Estimation of radiated energy using the EGF technique; what should be the upper limit of integration in the frequency domain?

The empirical Green's function (EGF) technique is frequently used to estimate the radiated seismic energy, E (sub R) , of an earthquake. An approximation of the moment-rate spectrum, M (sub 0) (f), of the target earthquake is obtained from the ratio of the spectrum of the target earthquake to the spectrum of the EGF earthquake, and the radiated seismic energy is computed by integrating Formula over frequency f. The choice of the upper limit of integration, f (sub u) , is critical. In this note we show that the optimum choice of f (sub u) for the omega (super 2) -source model is given by f (sub u) /fc (sub 1) approximately fc (sub 2) /fc (sub 1) , where fc (sub 1) and fc (sub 2) are the corner frequencies of the target and the EGF earthquakes, respectively. This result provides a useful guide in the application of the EGF technique to obtain a reliable estimate of the radiated seismic energy.