This study explores the empirical relationships between earthquake magnitude, focal depth, and the maximum dislocation of strong earthquake faults. The research is motivated by the significant challenges that civil engineering projects face to in seismically active regions, where understanding and predicting the behavior of seismic faults is crucial for disaster prevention and infrastructure resilience.

The study begins by highlighting the critical need for accurate seismic hazard assessment in regions with active faults. These areas are prone to surface or deep underground seismic faults that can severely impact engineering structures. Traditionally, the magnitude of an earthquake has been the primary factor in estimating the potential impact on fault dislocation. However, this research introduces focal depth as a vital parameter, arguing that its inclusion enhances the reliability of empirical models used for predicting fault behavior.

To develop a more accurate predictive model, the authors collected rupture data from 295 seismic events worldwide. This data set served as the foundation for constructing empirical relationships among earthquake magnitude, focal depth, and maximum fault dislocation. The study employed a neural network approach, specifically a back-propagation （BP） neural network model, to analyze the data and generate predictive equations. The neural network model was selected for its ability to handle complex non-linear relationships that are often present in seismic data.

The findings reveal that incorporating focal depth into the predictive model significantly improves its accuracy. The research identifies a clear linear relationship between the logarithm of earthquake magnitude, focal depth, and maximum fault dislocation. Furthermore, the study examines the influence of different fault types on these relationships, noting substantial variations in correlation coefficients and the goodness-of-fit across various fault types. This suggests that fault type plays a crucial role in determining the extent of fault dislocation during an earthquake.

The resulting empirical equations are designed to serve as a robust reference for engineers and urban planners working in earthquake-prone regions. By providing more reliable predictions of maximum fault dislocation, these equations can help in the design of structures that are better equipped to withstand the forces generated by seismic activity. This is particularly important for projects located near active fault zones, where the risk of significant ground displacement is high.

In conclusion, this study contributes to the field of seismic hazard analysis by improving the understanding of the relationships between earthquake magnitude, focal depth, and maximum fault dislocation. The integration of focal depth into predictive models represents a significant advancement in seismic risk assessment, offering a more comprehensive tool for evaluating the potential impact of earthquakes on engineering structures. The research underscores the importance of considering both deterministic and probabilistic approaches in seismic hazard assessment to ensure the safety and resilience of infrastructure in seismically active areas.

These findings are expected to have practical implications for the design and construction of infrastructure in regions susceptible to seismic activity. By enhancing the accuracy of fault dislocation predictions, this research supports the development of safer, more resilient structures that can better withstand the dynamic forces associated with earthquakes. The study also provides a foundation for future research aimed at further refining the empirical models and expanding their applicability to different seismic environments.