A magnitude-energy relation for large earthquakes

A relation between the magnitude of a shallow earthquake and the rupture parameters is derived by using a result of dislocation theory and assumptions as suggested from model studies: the average of the pre- and post-shock stresses on a fault and the seismic efficiency are approximately constant. Comparing this relation with observations of the rupture parameters for a number of large shallow earthquakes, the magnitude-energy relation log ⁡ E S = α + 1.7 M is obtained. The value of α is estimated to be approximately 10.