The Fracture Energy of Earthquakes

Abstract

Summary The arrest of a semi-infinite longitudinal shear crack is caused by either (1) the finiteness of available strain energy, or (2) an increase in fracture energy along the trajectory of the running crack. In the former case the following relationship may be used to evaluate the fracture energy: yo = RAa2/2ptn where yo is the fracture energy per unit length along the crack edge per unit extension of the cracktip (erg cm-2), R is the characteristic radius of the fault (cm), ACJ is the stress drop (dyne cm-2) and p is the rigidity (dyne cm-2). This leads to the following relationship: log Aa = -3 log R +f log (2ptny0) or from the Keylis-Borok relationship (1959): log Mo = 5/2 log R +* log (2ptny0)+0*64 where M, is the seismic moment in dyne cm-'. These two relationships are statistically acceptable for Southern California faults and the TongaKermadec Arc earthquakes. The fracture energy is found to vary from lo3 to lo9 erg cm-' with fresh fracture being associated with 10'-lQ9 erg cm-2 while frictional rupture with 103-107 erg cm-2. These values are in good agreement with other independent estimates.