https://ojs.acad-pub.com/index.php/JAM <p><em>Journal of AppliedMath&nbsp;</em>(JAM) is an international, peer-reviewed open access journal on mathematics. It publishes various article types including Original Research Articles, Reviews, Editorials, and Perspectives. Our aim is to encourage scientists to publish their experimental and theoretical results in as much detail as possible. There is no restriction on the length of the papers. The full account of the research must be provided so that the results can be reproduced.</p> Academic Publishing Pte. Ltd. en-US Journal of AppliedMath 2972-4805 https://ojs.acad-pub.com/index.php/JAM/article/view/1592 <p>The law of energy accumulation in the earthquake focus is presented, together with the temporal, energy and magnitude distributions of regular, background earthquakes. The background seismicity is characterized by two parameters—the seismicity rate and the Gutenberg-Richter parameter, which can be extracted by fitting the empirical earthquake distributions. Time-magnitude and temporal correlations are presented, and the information they can provide is discussed. For foreshocks the time-magnitude correlations can be used to forecast (with limitations) the mainshock. The temporal correlations indicate a decrease of the Gutenberg-Richter parameter for small magnitudes, in agreement with empirical observations for foreshocks. On the other hand, the aftershocks may be viewed as independent earthquakes with changed seismic conditions, so they may exhibit an increase of this parameter, also in accordance with empirical observations. The roll-off effect for small magnitudes and the modified Gutenberg-Richter distribution are discussed for temporal corralations, and the derivation of the Bath’s law is briefly reviewed.</p> Bogdan Felix Apostol Copyright (c) 2025 Bogdan Felix Apostol https://creativecommons.org/licenses/by/4.0/ 2025-01-03 2025-01-03 3 1 1592 1592 10.59400/jam1592