In this study, new ground motion models (GMMs) for the secondary parameters have been developed, using the referenced empirical method (REM) introduced by Atkinson (2008) to estimate significant durations (D5−75 and D5−95), Arias intensity (IA), and cumulative absolute velocity (CAV) based on the dataset from the Alborz region of northern Iran. The GMMs proposed by Sandıkkaya and Akkar (2017) for D5−75 and D5−95, and Campbel and Bozorgnia (2019) for IA and CAV have been used as reference models. We calculate the residuals as the differences between the logarithm of observed significant durations and those from Sandıkkaya and Akkar (2017) reference GMMs, and the differences in the logarithm of observed IA and CAV and those from Campbell and Bozorgnia (2019) reference GMMs. We employ a mixed-effects regression approach to develop correction factors that adjust the Sandıkkaya and Akkar (2017) and Campbell and Bozorgnia (2019) GMMs for the secondary parameters for the Alborz region. We have developed a simple functional form as a function of moment magnitude (Mw), Joyner-Boore distance (Rjb), and VS30. The robustness of the developed GMMs for secondary parameters has been evaluated through a comparison with observed data, previous models, and residual analyses. The residual analyses show that between-event, between-station, and event-site corrected residual components exhibit no observable bias or trend as a function of Mw, VS30, and Rjb. Our dataset consists of 775 acceleration records from 167 earthquakes, recorded at 309 stations from 1976 to 2020, with Rjb and Mw ranges of 1 km < Rjb < 160 km and 3.0 ≤ Mw ≤ 7.4, respectively.
