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 com-monly assumed. The lack of an accurate representation of Pn and Sn geometric spread-ing 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 geometric-spreading models in the form Gr; f 10n3f=r0r0=rn1f logr0=rn2f and nif ni1logf=f02 ni2 logf=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-ve-locity uppermost mantle. We apply the new spreading model to observed data in Eur-asia 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 con-stant uppermost-mantle velocities.