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

Summary. 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 eigen‐frequencies 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.