The local amplification of surface waves: A new observable to constrain elastic velocities, density, and anelastic attenuation

The deployment of USArray across the continental U.S. has prompted developments within surface wave tomography to exploit this unprecedented data set. Here, we present a method to measure a new surface wave observable: broadband surface wave amplification that provides new and unique constraints on elastic velocities and density within the crust and upper mantle. The method, similar to its phase velocity counterpart referred to as Helmholtz tomography, initiates by constructing phase travel time and amplitude maps across the array for each period and earthquake. Spatial differential operators are then applied to evaluate the amplitude variation, as well as the effect of focusing/defocusing. Based on the 2‐D damped wave equation, the amplitude variation corrected for focusing/defocusing is linked directly to both local amplification and intrinsic attenuation, which are separated by examining waves propagating in opposite directions. We apply the method to teleseismic Rayleigh waves observed across USArray between periods of 24 and 100 s and show that the observed amplification maps are strongly correlated with known geological features. Small‐scale attenuation measurements are contaminated by wavefield complexities, but larger‐scale anelastic attenuation is estimated reliably. The observed amplification maps compare well with predictions based on recent 3‐D shear velocity models of the western U.S. that were produced from ambient noise and earthquake data. Notably, predictions based on models with different prescribed density structures demonstrate the potential for using estimates of local amplification to constrain not only 3‐D velocity structure but also density.