On dependence of the source deactivation factor on the magnitude of main earthquake shock
Abstract
We have discovered an inverse relationship between the earthquake source deactivation coefficient and the magnitude of the main shock. Recently, this pattern was confirmed through an analysis of earthquakes in the Central Himalayas (Poudel et al., 2026). On the one hand, independent confirmation of a previously unknown pattern strengthens our confidence in the relevance of the phenomenological theory of aftershocks, upon which we have based our method for processing and analyzing aftershocks. On the other hand, Poudel et al. (2026) presented our method in a distorted manner. Poudel et al. mistakenly believe that our method is based on a modified Omori law. Both circumstances provide an occasion and a basis for a simple and clear explanation of the essence of our approach to the study of aftershocks. First and foremost, our approach to the problem is diametrically opposed to Omori approach. Omori law and its modification, proposed by Hirano and Utsu, describe the decay of aftershocks. In contrast, we formulated and solved the inverse problem. The essence of the inverse problem lies in the need to calculate the source deactivation coefficient based on aftershock observation data, without making any prior assumptions regarding the law governing the decay of aftershocks. A crucial concept in our theory is the rather complex notion of the proper time of a source. Proper time differs radically from astronomical time. The paper describes the continuous and discrete representations of proper time. This paper is methodological in nature and may prove useful to researchers studying the dynamics of an earthquake source following the formation of a main rupture within the rock mass. Keywords: earthquake source, main shock, relaxation, deactivation coefficient, proper time, inverse problem.
Related
- A New Way for Determining Earthquake Magnitude Based on Electromagnetic Radiation
- Attention-based learning for early earthquake magnitude estimation from strong-motion records
- Dependence of seismic hazard assessment on the observation time interval: insights from a synthetic earthquake catalogue in southeastern Spain
- Source Representation and Earthquake-Ocean Coupling in Tsunami Generation by the 2020 Samos Normal-Faulting Earthquake
- Adaptive Inversion Optimization of the Static Factor of Safety for Newmark-Based Earthquake-Induced Landslide Susceptibility Assessment
BibTeX
@misc{guglielmi2026dependence,
title = {{On dependence of the source deactivation factor on the magnitude of main earthquake shock}},
author = {A. V. Guglielmi and A. D. Zavyalov and O. D. Zotov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36775},
eprint = {2610.36775},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36775},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On dependence of the source deactivation factor on the magnitude of main earthquake shock
AU - A. V. Guglielmi
AU - A. D. Zavyalov
AU - O. D. Zotov
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36775
UR - https://arxiv.org/abs/2610.36775
AB - We have discovered an inverse relationship between the earthquake source deactivation coefficient and the magnitude of the main shock. Recently, this pattern was confirmed through an analysis of earthquakes in the Central Himalayas (Poudel et al., 2026). On the one hand, independent confirmation of a previously unknown pattern strengthens our confidence in the relevance of the phenomenological theory of aftershocks, upon which we have based our method for processing and analyzing aftershocks. On the other hand, Poudel et al. (2026) presented our method in a distorted manner. Poudel et al. mistakenly believe that our method is based on a modified Omori law. Both circumstances provide an occasion and a basis for a simple and clear explanation of the essence of our approach to the study of aftershocks. First and foremost, our approach to the problem is diametrically opposed to Omori approach. Omori law and its modification, proposed by Hirano and Utsu, describe the decay of aftershocks. In contrast, we formulated and solved the inverse problem. The essence of the inverse problem lies in the need to calculate the source deactivation coefficient based on aftershock observation data, without making any prior assumptions regarding the law governing the decay of aftershocks. A crucial concept in our theory is the rather complex notion of the proper time of a source. Proper time differs radically from astronomical time. The paper describes the continuous and discrete representations of proper time. This paper is methodological in nature and may prove useful to researchers studying the dynamics of an earthquake source following the formation of a main rupture within the rock mass. Keywords: earthquake source, main shock, relaxation, deactivation coefficient, proper time, inverse problem.
ER -