Diffuse seismic waves and site effects

The Green's function can be retrieved from averaging cross correlations of recorded motions within a diffuse field. When autocorrelation is performed the energy density at a point is proportional to the trace of the imaginary part of the Green's function tensor at the source itself. This is because the singularity of the Green's function is restricted to the real part. Thus, the Green's function availability may allow us to establish the theoretical energy density of a seismic diffuse field generated by a background equipartitioned excitation. We compute the imaginary part of the Green's functions for some cases and consider that it represents the spectral signature of the site. It is the pseudo-reflection response. The relative importance of the peaks of this energy spectrum, ruling out nonlinear effects, may have some bearing on the seismic site response for future earthquakes.