Constraints on the heterogeneity spectrum of Earth's upper mantle

We constrain the heterogeneity spectrum of Earth's upper mantle at scales from a few kilometers to tens of thousands of kilometers using observations from high-frequency scattering, long-period scattering, and tomography. Tomography and high-frequency scattering constraints are drawn from previous studies, but constraints on mantle heterogeneity at intermediate scales (5-500 km) are lacking. To address this, we stack similar to 15,000 long-period P coda envelopes to characterize the globally averaged scattered wavefield at periods from 5 to 60 s and at ranges from 50 to 98 degrees. To fit these observations, we consider models of random mantle heterogeneity and compute the corresponding global wavefield using both a ray theoretical "seismic particle" approach and full spectral element simulations. Von Karman random media distributed throughout the uppermost 600 km of the mantle with a = 2000 km, epsilon = 10%, and kappa = 0.05 provide a good fit to the time, range, and frequency dependence of the stacks, although there is a trade-off between epsilon and the thickness of the assumed scattering layer. This random media model also fits previously published 1 Hz stacks of P coda and agrees with constraints on long-wavelength structure from tomography. Finally, we explore geodynamically plausible scenarios that might be responsible for the RMS and falloff rate of the proposed spectrum, including a self-similar mixture of basalt and harzburgite.