The Pn phase for crustal earthquakes refracts through the uppermost mantle to become the first seismic‐wave arrival at distances of ∼200 to ∼1500 km. The amplitude of Pn is particularly sensitive to the mantle lid radial velocity gradient, and the elastic geometric spreading is frequency dependent. Lateral variations in the radial velocity gradient and in the crustal thickness encountered by Pn phases that traverse boundaries of geological provinces further complicate the frequency‐dependent geometric spreading behavior. We use 2D finite‐difference (FD) calculations to explore the effects of smoothly varying lateral structures in the lid and crust on Pn phases in the 0.4–10 Hz frequency range. Pn geometric spreading for 1D structures with mantle lid gradients is calculated first to ensure that the FD calculations correctly capture the expected frequency dependence. Then, 2D models with smooth laterally varying radial lid gradients are computed to explore how the phase samples the structures to give the overall geometric spreading. The direction of propagation through the laterally varying structure affects the frequency dependence and the transition from source‐side to receiver‐side dominance in the spreading. Laterally varying crustal thickness is explored in the context of the North Korean nuclear test site, for which many observations of Pn are made by stations with paths either through continental structure or along paths with variation from continental to oceanic to arc structure (in Japan). Frequency‐dependent amplitude effects are observed on the paths through oceanic structure. 2D FD calculations for structures with a central region of thin oceanic crust reproduce the observed first‐order frequency dependence of Pn along corresponding paths, including rapid amplitude decay for frequencies above 6 Hz. These analyses demonstrate that even though Pn propagation is very complex, modeling approaches can guide interpretations of the behavior when constraints on the structure are available.
Electronic Supplement:Figures of Pn‐wave snapshots, first Pn arrival times, and frequency dependence of the Pn amplitudes.