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Quantitative Measure of the Goodness-of-Fit of Synthetic Seismograms

John G. Anderson

Published 2004, SCEC Contribution #767

To develop credibility of synthetic seismograms for engineering applications, there is a need for a quantitative score that can be used to characterize the how well the synthetic matches the statistical characteristics of observed records. Recognizing that strong motion is a very complex time series and any measure that relies on a single parameter for the comparison is seriously incomplete, this paper examines use of a suite of measurements. To be specific, we score seismograms that have been filtered into up to ten narrow pass-bands. Each frequency band is scored on ten different characteristics. The characteristics scored are the peak acceleration, peak velocity, peak displacement, Arias intensity, the integral of velocity squared, Fourier spectrum and acceleration response spectrum on a frequency-by-frequency basis, the shape of the normalized integrals of acceleration and velocity squared, and the cross correlation. Each characteristic is compared on a scale from 0 to 10, with 10 giving perfect agreement. Scores for each parameter are averaged to yield an overall quality of fit. A score below 4 is a poor fit, a score of 4-6 is a fair fit, a score of 6 to 8 is a good fit, and a score over 8 is an excellent fit. One horizontal component of an actual seismogram typically fits the other horizontal component in the “good” range. The method is applied to a blind prediction of ground motions at a station 3 km from the fault in the M7.9 Denali Fault, Alaska, earthquake of November 3, 2002.

Anderson, J. G. (2004). Quantitative Measure of the Goodness-of-Fit of Synthetic Seismograms. Oral Presentation at 13th World Conference on Earthquake Engineering.