A study of the relations between ML, Me, Mw, apparent stress, and fault aspect ratio

Publication date: Available online 4 July 2019Source: Physics of the Earth and Planetary InteriorsAuthor(s): Robert F. MereuAbstractThe energy magnitude Me used here is based on the square root of the observed seismic trace Lg coda energy. This version of the magnitude is of great interest as it can be used as a more accurate replacement for ML. To-day the moment magnitude Mw is the magnitude that is used particularly for large earthquakes and unlike ML, it does not saturate. In this paper, it is shown that the theoretical “ratio” between the moment magnitude Mw and Me and therefore Mw and ML for an individual earthquake can be determined directly from the earthquake fault aspect ratio β using the equation Mw/Me = p where p = 2/3 (1 + β). In general, since β can vary mathematically from 0 to 1, the corresponding values of the ratio Mw/Me will vary within a limited range (2/3 to 4/3). These variations can account for much of the large scatter of points on observed (Mw, ML) plots. It is also shown that both the apparent stress σa and the corner frequency fc are simple functions of the aspect ratio and magnitude and that these relations have important implications to the self-similar problem. The results of an analysis of 3454 earthquakes from the eastern Mediterranean seismic zone are presented which support the theoretical relations reviewed in this paper.

Source: Physics of the Earth and Planetary Interiors - July 5, 2019 Category: Physics Source Type: research