A linear inversion approach to measuring the composition and directionality of the seismic noise field

We develop a linear inversion technique for measuring the modal composition and directionality of ambient seismic noise. The technique draws from similar techniques used in astrophysics and gravitational-wave physics, and relies on measuring cross-correlations between different seismometer channels in a seismometer array. We characterize the sensitivity and the angular resolution of this technique using a series of simulations and real-world tests. We then apply the technique to data acquired by the three-dimensional seismometer array at the Homestake mine in Lead, SD, to estimate the composition and directionality of the seismic noise at microseism frequencies. We show that, at times of low-microseism amplitudes, noise is dominated by body waves (P and S), while at high-microseism times, the noise is dominated by surface Rayleigh waves.