This paper presents a spatio-temporal binary grid-based clustering model for determining complex earthquake clusters with different shapes and heterogeneous densities present in a catalog. The 3D occurrence of earthquakes is mapped into a 2D-low memory sparse matrix through a grid mechanism in the binary domain with consideration of spatio-temporal attributes. Then, image-transformation of a non-empty sets binary feature matrix, a clustering strategy is implemented with logical AND operator as similarity measure among the binary vectors. This approach is applied to solve the problem of seismicity declustering which separates the clustering and non-clustering patterns of seismicity for real-world earthquake catalogs of Japan (1972–2020) and Eastern Mediterranean (1966–2020). Results demonstrate that the proposed method has a significant reduction in both computation and memory footprint with few tuning parameters. Background earthquakes have an impression on the homogeneous Poisson process with fair memory-less characteristics in the time domain as evident from graphical and statistical analysis. Overall seismicity and observed background activity both have similar multi-fractal behavior with a deviation of \(\pm 0.04\). The comparative analysis is carried out with benchmark declustering models: Gardner–Knopoff, Uhrhammer, Gruenthal window-based method, and Reasenberg’s approach, and superior performance of the proposed method is found in most cases.

本文提出了一种基于时空二元网格的聚类模型，用于确定目录中存在的具有不同形状和异质密度的复杂地震群。考虑时空属性，通过二元域中的网格机制将3D地震发生映射到2D低记忆稀疏矩阵。然后，对非空集二元特征矩阵进行图像变换，以逻辑与运算符作为二元向量之间的相似性度量来实现聚类策略。该方法用于解决地震活动分簇问题，将日本（1972-2020）和东地中海（1966-2020）现实世界地震目录的地震活动的聚类和非聚类模式分开。结果表明，所提出的方法在调整参数很少的情况下显着减少了计算和内存占用。从图形和统计分析中可以明显看出，背景地震对时域中具有相当无记忆特征的均质泊松过程有影响。总体地震活动和观测到的背景活动都具有相似的多重分形行为，偏差为\(\pm 0.04\)。与基准去簇模型：Gardner–Knopoff、Uhrhammer、Gruenthal 基于窗口的方法和 Reasenberg 方法进行了比较分析，在大多数情况下发现该方法具有优越的性能。