On measuring surface wave phase velocity from station-station cross-correlation of ambient signal

7 We apply two different algorithms to measure surface-wave phase velocity, as a function of 8 frequency, from seismic ambient noise recorded at pairs of stations from a large European 9 network. The two methods are based on consistent theoretical formulations, but differ in the 10 implementation: one method involves the time-domain cross-correlation of signal recorded 11 at different stations; the other is based on frequency-domain cross-correlation, and requires 12 finding the zero-crossings of the real part of the cross-correlation spectrum. Furthermore, 13 the time-domain method, as implemented here and in the literature, practically involves 14 the important approximation that interstation distance be large compared to seismic wave15 length. In both cases, cross-correlations are ensemble-averaged over a relatively long period 16 of time (one year). We verify that the two algorithms give consistent results, and infer that 17 phase velocity can be successfully measured through ensemble-averaging of seismic ambient 18 noise, further validating earlier studies that had followed either approach. The description of 19 our experiment and its results is accompanied by a detailed though simplifed derivation of 20 ambient-noise theory, writing out explicitly the relationships between the surface-wave Green 21 function, ambient-noise cross-correlation, and phase and group velocities. 22