The spatial-temporal clustering by fast search and find of density peaks (ST-CFSFDP) algorithm faces several critical limitations. Its local density calculation struggles to distinguish density variations within regions, leading to erroneous cluster centers selection. The assignment strategy lacks sufficient spatial-temporal constraints, causing misassignment of non-peak points that exhibit significant temporal differences despite spatial proximity. Furthermore, the absence of an independent noise identification mechanism renders noise detection entirely dependent on sample assignment accuracy, significantly degrading precision when assignment errors occur. In order to address these challenges, this paper proposes a spatial-temporal density peak clustering with shared neighbors weighting and membership point allocation (SNMP-STDPC) algorithm. A shared nearest neighbors weighting strategy is introduced to construct a spatial-temporal distance similarity matrix, which precisely reflects density differences among samples and enhances the reliability of density peak identification. The algorithm incorporates enhanced spatial-temporal constraints leveraging shared nearest neighbors, categorizing non-peak points into must-link points and may-link points to ensure accurate sample assignment. Additionally, a novel noise identification mechanism is proposed, calculating sample anomaly scores and employing a dynamic threshold to significantly improve noise identification effectiveness. The SNMP-STDPC algorithm is compared with current mainstream spatial-temporal clustering methods on simulated datasets, and it is further applied to identify foreshock-aftershock sequences in real-world seismic observation data. Experimental results demonstrate that the SNMP-STDPC algorithm significantly enhances clustering performance on synthetic datasets and delivers robust results on real-world data.