Precursory stress changes before large earthquakes; on a new physical law for earthquakes

Abstract

In this article, we first review the progress in our understanding of tectonic stresses in the Earth's crust achieved in last three to four decades. We briefly review the literature on roughly four groups of studies; (1) World's Stress Map project (WSM), (2) fault-slip data and paleostress analyses, (3) Coulomb stress transfer, and (4) theories of the generalized continua with emphasis on the Cosserat continuum. Based on these studies, we develop a new numerical algorithm to calculate tectonic strain rate, tectonic stress, and normalized tectonic shear stress fields from the earthquake focal mechanisms. We show that this field changes over time, and is therefore far from being constant. Further on, we focus our efforts on the analysis of the relationship between the magnitudes of the earthquakes and the normalized tectonic shear stress. We discover a new and previously unknown physical law, which we call the maximum magnitude law (MM-law). We discuss further the origin and physical background of this law and its importance in earthquake studies.