Ground motion prediction models, also known as ground motion prediction equations （GMPEs） or attenuation relationships, utilize mathematical formulations to estimate the median values and variability of ground motion parameters. They serve as a critical component in engineering practices such as seismic zoning and seismic safety evaluations for major engineering sites. The attenuation characteristics of ground motion parameters exhibit regional specificity and are closely related to the tectonic and geological context of the earthquake source and the affected area.

In seismic hazard analysis, it is common to consider the probability of engineering structures being subjected to ground motions exceeding a specified threshold. Since ground motions generated by small earthquakes typically do not significantly impact engineering structures, the primary focus of engineering seismology is often on relatively intense and destructive earthquakes. Certain regions often occur induced seismicity due to human production activities, such as oil and gas extraction or geothermal field operations. Induced earthquakes often occur at shallow depths. Even small to moderate seismic events can generate relatively high-frequency ground motions in near-field areas, which may cause destructive effects on low-rise residential buildings.

The attenuation characteristics of ground motions induced by human activities differ significantly from those of typical shallow-crustal earthquakes. In China, research on ground motion attenuation laws related to energy extraction-induced seismicity started late in progress. Most existing studies focus on reservoir-induced seismicity caused by water impoundment, while research on ground motion attenuation laws and prediction models for seismicity induced by fluid injection activities, such as shale gas hydraulic fracturing, remains young. Therefore, developing ground motion prediction models that account for shallow, small-to-moderate induced earthquakes holds significant engineering importance for regions frequently affected by industrial extraction-induced seismicity.

The prediction model presented in this study adopts surface-wave magnitude as the magnitude parameter and hypocentral distance as the distance parameter. It employs a linear magnitude term combined with a near-field saturation factor, which effectively captures near-field distance saturation effects. The model is capable of accounting for depth influence while maintaining consistency with commonly used engineering models and seismic hazard analysis frameworks in China.

Taking the southern Sichuan region of China as an example, this area belongs to a moderate-to-strong seismic zone where small to moderate shallow crustal earthquakes predominantly occur. First, strong-motion data from the NGA-West2 database were collected and compiled. Using the western United States as a reference region, the intensity attenuation relationship for moderate-to-strong seismic zones in China was re-regressed based on recently supplemented intensity data. Subsequently, the intensity analogy method was employed to establish a baseline prediction model for peak ground acceleration suitable for moderate-to-strong seismic zones. By incorporating seismological records of small to moderate earthquakes in southern Sichuan, the baseline model was refined, resulting in the development of a horizontal peak bedrock acceleration prediction model for shallow small to moderate earthquakes in this region.

Data from the high-density broadband seismic network around the industrial areas of southern Sichuan, where seismic activity has been relatively frequent in recent years, were utilized. The dataset covers earthquakes with surface-wave magnitudes ranging from 4.0 to 6.0, recorded between January 2015 and February 2021. A total of 93 free-field bedrock events and 2246 broadband records were selected, with hypocentral distances extending up to 200 km. These data were used to refine the baseline prediction model for moderate-to-strong seismic zones. The final revised model for horizontal peak bedrock acceleration in southern Sichuan is applicable within the magnitude range of 4.0–6.0 and distance range of 0–200 km.

The revised prediction model shows good agreement with the regression data. Comparison with the limited number of local bedrock strong-motion records indicates that the results of this study are reasonably conservative. When compared with internationally commonly used ground-motion models for oil and gas field induced seismicity, the results of this study are similar in the near-field for earthquakes below magnitude 5.0. However, given the broader magnitude-distance range covered by the dataset in this study, the proposed model is expected to offer greater reliability for higher-magnitude events.

This paper proposes a method for developing ground motion prediction models tailored to shallow, small-to-moderate earthquakes closely linked to industrial activities. Taking the industrial extraction region in southern Sichuan as a case study, a horizontal peak bedrock acceleration prediction model was recalibrated, applicable for surface-wave magnitudes ranging from 4.0 to 6.0 and distances up to 200 km. The new model maintains consistency in form with commonly used engineering ground motion prediction models while incorporating depth effects. It effectively extends the lower magnitude limit of existing models and supports refined regional ground motion attenuation predictions.

In the future, more dense and reliable arrays of strong-motion and broadband seismic stations will be able to support further research.