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Geometric Spreading of P_n and S_n in a Spherical Earth Model

Geophysics Group, Earth and Environment Sciences Division, Los Alamos National Laboratory, EES-11, MS D408, Los Alamos, New Mexico 87545

Thorne Lay

Department of Earth and Planetary Sciences, University of California, Santa Cruz, Santa Cruz, California 95064

Xiao-Bi Xie

Institute of Geophysics and Planetary Physics, University of California, Santa Cruz, Santa Cruz, California 95064

Michael S. Thorne

Arctic Region Supercomputing Center, University of Alaska, Fairbanks, Fairbanks, Alaska 99775

Geometric spreading of P_n and S_n 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 P_n and S_n geometric spreading in a spherical Earth model impedes our ability to characterize Earth properties including anelasticity. We conduct numerical simulations to quantify P_n and S_n geometric spreading in a spherical Earth model with constant mantle-lid velocities. Based on our simulation results, we present new empirical P_n and S_n geometric-spreading models in the form G(r,f)=[10^n₃(f)/r₀](r₀/r)^{n₁(f)log(r₀/r)+n₂(f)} and n_i(f)=n_i1[log(f/f₀)]²+n_i2log(f/f₀)+n_i3, 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 n_ij by fitting the model to computed P_n and S_n 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 P_n attenuation, obtaining more reasonable results compared to using a standard power-law model. Our new P_n and S_n geometric-spreading models provide generally applicable reference behavior for spherical Earth models with constant uppermost-mantle velocities.

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