A critical testing of the applicability of some empirical relations used in the science and engineering of earthquakes through the 2011 Great East Japan earthquake

Many empirical relations have been proposed for estimating the fundamental characteristics of earthquakes and the induced tsunamis as well as for the strong-motion parameters, liquefaction potential, limiting distances for slope failures, damage to underground openings and even the possibility of surface damage due to room and pillar mines and quarries. The 2011 Great East Japan earthquake is probably the only mega-earthquake providing abundant quatitative information for the science and engineering of earthquakes although the rupture observations were obscured. The quantitative data from this earthquake should be quite useful for testing many empirical relations used in the science and engineering of earthquakes as they comprise an almost upper limit for the magnitude of earthquakes. The author compares the available empirical relations utilized for estimating the fundamental characteristics (i.e., relative slip, length, area, duration) of earthquakes as a function of their moment magnitude and attenuation of strong motion parameters such as maximum ground acceleration and velocity. Furthermore, some available empirical relations used from estimating the limiting hypocentral distances for ground liquefaction, slope failures, damage to underground openings and even the possibility of surface damage due to room and pillar mines are compared with observations made during the reconnaissance visits by various researchers including those provided by the author. The available empirical relations are compared with observations and instrumental data, and their applicability and limits are critically discussed in this article.