Surface wave tomography with USArray based on phase front tracking and amplitude mapping: isotropic, anisotropic, and intrinsic attenuation structures

The deployment of the EarthScope/USArray Transportable Array has promoted new and better ways to utilize the dense array configuration and to resolve higher resolution crustal and upper mantle structures beneath the US. Here, we present a local inversion method for surface wave that utilizes the USArray first to determine the surface wave wavefield empirically and then to directly measure the surface wave propagation characteristics such as isotropic velocity, azimuthal anisotropy, and intrinsic attenuation by solving the 2D Helmholtz wave equation. The method starts with single event analysis, where for each period and earthquake all measurements across the array are aggregated to determine maps of phase travel time and amplitude on a fine spatial grid, which essentially describes the surface wave wavefield. The solution of the 2D wave equation contains real and imaginary parts, which are relevant to velocity and attenuation measurements, respectively. For the real part, directionally dependent phase velocities at each location are estimated from the gradient of phase travel time along with the Laplacian of amplitude. For the imaginary part, on the other hand, intrinsic attenuation at each location is estimated from the dot product of the gradients of phase travel time and amplitude along with the Laplacian of phase travel time. In both cases, the terms that contain the gradient operator are directly related to traditional ray theoretic approaches (e.g., eikonal equation for velocity measurement) whereas the terms involving the Laplacian operator provide corrections for off-ray sensitivity. In principle, by applying the correction terms, finite frequency effects such as wave interference, wavefront healing, and backward scattering are accounted for in phase velocity measurements and focus/defocusing is accounted for in attenuation measurements. We apply the method to Rayleigh wave measurements between 30 and 100 sec period from more than 700 earthquakes and all measurements from single event analysis are statistically summarized to estimate the final maps for isotropic, anisotropic, and attenuation structures and their uncertainties. For velocity tomography, we show that at long period (>50), the method, called Helmholtz tomography, better resolves sub-wavelength velocity structures and unbiased azimuthal anisotropy than its ray theoretic analog, eikonal tomography. For attenuation tomography, we present preliminary attenuation maps for the western US and emphasize the importance of accounting for focusing-defocusing effects in resolving intrinsic attenuation structures.