ON THE SPATIAL CORRELATION OF SEISMIC NOISE IN AN ATTENUATING MEDIUM

Traditionally, for the tomography based on the correlation of seismic noise, primarily the phase information of ambient noise correlation function (NCF) is used to extract the seismic velocity and anisotropy of the earth by travel time inversion. Researchers recently utilize the amplitude of NCF to extract the earth's attenuation. According to the theory, NCF is proportional to the first kind of zero-order Bessel function in 2-D elastic case, which is directly extended to dissipative medium by introducing an exponential attenuation coefficient. The attenuation of the structure is then obtained by comparing the observed data from NCF to the Bessel function multiplied by a decaying exponential term. The NCF, however, is affected by the azimuth averaging of ambient noise source distribution in attenuating media. This empirical and simple extension may not be used to extract reliable decay coefficient. In this paper, we study the theoretical expressions of NCF in frequency domain between two stations under different coordinate systems and accordingly different source distributions which are composed by superposition of plane waves. We show that the coherency expressions in dissipative media vary with coordinate systems. The expressions are different for different normalizing factors. The attenuation coefficient obtained by fitting the coherency J₀(k₀r)e^−α(ω)r with the observed data is smaller than the real one.