Broadband SH and P wave fields are pseudospectrally modeled in three forms of the heterogeneity spectrum of the mantle, each having a transition in the power spectrum of heterogeneity in the lowermost mantle. With D defined as a zone of increased heterogeneity, low-pass and high-pass filters of models of the heterogeneity spectrum demonstrate that the thickness of D inferred from an incident seismic wave field can depend on the dominant wavelength of that wave field. A model of D heterogeneity that agrees with the coda power between S and ScS and between P and PcP is a simple linear extrapolation of the spectrum of heterogeneity power versus depth determined from global tomography to wavenumbers corresponding to short-period body waves. The negligible decay in the power spectrum of heterogeneity across a band of wavenumbers from 0.0001 to 1 km-1 is consistent with a pervasive entrainment of small scale chemical heterogeneities by convective motions. The lack of strong scattering attenuation in observed ScS and PcP waveforms is used to establish upper bounds in this wavenumber band of 3% and 1.5% on the root-mean-square variations of S and P velocity, respectively. Some realizations of the preferred model of the heterogeneity spectrum generate an SdS waveform from scattering by an elongated, high velocity anomaly, roughly parallel to the core-mantle boundary. The high topography of similarly shaped anomalies needed to account for the amplitude of narrow angle scattering observed from D argues against such anomalies having the high-density perturbation expected for a chemically distinct or phase-transformed layer.