Period-dependent behavior of conditional dispersion in probabilistic seismic demand models

Accuracy and conditional independence are fundamental requirements for probabilistic seismic demand models, which are commonly described by conditional mean demand and conditional dispersion. While the former has been extensively studied in intensity-measure (IM) evaluation, conditional dispersion is often treated as a scatter measure. This study evaluates conditional dispersion for 14 ground-motion IMs and 15 structural models ( T 1 = 0.15 – 4.01 s ). Two metrics are estimated using an event-based block bootstrap procedure: σ E D P ∣ I M provides reference-level estimates of conditional dispersion, reflecting record-to-record variability of the engineering demand parameter (EDP) conditional on an IM, and Δ σ E D P ∣ I M , X characterizes dependence on ground-motion attributes by measuring the maximum variation of attribute-conditioned dispersions with respect to magnitude ( M ), distance ( R ), and site class ( S I ). Limited estimation uncertainty supports the reliability of the estimates, which reveal clear period-dependent behavior. Acceleration-related IMs, especially S a ( T 1 ) , show low dispersion and weak-to-limited attribute dependence for the investigated structures with T 1 = 0.15 – 0.61 s in the acceleration-sensitive region. Velocity-related IMs, especially S v ( T 1 ) , show similar favorable behavior for the investigated structures with T 1 = 0.83 – 4.01 s in the velocity-sensitive region. Response spectral-shape analysis explains this period dependence through the distribution of demand-relevant spectral content and further explains the comparable behavior of simple spectral ordinates and advanced spectral-shape IMs through stable or relatively flat spectral-shape regions. Overall, conditional dispersion is statistically stable and spectrally interpretable. Together with practical seismic-hazard computability, these findings support S a ( T 1 ) and S v ( T 1 ) as appropriate IMs for the corresponding period ranges, facilitating practical decoupling between seismic hazard and demand analyses and helping prevent large dispersion and ground-motion attribute dependence from propagating into downstream performance assessment.