# Characterization of HVSR and VRSR in the Loess Plateau of China Based on Strong-Motion Data
## 1 Introduction  
The influences of site conditions on seismic wave propagation and earthquake damage have been well-documented through numerous theoretical studies and field investigations following destructive earthquakes [1, 2, 3, 4, 5, 6]. The impact of site conditions on ground motion remains a significant area of research in engineering seismology. The horizontal-to-vertical spectral ratio method originated from microtremor measurements. In 1908, a Japanese researcher observed weak ground vibrations using a seismometer and published the paper \"On Microtremors\" [7]. In the mid-20 th century, a Japanese scholar advanced the study of microtremors and explored the use of microtremor measurements to evaluate the dynamic characteristics of engineering sites [8, 9, 10], drawing significant attention from the academic community. In 1970, researchers proposed estimating site transfer functions by calculating the Fourier spectral ratio using strong-motion records from soil layers and nearby reference rock stations. This method was used to assess site amplification effects [11]. Over time, this method evolved into the spectral ratio method based on seismic observations of soil layers and bedrock through boreholes; it is commonly referred to as the soil-bedrock spectral ratio (SBSR) method. While the SBSR method offers clear physical insights and issuitable for scientific research, its application in evaluating the dynamic characteristics of specific engineering sites presents certain challenges. The HVSR method, also known as the single-station spectral ratio method, was introduced by [PERSON] [12] to evaluate site dynamic characteristics using the spectral ratio of horizontal Fourier amplitude spectra to vertical Fourier amplitude spectra for microtremors. Subsequent studies further clarified this method [13; 14]. The Nakamura method estimates the site's predominant period and amplification effect based on three assumptions: (1) the spectral characteristics of microtremors at the same site remain consistent across different measurements; (2) the HVSR of bedrock is 1; and (3) while the horizontal component experiences significant amplification, the vertical component remains largely unaffected, implying a vertical transfer function of 1. Initially, this method was applied to microtremor studies, yielding promising results [15; 16]. Japanese scholars [17] introduced the Nakamura method into strong-motion observations by replacing the smoothed Fourier amplitude spectra with velocity response spectra, thereby establishing the velocity response spectrum spectral ratio (VRSR) method. This approach demonstrated that spectral ratios derived from strong-motion records, particularly for the S-wave, effectively reduce the influences of magnitude, epicentral distance, and focal depth, better reflecting site effects. This innovation laid the theoretical foundation for using strong-motion records in site effect studies, advancing research and applications of the horizontal-to-vertical spectral ratio (HVSR) method [18; 19; 20; 21; 22; 23]. Additionally, the VRSR method has been extended to site classification and the study of nonlinear site behavior [24; 25], enabling a reasonable assessment of site effects on seismic ground motion using HVSR and VRSR methods. The Loess Plateau, renowned for its vast loess coverage and unique geomorphology, as well as its active neotetocnics, is the world's largest and thickest loess deposit. This region experiences frequent seismic activity, with a history of devastating earthquakes, including the 2008 \(M_{\text{S}}\)8.0 Wenchuan earthquake, the 2013 \(M_{\text{S}}\)6.6 Zhangxian-Minzian earthquake, and the 2023 \(M_{\text{S}}\)6.2 Jishishan earthquake. These earthquakes caused severe destruction in the epicentral regions and significantly impacted the distant Loess Plateau areas. Notably, the far-field effects of the Wenchuan earthquake were pronounced, with unusually high seismic intensities observed in the Loess Plateau.