## 1 Introduction  
On 15 November 2017, Pohang, South Korea, was struck by an earthquake measuring \(M_{\mu\
u}\) 5.4 according to the Korea Meteorological Administration (KMA) or \(M_{\mu\
u}\) 5.5 by the U.S. Geological Survey (USGS), marking it the second largest earthquake event in the country over the past century [1, 2]. This event called attention to the seismic risk on the Korean Peninsula, a region generally characterized by low-to-moderate seismicity, and highlighted the necessity for robust seismic safety assessments, especially for critical infrastructures such as high-rise buildings, large dams, and nuclear power plants near the epicenter [3, 4]. Given the limited availability of large-scale actual data, it is essential to generate artificial earthquakes that account for the stochastic nature of Peak Ground Acceleration (PGA), which ensures a diverse range of rational input ground motions for comprehensive seismic performance assessments. Artificial earthquakes can be generated by means of: (1) scaling historical earthquakes, (2) matching a target spectrum through random vibration theory [5], or (3) simulating ground motions through stochastic approaches [6, 7, 8, 9]. While scaling historical records offers simplicity and availability, they represent only a limited range of earthquake event scenarios [10, 11, 12]. Since a recorded PGA only reflects the strongest ground motion and does not account for surface characteristics or the complexity of seismic events, amplifying historical records to match a target PGA leads to inadequate generation results. The 2017 Pohang Earthquake, with a focal depth of 7 km (KMA) and a rare combination of reverse and strike-slip faulting [1], exemplifies the limitations of relying solely on historical data for earthquake prediction. Meanwhile, the second method, generating earthquakes to match a design spectrum [5], which is conventionally constructed using a single predetermined PGA and simplified envelope curves, often fails to fully capture the complex dynamic characteristics of actual earthquakes [13]. This is because design spectra frequently underestimate or overestimate the spectral acceleration at certain periods [14; 15]. For a stochastic approach to ground motion generation, a Ground Motion Model (GMM) is employed. These models are categorized into two types: empirical and physics-based [6; 7; 8; 9]. Empirical GMMs, using simplified representations of seismic and geological properties [8; 9], lead to less accurate predictions in capturing the complex interactions of seismic activity [16]. In contrast, physics-based GMMs provide higher accuracy by integrating seismic sources, wave propagation, and site characteristics, making them more suitable for regions like the Korean Peninsula, where historical records of large-magnitude earthquakes are limited [16; 17]. Due to the significant computational costs required for 3D crustal modeling [18], this study employs a stochastic point-source model, a simplified version of physics-based GMMs [19]. In regions with low-to-moderate seismic activity, the limited availability of records from similar epicentral distances, despite data collection from various stations, hinders the development of probability distributions of PGA for specific source-to-site distances. PGA's variability is influenced by factors beyond distance and magnitude, including seismic event uncertainties, site conditions, and complex wave propagation. Simple interpolation can lead to inaccuracies, since PGAs fluctuate randomly even at the same distance. Moreover, the limited proximity of stations to epicenters and restricted access to seismic data further complicate sufficient data acquisition. To address these challenges, it is crucial to determine a rational probability distribution for PGA, which can facilitate a well-established description of the target response spectrum for fragility and risk analysis of critical infrastructures subjected to extreme seismic events.