Frequency‐Dependent Effects of 2D Random Velocity Heterogeneities in the Mantle Lid onPnGeometric Spreading

Geometric spreading of the Pn phase for shallow sources, which refracts through the uppermost mantle and is the first seismic‐wave arrival at distances of ∼200 to ∼1500 km, is expected to be frequency dependent for most velocity structures. The smoothly varying distance and frequency dependence of Pn geometric spreading predicted for simple 1D spherical structures are dependent upon precise interference of multiple underside reflections from the Moho boundary. This interference is strongly impacted by lateral variations in the velocity structure. Prior work has shown that the presence of 2D random heterogeneities in the mantle lid or topography of the Moho boundary modifies Pn geometric spreading for ∼1 Hz signals, suppressing the distinctive character of the distance dependence for a 1D structure and approaching a power‐law behavior as the root mean square (rms) strength of the heterogeneity increases. Here, 2D finite‐difference calculations of the effects of random heterogeneities in the mantle lid on the Pn geometric spreading are extended to frequencies of up to 10 Hz, quantifying the frequency dependence. Although the shape of the distance dependence is still systematically modified, the strength of the frequency dependence is actually increased from that for homogeneous models for many suites of models with varying rms perturbations and correlation lengths of exponential random heterogeneity distributions superimposed on constant and linear gradient background mantle lid velocity structures. This indicates that assumption of frequency‐independent power‐law spreading for Pn directly introduces artificial frequency dependence to inferred attenuation coefficients. Similar behavior is expected for Sn phases. Efforts to characterize the mantle lid heterogeneity spectrum are required to overcome this trade‐off with anelasticity representations. Electronic Supplement: Figures showing calculated Pn ‐wave spectral amplitudes versus distance.