Effects of 2D Random Velocity Heterogeneities in the Mantle Lid and Moho Topography on Pn Geometric Spreading

P-n-wave energy refracts through the uppermost mantle, with the first seismic wave arrival at distances of similar to 200 to similar to 1500 km from crustal sources. The P-n 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 P-n geometric spreading correction and specifying its uncertainties, a requirement for accurately determining frequency-dependent attenuation models for P-n, depends on improved understanding of the behavior of P-n 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 P-n 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. P-n 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 P-n, 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 P-n path, the preferred geometric spreading parameterization is the frequency-dependent model for a constant mantle lid velocity structure unless P-n travel-time branch curvature can constrain the radial gradient in the mantle lid.