## 1 Introduction  
Attenuation of seismic waves is one of the key factors in seismic hazard assessment for earthquake-prone regions as well as being important for the quantification of earthquakes and plays a significant role in studies of seismic source and crustal structure [1]. The Fourier amplitude spectrum (FAS) of ground motion is influenced by source parameters, propagation path, and local site conditions as modelled by the [PERSON]'s [2] theoretical omega-square source model. [PERSON] [3] was one of the first who observed the \"crashing spectrum syndrome\" in the acceleration spectrum of shear waves (S-waves) on strong-motion accelerations recorded at close distances. The high-frequency band limitation parameter (\(f_{max}\)) was defined as the cut-off frequency at which the spectrum starts to decay very rapidly. [PERSON] [3] concluded that the \(f_{max}\) observed in acceleration FAS is controlled by the local site conditions, particularly by the subsurface geological structures below and near the site. One of the first uses of the term \"site attenuation parameter\" to model the high-frequency spectral attenuation was by [PERSON] [4]. Empirical spectral decay parameter kappa (\(\kappa\)) was introduced by [PERSON] and [PERSON] [5] to describe the difference between the observed acceleration spectrum of S-waves and [PERSON]'s [2] omega-square source model at the high-frequency part of the FAS. [PERSON] and [PERSON] [5] observed a linear relation between the \(\kappa\) of the ground motion and the epicentral distance (\(R_{e}\)) of the recording station. The zero-distance intercept \(\kappa_{0}\) (also called the near-site attenuation or site-kappa) represents the attenuation contribution to \(\kappa\) from subsurface geological structure beneath the site. The slope (\(\kappa_{R}\)) is related to the regional attenuation due to the horizontal propagation of S-waves through the crust below and near the site within a few kilometres (e.g., [5; 6; 7]). Over the last three decades, the near-site attenuation parameter \(\kappa_{0}\) has been used in a variety of applications. Particularly in the creation and calibration of ground-motion models (GMMs) based on stochastic simulations (e.g., [8; 9; 10; 11]), host-to-target adjustments of GMMs (e.g., [12; 13]) and site-specific ground response analysis using Random Vibration Theory (e.g., [14]) for critical facilities where the choice of seismological parameters play an important role.  
On 22 March 2020 Zagreb was struck by the strongest ever instrumentally recorded earthquake (M5.5) that caused significant damage in the city itself. The seismological data were reliable enough for preliminary 3D interpretation of the rupture along a segment of an active NW verging thrust fault in the subsurface of the Medvednica Mountains [15]. The aim of this paper is a more reliable interpretation of near-site attenuation or site-kappa based on seismological data obtained up to now.  
The objective of this contribution is to present the calculation of high-frequency attenuation spectral parameter \(\kappa\) and its local site-specific component \(\kappa_{0}\) for two seismological stations: Puntijarka-PTJ (situated on the top of Medvednica Mountains) and Zagreb-ZAG (situated in Zagreb city), using classical [PERSON] and Hough [5] approaches. The results from this study of the high-frequency attenuation will contribute to a better knowledge of the effect of local structures on local attenuation and of deep structures on the attenuation at long distances. Additionally, attenuation parameters (\(\kappa\), \(\kappa_{0}\)) should be considered as a step towards a better analysis of seismic hazard and finally towards seismic hazard assessment for the wider area of the city of Zagreb that has a population close to 1 million and the city's strategic infrastructure.