A Probabilistic Method for the Magnitude Estimation of a Historical Damaging Earthquake Using Structural Fragility Functions

A method is proposed here to estimate the magnitude of a historical earthquake by using fragility functions and written descriptions of damage. Probabi- listic descriptions are used to describe the distribution of potential earthquake events, the resulting intensity of ground shaking at the site, and the distribution of resulting damage to structures. This information is then combined using Bayes' theorem to compute the posterior distribution of the magnitude that caused a past damaging event. To validate the proposed method, the magnitude of the Northridge earthquake that occurred on 17 January 1994 is estimated. As an application example, the magnitude of a Korean earthquake that occurred in 1613 is estimated. Bins of input ground mo- tions are created by a spectral matching method using an attenuation relationship of Korea, and probability-of-collapse estimates are obtained by performing incremental dynamic analysis (IDA). A basic formulation is presented and then extended to take the correlation of collapse capacity between structures, the effect of aging on structural response, and the site effects into account. Sensitivity analyses are performed to deter- mine the importance of assumptions regarding the number of historically damaged buildings, the distributions of plausible magnitudes and distances, and the choice of attenuation relationship. The proposed method provides a comprehensive and straightforward procedure for magnitude estimation that can incorporate all relevant uncertainties.