# Prediction Equation for Horizontal Ground Motion Peak Values in the Loess Plateau Region
## 7 Conclusions  
This paper introduces the attenuation research dataset for the Loess Plateau region, details the data processing methods, and analyzes the distribution of strong motion records. It also presents two attenuation relationship models and two-step fitting methods. The results indicate that the magnitude grouping scheme effectively reduces the dispersion of statistical samples in the magnitude component, thereby improving the fitting results. Based on regression statistics on 1149 data samples using the proposed models, Models I and II, we derive the prediction equations for PGA, EPA, and PGV for horizontal soil layers in the Loess Plateau region and plot the corresponding attenuation relationship graphs. A comparative analysis between the observed values and the prediction equation curves provides the following conclusions:  
1. For magnitudes \(\geq M_{\rm S}\) 6.0, the fitting results of attenuation Models I and II are quite close. However, for magnitudes less than \(M_{\rm S}\) 6.0, the differences gradually increase as the magnitude decreases;
2. Model I uses a fixed attenuation coefficient, which does not vary with magnitude, resulting in parallel attenuation curves. In contrast, Model II's attenuation coefficient is a linear function of magnitude, leading to a faster attenuation rate as magnitude increases, causing the different magnitude attenuation curves of Model II to converge at greater epicentral distances;  
Figure 25: Distribution of PGV fitting residuals by magnitude. 3. By comparing the observed values and prediction equation curves for magnitudes \(M_{\text{S}}\) 4.2 and \(M_{\text{S}}\) 5.0, it is apparent that Model II slightly outperforms Model I, exhibiting a lower standard error in fitting ground motion parameters;
4. When comparing the standard deviations, Model II's fitting results are slightly better than those of Model I, with its fitting standard deviation about 80% of that of Model I. Analyzing the residual distribution for peak parameter attenuation reveals differences in the average residuals across magnitude brackets, with most brackets showing lower overall deviations using Model II. However, some brackets still show smaller fitting deviations with Model I. Considering the advantages and disadvantages of both models, this paper uses both attenuation models to establish ground motion parameter prediction equations for the Loess Plateau region;
5. When using the seismic motion parameter prediction equations provided in this paper, to ensure safety, it is recommended to calculate the predictions of both Model I and Model II and use the higher of the two values as the basis for seismic design calculations. Conceptualization, J.B. and W.W.; methodology, W.W.; software, D.P. ; validation, W.W.; formal analysis, W.W.; investigation, W.W.; data curation, W.W. and D.P. ; writing--original draft preparation, W.W.; writing--review and editing, J.B. and D.P. ; visualization, W.W.; supervision, J.B.; project administration, W.W. All authors have read and agreed to the published version of the manuscript. This work was funded by the Hebei Key Laboratory of Earthquake Disaster Prevention and Risk Assessment (No. FZ201101), the Science Research Project of Hebei Education Department (No. QN2021308), and the Fundamental Research Funds for the Central Universities (No. _ZY_20215128). Not applicable. The strong motion data used in this study were obtained from the Strong Motion Observation Center of the Institute of Engineering Mechanics, China Earthquake Administration. The authors extend their sincere gratitude to the Strong Motion Observation Center of the Institute of Engineering Mechanics, China Earthquake Administration, for providing invaluable strong motion data from the Loess Plateau region of China. Special thanks are also due to the China Earthquake Networks Center for supplying extensive strong motion data that served as a crucial foundation for this study.