Conditional probability modeling of intensity measures for offshore mainshock-aftershock sequences

Abstract

Offshore structures are typically subjected to offshore mainshock (MS)–aftershock (AS) sequences. The realistic statistical modeling of intensity measures (IMs) for offshore MS–AS sequences is crucial for the seismic risk assessment and optimal design of offshore structures. This paper develops a framework to forecast the AS IMs given the offshore MS IMs. In particular, using the IMs of offshore MS–AS seismic motions selected from the Japan's K-NET seismograph network, the standard kernel density estimation (KDE) and transformation KDE (TKDE) (i.e., logarithmic TKDE (log-TKDE) and square root TKDE (sqrt-TKDE)) are employed to estimate the marginal cumulative distributions (MCDs) of IMs. Several bivariate copulas are used to model the joint probability distributions (JPDs). Furthermore, the copula-based conditional distribution is used to calculate the conditional probability for the AS IMs under the conditions of the MS IMs. The results demonstrate the ability of the proposed bivariate model to realistically characterize the statistical characteristic and dependent structures for MS–AS IMs. Finally, given the offshore MS IMs, the copula-based conditional probability can be used to accurately estimate the range and probability of occurrence for offshore AS IMs.