Distribution of stress drop, stiffness, and fracture energy over earthquake rupture zones

Using information provided by slip models and the methodology of McGarr and Fletcher (2002), we map static stress drop, stiffness (k = ????/u, where ???? is static stress drop and u is slip), and fracture energy over the slip surface to investigate the earthquake rupture process and energy budget. For the 1994 M6.7 Northridge, 1992 M7.3 Landers, and 1995 M6.9 Kobe earthquakes, the distributions of static stress drop show strong heterogeneity, emphasizing the importance of asperities in the rupture process. Average values of static stress drop are 17, 11, and 4 Mpa for Northridge, Landers, and Kobe, respectively. These values are substantially higher than estimates based on simple crack models, suggesting that the failure process involves the rupture of asperities within the larger fault zone. Stress drop as a function of depth for the Northridge and Landers earthquakes suggests that stress drops are limited by crustal strength. For these two earthquakes, regions of high slip are surrounded by high values of stiffness. Particularly for the Northridge earthquake, the prominent patch of high slip in the central part of the fault is bordered by a ring of high stiffness and is consistent with expectations based on the failure of an asperity loaded at its edge due to exterior slip. Stiffness within an asperity is inversely related to its dimensions. Estimates of fracture energy, based on static stress drop, slip, and rupture speed, were used to investigate the nature of slip weakening at four locations near the hypocenter of the Kobe earthquake for comparison with independent results based on a dynamic model of this earthquake. One subfault updip and to the NE of the hypocenter has a fracture energy of 1.1 MJ/m2 and a slip-weakening distance, Dc, of 0.66 m. Right triangles, whose base and height are Dc and the dynamic stress drop, respectively, approximately overlie the slip-dependent stress given by Ide and Takeo (1997) for the same locations near the hypocenter. The total fracture energy for the Kobe earthquake, 3.7 ?? 1014 J, is about the same as the seismic energy (Ea = 3.2 ?? 1014 J.