Analysis of the site-specific and regional components of kappa across crustal domains in Belgium

Understanding high-frequency seismic attenuation is essential for seismic hazard assessment but remains challenging in low-to-moderate seismicity regions such as Belgium. We present a comprehensive analysis of the anelastic attenuation parameter kappa (\(\:\kappa\:\)) for horizontal (H) and vertical (Z) components using waveform data from the Belgian ground-motion database (BELSHAKE). \(\:\kappa\:\) values are derived from S-wave acceleration Fourier amplitude spectra following Anderson and Hough (1984). A filtering procedure removes \(\:\kappa\:\) estimates associated with induced or shallow events, improving the \(\:\kappa\:\)–distance relationship. The refined dataset is used to estimate site-specific kappa (\(\:\kappa\:₀\)) and the regional kappa gradient (\(\:{\kappa\:}_{r}\)) across four crustal domains in Belgium. Three approaches are evaluated: free kappa gradient, joint kappa gradient, and mixed-effects regression. The mixed-effects method provides the most robust and stable estimates, while the joint kappa gradient approach offers a good compromise between accuracy and consistency; the free gradient method is more sensitive to data coverage. Station-specific \(\:\kappa\:₀\) values range from ~ 14–59 ms (H) and ~ 12–53 ms (Z). Regional \(\:{\kappa\:}_{r}\) values range from 0.13–0.17 \(\:ms/km\) (H) and 0.05–0.10 \(\:ms/km\) (Z). Assuming an average S-wave velocity of 3.6 \(\:km/s\), the inferred frequency independent quality factor (\(\:Q\)) ranges from ~ 1600–2100 (H) and ~ 2700–3900 (Z). These results improve constraints on attenuation in Belgium and support the development of refined GMPEs for stable continental regions.