Distribution of noise sources for seismic interferometry

We demonstrate that the distribution of seismic noise sources affects the accuracy of Green's function estimates and therefore isotropic and anisotropic tomographic inversions for both velocity and attenuation. We compare three methods for estimating seismic noise source distributions and quantify the potential error in phase velocity, azimuthal anisotropy and attenuation estimates due to inhomogenous source distributions. The methods include: (1) least-squares inversion of beamformer output, (2) a least-squares inversion of year long stacked noise correlation functions assuming both a 2-D plane wave source density model and (3) a 3-D plane wave source density model. We use vertical component data from the 190 stations of the Southern California Seismic Network and some US Array stations for 2008. The good agreement between the three models suggests the 2-D plane wave model, with the fewest number of unknown parameters, is generally sufficient to describe the noise density function for tomographic inversions. At higher frequencies, 3-D and beamforming models are required to resolve peaks in energy associated with body waves. We illustrate and assess isotropic and azimuthally anisotropic phase velocity and attenuation uncertainties for the noise source distribution in southern California by inverting isotropic lossless synthetic Fourier transformed noise correlation function predictions from modelled 2-D source distribution. We find that the variation in phase velocity with azimuth from inhomogeneous source distribution yields up to 1 per cent apparent peak-to-peak anisotropy. We predict apparent attenuation coefficients from our lossless synthetics on the same order of magnitude as those previously reported for the region from ambient noise. Since noise source distributions are likely inhomogeneous varying regionally and with time, we recommend that noise correlation studies reporting attenuation and anisotropy incorporate source density information.