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 ∼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°. 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 Kármán random media distributed throughout the uppermost 600 km of the mantle with a = 2000 km, ε = 10%, and κ = 0.05 provide a good fit to the time, range, and frequency dependence of the stacks, although there is a trade‐off between ε 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.