Global constraints on detectable coherent linear migration in statistically defined Earthquake clusters

Persistent space–time migration is widely documented in individual earthquake sequences, but its detectability across a global population of clustered seismicity remains poorly constrained. Here, I quantify persistent, approximately linear epicentral migration in statistically defined earthquake clusters identified from the USGS ComCat catalogue over 1980–2024. The analysis uses 352,852 earthquakes with generic catalogue magnitude M ≥ 3.5 and hypocentral depth 0 – 40 km. Earthquakes are grouped using a reproducible density-based space–time clustering procedure (DBSCAN) procedure, yielding 315 clusters with N ≥ 30 events. For each cluster, epicentres are projected onto the first principal spatial axis and the sequence-scale distance–time relation is characterized by the absolute apparent migration velocity | v | and linear coherence R 2 . A pre-defined kinematic screen, R 2 ≥ 0.30 and | v | ≥ 0.5 kmda y − 1 , identifies 17 candidates (5.40%). All 17 remain significant under within-cluster time-permutation tests after Benjamini–Hochberg correction across all 315 clusters. Event-resampling bootstrap analysis reduces this set to three sampling-stable cases, and subsequent model-form diagnostics distinguish two clusters exhibiting robust approximately linear migration from one case characterized by nonlinear or reversing evolution. Thus, only 2 / 315 clusters (0.63%) satisfy the full set of criteria for robust approximately linear migration. Sensitivity tests across catalogue magnitude thresholds, space–time clustering scales, kinematic thresholds, and epicentral-location perturbations show that the population-level result is not attributable to a single parameter choice, although individual-cluster classification remains resolution dependent. These results constrain the frequency with which persistent linear migration is detectable at the magnitude, spatial, and temporal resolution of a heterogeneous global catalogue. They do not quantify the prevalence of nonlinear, episodic, radial, multi-directional, or microseismic migration, nor do they imply that clusters without a detected coherent linear component lack physically meaningful migration processes.