Probabilistic characterization of aftershock multi-component ground motions based on within-sequence generalized intensity measure correlation models

Recent studies have placed growing emphasis on the significant role of mainshock-aftershock (MS-AS) sequences in seismic structural fragility and risk analyses. An important step involved is the probabilistic characterization of aftershock ground-motion intensity measures (IMs) (e.g., 5%-damped spectral acceleration). This study presents a versatile framework to construct the damping-dependent conditional joint distribution of aftershock multi-component IMs based on novel generalized intensity measure correlation models (GIMCMs). A step-by-step procedure with mathematical expressions is provided to facilitate the implementation of this framework. As a key feature, the GIMCMs quantify damping-dependent correlations between MS-AS pairs of ten representative IMs in both horizontal and vertical directions for the first time, based upon a substantial database and machine learning. The MS-AS correlations are found to be generally stronger when IM pairs correspond to larger damping ratio, or more similar ground-motion frequency ranges (e.g., same-IM pairs), or identical (horizontal or vertical) directions. The presented framework is applied to two examples for modeling aftershock IMs conditioned on a vector of recorded mainshock IM values and a specified mainshock IM value from seismic-hazard disaggregation, respectively. When utilizing recorded mainshock IM values as conditioning information, the framework can significantly improve IM prediction with a reduction in the mean absolute error by over 20% relative to the conventional unconditional approach. This study could be useful for seismic risk assessment of damping-specific structures and geotechnical systems subjected to MS-AS multi-component ground-motion sequences.