## 1 Introduction
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Testing Method** & **Operation Method** & **Advantages** & **Disadvantages** \\ \hline \multirow{8}{*}{Borehole Method} & Single borehole & Place a geophone in a single borehole and generate waves using a seismic source. Record the waveform to calculate the \(V_{s}\) of the soil. & Simple principle, easy calculation, large data volume at different depths, low cost ([PERSON] et al., 1981). & Weak anti-interference capability, limited testing depth. \\  & & & \\  & & & \\  & & & \\  & & & \\ \cline{2-4}  & & & \\ \cline{2-4}  & Cross-Hole & Generate shear waves in one borehole and receive them in two other borehole. Calculate the \(V_{s}\) based on the propagation distance and time. & Strong anti-interference capability, wide application range, large testing depth. & High cost, high construction requirements, significant limitations due to borehole inclination ([PERSON] et al., 2018). \\ \cline{2-4}  & Transient Surface Wave & The exciter generates signals and the geophone records Rayleigh waves. The \(V_{s}\) is obtained after conversion [15]. & No need for drilling, fast testing speed, strong adaptability, wide application. & Requires conversion of Rayleigh waves, resulting in larger errors. \\ \cline{2-4}  & Steady-State Surface Wave & The exciter emits fixed-frequency Rayleigh waves. Measure the wavelength and convert to \(V_{s}\). & Compensates for the low excitation energy & Complex equipment, long measurements. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(V_{s}\) testing methods and characteristics. depths of 10-20 m [24]; and the 2008 Wenchuan earthquake (\(M_{W}\) 7.9) produced fewer sand boils than previous major earthquakes, but the ejected materials were more diverse, including silt, fine sand, medium sand, coarse sand, gravel, and pebbles [25]. These new phenomena challenge traditional understanding and necessitate the optimization and upgrading of traditional liquefaction risk assessment methods. Researchers have adopted emerging machine learning techniques as novel methods for studying liquefaction problems, leading to innovative research. For example, [PERSON] et al. (2021) [26] proposed a deep learning (DL)-based approach for soil liquefaction assessment; [PERSON] et al. (2021) [27] analyzed the application of four machine learning techniques in evaluating the likelihood of seismic liquefaction based on CPT data; [PERSON] et al. (2022) [28] discussed the applicability of seven machine learning methods for predicting the liquefaction of fine-grained soils; and [PERSON] et al. (2024) [29] explored the use of random forest (RF) and support vector machine (SVM) models in SPT-based liquefaction studies. Drawing on the valuable research mentioned above and considering the advantages and limitations of existing methods, this paper proposes a new \(V_{s}\)-based liquefaction probability model that integrates random forest feature importance ranking and Logistic regression. This study is primarily divided into two parts. Part 1. Based on publicly available \(V_{s}\) liquefaction survey data, two databases (Database A and Database B) were established to evaluate the performance of the existing formulae and to construct and validate the new models. A detailed comparative analysis of existing \(V_{s}\)-based seismic liquefaction probability assessment methods was conducted, studying the performance differences of various formulae at different probability contours and fines content. Part 2. A new liquefaction probability model was developed using the random forest feature importance ranking algorithm to select key parameters, including the moment magnitude (\(M_{W}\)), \(V_{s1}\), cyclic stress ratio that was adjusted to the reference state of \(M_{W}=7.5\) (\(CSR_{7.5}\)), depth (Z), and fines content (FC). A new evaluation formula was constructed using the logistic regression model.