1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Université Pierre et Marie Curie4 Swiss Federal Institute of Technology5 Columbia University6 Department of Applied Mathematics and Computer Science, Technical University of Denmark7 Columbia University
We apply two different algorithms to measure surface wave phase velocity, as a function of frequency, from seismic ambient noise recorded at pairs of stations from a large European network. The two methods are based on consistent theoretical formulations, but differ in the implementation: one method involves the time-domain cross-correlation of signal recorded at different stations; the other is based on frequency-domain cross-correlation, and requires finding the zero-crossings of the real part of the cross-correlation spectrum. Furthermore, the time-domain method, as implemented here and in the literature, practically involves the important approximation that interstation distance be large compared to seismic wavelength. In both cases, cross-correlations are ensemble-averaged over a relatively long period of time (1 yr). We verify that the two algorithms give consistent results, and infer that phase velocity can be successfully measured through ensemble-averaging of seismic ambient noise, further validating earlier studies that had followed either approach. The description of our experiment and its results is accompanied by a detailed though simplifed derivation of ambient-noise theory, writing out explicitly the relationships between the surface wave Green’s function, ambient-noise cross-correlation and phase and group velocities.