We conduct a probabilistic analysis of the scattering of normal mode Q−1 measurements caused by the multiplet splitting from the earth's lateral heterogeneity. We apply our probabilistic results to a data set of unstacked Q−1 measurements for fundamental spheroidal modes from 0S13 through 0S28. Multiplet broadening of only 14 × 10−4 of the central frequency is sufficient to account for the scatter of the observed data. The observed scatter of Q−1 data is caused by a combination of three effects: lateral heterogeneity of density and velocities, actual lateral heterogeneity of Q−1 in the earth, and measurement error. The last two effects can only reduce the amount of lateral heterogeneity of density and velocities which is required to produce the observed scatter. Thus, by attributing the entire multiplet broadening to lateral heterogeneity of elastic properties, we can obtain an upper bound on its effect. It seems reasonable to assume that the maximum fraction of lateral heterogeneity in the mantle at the depths sampled by these modes (roughly from the surface to 1000 km deep) is on the same order (14 × 10−4) as the maximum multiplet broadening found by our analysis.

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