Determination of surface‐wave phase velocities across USArray from noise and Aki's spectral formulation

We use expressions for the cross‐correlation of stochastic surface waves originally derived by Aki (1957) to develop an algorithm for determining inter‐station phase‐velocity measurements from continuous seismic data. In the frequency domain, the cross correlation of azimuthally isotropic noise is described by a Bessel function, and we associate zeros in the observed spectrum with zeros of the Bessel function to obtain phase‐velocity estimates at discrete frequencies. Phase velocities derived in this way at several frequencies are joined to form a dispersion curve, which is then sampled to obtain phase‐velocity estimates at arbitrary frequencies. We collect a set of dispersion curves for more than 30,000 station pairs of the transportable component of USArray, and derive Rayleigh wave phase‐velocity maps at periods of 12 and 24 s for the western United States. The spectral method lends itself well to automation, and avoids limitations at short inter‐station distances associated with time‐domain methods.