Empirical Modeling of Source Directivity Effects into a Ground-Motion Model for Central Italy

Assessing the spatial variability of seismic shaking in the epicentral area of an earthquake is one of the major challenges to be addressed in seismic hazard estimates. Among the main contributions to the ground-motion variability, source directivity plays a predominant role, inducing spectral amplifications in the direction of rupture propagations, even for small- to moderate-magnitude earthquakes. The scope of this work is to provide an empirical predictive model that can be used to modulate the ground-motion amplitudes, according to the expected source directivity effects. The proposed directivity corrective term is built for acceleration spectral ordinates, parameterizing the azimuthal trend of the leftover residuals of a fully nonergodic regional model, after removing the systematic effects of source, site, and propagation. Our study is focused on the area of Central Italy, which is dominated by a complex system of normal faults that has generated several seismic sequences in the past 30 yr. The residual analysis is carried out using the recordings of 456 events in magnitude ranging from 3.2 to 6.5, showing that about one-third of the examined earthquakes exhibit a clear ground-motion azimuthal pattern. The directivity correction model is based on three empirical relations, which describe (1) azimuthal variations modeled via a theoretical directivity factor, (2) spectral variation of directivity amplitude using a first-order Gaussian function, and (3) the correlation between moment magnitude and the period of maximum directivity effect. We demonstrated that the introduction of a source directivity correction, applied to a real-case scenario, has a considerable impact and may result in a 20% reduction of aleatory variability with respect to the uncorrected nonergodic model. This model offers an empirically based and physically consistent framework for capturing spatial variations in ground shaking, thereby improving the reliability of seismic hazard evaluations and informing risk mitigation strategies.