## 1 Introduction
[22] revisit the KY formula for predicting responses based on recorded responses from 54 instrumented buildings at both the base and top floors (or roofs). Despite its simplifications, the KY formula is effective for many structures and motions, offering a helpful tool for earthquake engineering and post-event building response assessments. The prediction error increased for buildings with non-linear responses or irregularities but remained within practical margins. The error is attributed to foundation rocking, structural irregularities, and deviations from the 1D wave propagation assumption [22]. Many researchers have introduced and applied microtremor analysis to determine the dynamic characteristics of both soil and structures [23; 24; 25; 26; 27; 28]. [PERSON]'s technique, when applied to buildings--considered as wave propagation media (which differ substantially from soils)--models the structure as an equivalent system of virtual linear systems. In this approach, the horizontal components of the recorded signal are treated as outputs, while the vertical component serves as the input. This setup corresponds to a classic \"black box\" problem, in which the internal characteristics of a system are inferred from its input and output signals. The H/V spectral ratio yields the spectral features of the transfer function or the spectral response of this \"black box.\" [PERSON]'s method [29] establishes a direct relationship between the transfer function's characteristics and the amplitude of possible shear deformations within the building. Consequently, resonance peaks in the transfer function indicate the presence of resonant shear deformations at specific frequencies thereby marking frequency ranges with increased susceptibility to damage under external excitation. The use of the Floor Spectral Ratio (FSR) method to identify the predominant (natural) frequency of a structure was proposed by [PERSON] [30]. It is a helpful tool in seismic engineering that provides insight into how different parts of a building amplify or attenuate earthquake energy, revealing crucial dynamic characteristics for safety, design, and monitoring. FSR employs the spectral ratio of the horizontal component (usually acceleration or velocity of one floor to another) of the structure's microtremor data relative to that of the ground or free field. A peak in the FSR at a specific frequency indicates a resonance or mode shape, which is critical for assessing building vulnerability. [PERSON] [31] was one of the first researchers to investigate damping in high-rise buildings using the Random Decrement Method (RDM). Subsequent studies by [PERSON] and [PERSON] [32], [PERSON] [33], [PERSON] et al. [34], [PERSON] and [PERSON] [35], and [PERSON] and [PERSON] [36; 37], as well as [PERSON] et al. [38], applied RDM and other techniques to estimate structural damping ratios. [PERSON] et al. [39] demonstrated that the damping ratio of a structure can be calculated from microtremor data using the RDM technique. [PERSON] [23; 24] applied RDM, non-parametric, and spectral analyses to determine natural frequencies and damping ratios, showing that the parameters derived from ambient vibrations are stable. [PERSON] et al. [26] further confirmed that both the natural frequency and damping ratio obtained through the combined application of spectral and RDM analyses depend on the structural integrity of the building. This study expands on previous analyses of earthquake recordings from the 22 May 2012 Pernik region earthquake, published by [PERSON] et al. [7; 8], [PERSON] and [PERSON] [40; 41], and [PERSON] et al. [20]. We analyzed two real accelerograms--three-component recordings of the 2012 Pernik earthquake at stations installed in the basement (SGL1) and on the sixth floor (SGL2) of a six-story building in the center of the Bulgarian capital, Sofia. These stations belong to the Strong Ground Motion Network of the National Institute of Geophysics, Geodesy, and Geography at the Bulgarian Academy of Sciences (NIGGG-BAS).