The exact and approximate conditional spectra in the multi-seismic-sources regions

The exact and two approximate conditional spectra are compared in this manuscript as a target spectrum for the purpose of ground motion selection. The considered site is a real offshore site located at South Pars Gas Field in the Persian Gulf region. This case study site is influenced by four major seismic area sources in which the deaggregation results confirm that many comparable seismic scenarios can be taken into account. Therefore, an alternative to the conventional approximate conditional spectrum is proposed that has a small deviation from the exact solution. In addition, the use of different conditioning status of the probabilistic seismic hazard deaggregation (i.e., occurrence versus exceedance of the target spectral acceleration) for calculating the exact distribution of conditional spectrum was investigated. The results show that one of the proposed approximate approaches leads to conditional distributions which provide acceptable agreement with those obtained from the exact solution.

► The exact and two different approximate CS are compared.
► A simple seismic source can produce bias in estimating the distribution of CS.
► The proposed approximate approach has the minimum deviation from the exact solution.
► The proposed approximate approach with the lower-bound epsilon is biased.
► The proposed approach is acceptable in all four different intensity measures.