ABSTRACT
In general, with a pair of seismic recordings at two locations, GFRF is obtainable as Fourier spectral ratio of the two recordings. One can first calculate the recording-based GFRF as
where U˜ is the seismic recordings in the frequency domain, superscript asterisk indicates the complex conjugate, and ε is a positive small number, implying the added white noise. The white noise is used primarily to avoid unstable calculation of GFRF at some frequencies near the notches in the spectrum |U˜0|2. As ε approaches zero, D˜j0(ω) ⇒ U˜j/U˜0, which is the Fourier spectral ratio or the definition of GFRF. Note that the tilde over quantities D and U is used to distinguish the recording-based quantities from those based on modeling.
