Pn-wave energy refracts through the uppermost mantle, with the first seismic wave arrival at distances of ∼200 to ∼1500 km from crustal sources. The Pn phase provides important constraints on source type, location, and magnitude, but its propagation is complicated by frequency-dependent sensitivity to the Earth’s sphericity and lithospheric velocity structure. Converging on an acceptable Pn geometric spreading correction and specifying its uncertainties, a requirement for accurately determining frequency-dependent attenuation models for Pn, depends on improved understanding of the behavior of Pn geometric spreading for various heterogeneous models. We investigate the effects of radial mantle lid velocity gradients, mantle lid random volumetric velocity heterogeneities, and Moho topography on Pn geometric spreading using reflectivity and two-dimensional (2D) finite-difference 1-Hz wave propagation calculations for elastic Earth models. Mantle lid velocity gradients systematically modify the frequency-dependent geometric spreading from that found for models with constant velocity but retain the same overall functional form. Pn amplitudes are also sensitive to the presence of modest 2D random lateral velocity heterogeneities within the uppermost mantle, with geometric spreading approaching a power-law behavior as the root mean square strength of heterogeneity increases. 2D Moho topography introduces scatter into the amplitude of Pn, but the overall behavior remains compatible with that for a laterally homogeneous model. Given the lack of knowledge of specific small-scale structure for any particular Pn path, the preferred geometric spreading parameterization is the frequency-dependent model for a constant mantle lid velocity structure unless Pn travel-time branch curvature can constrain the radial gradient in the mantle lid.

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