Total Probability Theorem Versus Shakeability: A Comparison between Two Seismic‐Hazard Approaches Used in Central Asia

Probabilistic Evaluation of Fault Sources Based on Paleoseismic Evidence From Mass‐Transport Deposits: The Example of Aysén Fjord, Chile

“…In this equation, f M and f R are probability density functions for magnitude and distance in that particular source, and P ( Y > y | m , r ) represents the conditional probability that ground‐motion level y is exceeded, given an earthquake rupture with magnitude m at distance r . Depending on whether the considered ground‐motion measure is spectral acceleration or intensity, this exceedance probability is given by a ground‐motion prediction equation (GMPE) or an IPE (e.g., Bindi & Parolai, ). In PSHA, the aleatory uncertainty associated with the GMPE (lognormally distributed) or IPE (assumed to be normally distributed) is integrated over all considered magnitudes and distances, whereas for the purpose of this study we consider individual earthquake rupture scenarios, for each of which we compute, at a site where an MTD is observed, the probability of exceeding the corresponding intensity threshold, as shown in Figure .…”

“…Probability of exceeding intensity VII at a site at 10 km distance from an M = 6.5 earthquake (modeled as a point) according to two different IPEs. Note that IPE uncertainties are generally modeled as normal distributions (e.g., Bindi & Parolai, ), and that the AllenEtAl2012 IPE has a significantly larger standard deviation than the AtkinsonWald2007 IPE (see Table ). MMI = Modified Mercalli Intensity; IPE = intensity prediction equation.…”

“…This does not matter when comparing probabilities for different ruptures with respect to a given set of observations, but to facilitate comparison between different sets of observations, possibly involving different numbers of sites, we normalize the total probability by taking the 1/nth power, where n is the total number of sites with positive and negative evidence: Probability of exceeding intensity VII at a site at 10 km distance from an M = 6.5 earthquake (modeled as a point) according to two different IPEs. Note that IPE uncertainties are generally modeled as normal distributions (e.g., Bindi & Parolai, 2015), and that the AllenEtAl2012 IPE has a significantly larger standard deviation than the AtkinsonWald2007 IPE (see Table 1). MMI = Modified Mercalli Intensity; IPE = intensity prediction equation.…”

Reply to “Comment on ‘Total Probability Theorem Versus Shakeability: A Comparison between Two Seismic‐Hazard Approaches Used in Central Asia’ by D. Bindi and S. Parolai” by A. A. Gusev

“…We also thank Kevin Fleming for his support in the preparation of this article and Leonardo Alvares, who pointed out that we misspelled the name of his software in Bindi and Parolai (2015). The correct name is sacudida, from the Spanish word for shake.…”