Geometric Spreading of Pn and Sn in a Spherical Earth Model

Geometric spreading of Pn and Sn waves in a spherical Earth model is different than that of classical headwaves and is frequency dependent. The behavior cannot be fully represented by a frequency-independent power-law model, as is commonly assumed. The lack of an accurate representation of Pn and Sn geometric spreading in a spherical Earth model impedes our ability to characterize Earth properties including anelasticity. We conduct numerical simulations to quantify Pn and Sn geometric spreading in a spherical Earth model with constant mantle-lid velocities. Based on our simulation results, we present new empirical Pn and Sn geometricspreading models in the form G r; f 103 f =r0 r0=r n1 f log r0=r n2 f and ni f ni1 log f=f0 2 ni2 log f=f0 ni3, where i 1, 2, or 3; r is epicentral distance; f is frequency; r0 1 km; and f0 1 Hz. We derive values of coefficients nij by fitting the model to computed Pn and Sn amplitudes for a spherical Earth model having a 40-km-thick crust, generic values of P and S velocities, and a constant-velocity uppermost mantle. We apply the new spreading model to observed data in Eurasia to estimate average Pn attenuation, obtaining more reasonable results compared to using a standard power-law model. Our new Pn and Sn geometric-spreading models provide generally applicable reference behavior for spherical Earth models with constant uppermost-mantle velocities.