The return period and probabilities of earthquakes occurrence in North-East, India (Eastern-Himalayas) and its vicinity inferred from Gutenberg–Richter relation

North-Eastern (NE), India and its adjoining region is one of the sixth most seismically active regions of the world. In the present investigation, the return period of earthquake and probability of occurrence inferred from Gutenberg–Richter (GR) relation was estimated for NE, India region and its vicinity. When we consider the entire NE, India region and its vicinity, it evidently suggested that the return period of earthquakes of 7 ≤ Mw ≤ 8.6 is short, which ranges from 32.73 to 162.59 years. It was observed that the earthquake occurrence from infinitesimally short interval t~0 for Mw~3.6–4 is embedded with 100% probability. The earthquakes of Mw~4.1–5.3 reach 100% in 10 years. Similarly, Mw~5.4–5.7 reaches to 100% in 20 years. Likewise, Mw~5.8–5.9, 6.0–6.1 and 6.2 reach ~100% in 30, 40 and 50 years, respectively. For large earthquakes of Mw~7.0–8.0, the probability of occurrence reaches >80% in 100 years. This observation strongly indicates that the likelihood of earthquakes occurring in the north-eastern region of India and its surrounding areas tends to increase over time. Further, the region was divided into four zones, namely Block I (26.5–28.5ºN; 89–95ºE), Block II (26.5–28.5ºN; 95–97.5ºE), Block III (23–26.5ºN; 93–97.5ºE) and Block IV (23–26.5ºN; 89–93ºE) based on seismicity and the major tectonic domains of the region. In terms of return period based on GR-relation and stochastic observations, we may conclude that the risk associated with occurrence of earthquake is highest in Block IV, followed by Block III, Block I and Block II respectively. Further, a comparison of the probabilities of earthquake return period considering seismogenic depths along with hypocentral depth data for different blocks was investigated for a comprehensive understanding of seismic occurrences over time. However, overall, the patterns and trends observed remain consistent, emphasizing the seismic activity within each block and its associated return periods. The stochastic observations and findings are elaborately accentuated in the article.