THE GOODNESS-OF-FIT BETWEEN OBSERVED AND SIMULATED WAVES: Modification of the frequency domain error and application to verification and validation

Verification and validation (V & V) are important the simulation of seismic waves. To objectively perform the V & V, indexes to quantitatively evaluate the goodness of fit (GOF) between observed and simulated waves is needed. In this study, we proposed indexes of GOF considering both the amplitude and the phase of the waveform. The main points of this paper are summarized as follows. 1) The indexes are originally derived from the frequency domain error (FDE) proposed by Dragovich and Lepage (2009)18). We modified the FDE to expand finite frequency bands. 2) We also newly propose the GOF of envelope of waveform based on the similar concept of FDE. 3) The indexes were correlate to four ranks from Excellent, Good, Fair, and Poor. These ranks are almost corresponding to the previous studies (Anderson (2004)6) etc.). We check the effectiveness of these indexes and their ranks by artificially generated waves. 4) We apply the proposed indexes to V & V of benchmark tests for strong ground motion prediction methods (Yoshimura et al., 201325)), and strong motion simulations of the 2004 Rumoi earthquake (Motoki et al., 20155)). We conclude that the indexes can quantitatively judge the GOF between observed and simulated waves.