Seismic array noise studies at Roosevelt Hot Springs, Utah geothermal area; discussion

Douze and Laster (1979) considered the problem of identifying the mode of propagating isotropic seismic noise by the characteristics of the cross-spectrum between two geophones. For the vertical component of isotropic single-mode Rayleigh wave noise, they derived the theoretical relation where Ψ(ω) is the power spectrum, Ψ₁₂(ω) is the cross-spectrum between geophones 1 and 2, Δx is the geophone separation, V is the phase velocity of the waves at angular frequency ω, and J₀ is the zero-order Bessel function. They noted that the cross-spectrum is purely real and “no apparent phase velocities can be obtained from the data.”