A first-order second-moment calculation for seismic hazard assessment with the consideration of uncertain magnitude conversion

Abstract. Earthquake size can be described with different magnitudes for different purposes. For example, local magnitude M_L is usually adopted to compile an earthquake catalog, and moment magnitude M_w is often prescribed by a ground motion model. Understandably, when inconsistent units are encountered in an earthquake analysis, magnitude conversion needs to be performed beforehand. However, the conversion is not expected at full certainty owing to the model error of empirical relationships. This paper introduces a novel first-order second-moment (FOSM) calculation to estimate the annual rate of earthquake motion (or seismic hazard) on a probabilistic basis, including the consideration of the uncertain magnitude conversion and three other sources of earthquake uncertainties. In addition to the methodology, this novel FOSM application to engineering seismology is demonstrated in this paper with a case study. With a local ground motion model, magnitude conversion relationship and earthquake catalog, the analysis shows that the best-estimate annual rate of peak ground acceleration (PGA) greater than 0.18 g (induced by earthquakes) is 0.002 per year at a site in Taipei, given the uncertainties of magnitude conversion, earthquake size, earthquake location, and motion attenuation.