest order geometrical optics approximation, namely that measured normal mode eigenfrequencies reflect the average structure underlying the source-receiver great circle path, becomes less valid near nodes in the source radiation pattern and near the surface wave foci at the source and its antipode. These failures are a consequence of singlet interference within an isolated normal mode multiplet. The technique of determing frequency by fitting a single resonance peak to a multiplet yields results which agree well with the first-order theory for slow and fast paths where excitation is dominated by one pair of singlets but on intermediate paths where singlet interference is more of a problem, agreement is not as good. Inversion of small data sets is particularly sensitive to frequency fluctuations near radiation nodes, while larger sets are influenced more by antipodal deviations from geometrical optics. The latter leads to inversions which fail to recover the short wavelength structure of the starting model. Basing inversions directly upon first-order theory shows promise of improving recovery of short wavelengths.

Characterizing Long-Period Seismic Effects of Long-Wavelength Elastic and Anelastic Models

“…Observations of the elastic phase shift are familiar from such studies as Davis & Henson (1986), Romanowicz & Roult (1986) and Romanowicz (1987). Our observations of these effects in coupled normal mode synthetics closely resemble the data described and discussed by those authors.…”

3-D upper mantle shear velocity and attenuation from fundamental mode free oscillation data

“…Systematic fluctuations as a function of angular order of measured eigenfrequencies are attributed to departures from the lowest order asymptotic expression of the geometrical optics approximation (Davis & Henson 1986;Romanowicz & Roult 1986). To order 1/1 the observed frequencies mobs have the form o,,=Q,+-tan " ( 1 k d -c + X ) +~( ; ) , 4 where k = 1 + f ; Q, is the great circle average corresponding to the lowest order approximation (Jordan 1978); D depends on great circle averages of transverse derivatives of local phase velocity and x on the source mechanism.…”

“…We increased the spheroidal mode data set used in Paper I, also including the analysis of toroidal fundamental mode data. Our analysis differs from previous free oscillation studies (Masters et al 1982;Davis & Henson 1986) in several aspects: a broader range of frequencies, giving better depth resolution, and careful account of higher order effects in the measurement of eigenfrequencies after extraction of the fundamental mode by variable filtering. It is also the first 3-D analysis of toroidal fundamental mode eigenfrequency shift data.…”

First-order asymptotics for the eigenfrequencies of the Earth and application to the retrieval of large-scale lateral variations of structure

“…Davis & Henson 1986) show that the global large-scale models available at present are still somewhat inadequate to explain data on particular great circle paths. More importantly to us here, there is clearly some additional information contained in the amplitudes of the fluctuations, that could be exploited to constrain global earth models better.…”