Statistical properties of the seismic noise field: influence of soil heterogeneities

Seismic noise is generally considered as a reproducible and temporarily stationary natural source of energy. We present a study on the statistical features of the soil motion due to the seismic noise wavefield and the dependencies on the near-surface geology. We have investigated the variations of the 3-D average squared soil displacement over different timescales. The results clearly indicate ballistic behaviour for short timescales being indicative for the properties of the shallow material. Differences in the structural heterogeneity of the subsoil produce different scattering properties, changing the character of motion from nearly ballistic to diffusive on frequency-dependent timescales for all materials. Although in a strict sense the seismic noise wavefield is not completely isotropic, an ultimate pre-condition for a diffusive wavefield, the deviations compared to a uniform distribution are rather small. This means that the emergence of the Green's function is effective for all network sites after a sufficient self-averaging process that is provided by the scattering and the random spatial-temporal noise source distribution.