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Complicated radially symmetric models of the seismic velocity structure at the base of the mantle (Bullen's D" region) and the uppermost outer core have been inferred from analyses of the waveforms and relative amplitudes of S, SKS and ScS phases. Using radially symmetric structure, it has been difficult to construct physically realizable models of the rheology of D" that simultaneously satisfy P and S amplitudes and slownesses in the core shadow. These data are reviewed in the light of an increasing body of evidence that the structure of D" is characterized by heterogeneities having a broad spectrum of scale lengths. Depending on the region and range interval of D" sampled, S waveforms can be found that support either a radially simple or complex model of D". The complex models have one or more first-order discontinuities in velocity. The particle motion measured by three-component recordings of some S + ScS waveforms is consistent with a discontinuous increase in S velocity 250--300 km above the core-mantle boundary. The observed particle motion in these examples cannot readily or alternatively be explained by either general anisotropy or by strong lateral velocity gradients in D". Sufficient variability in S waveforms and travel times exists, however, that any radially symmetric model having a strong degree of complexity should be accepted with caution until all of the competing effects of lateral heterogeneity and possible anisotropy in D" are fully investigated. The distribution and scale lengths of heterogeneities in D" may account for regional differences in the properties of D" inferred from waveform data, including features that mimic intrinsic attenuation and anisotropy.
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