Mechanics of dip‐slip faulting in an elastic half‐space

Abstract

The mechanics of dip‐slip faulting is examined using a model of a crack in a plane strain elastic half‐space loaded by remote stresses: vertical stresses are equal to the overburden and horizontal stresses are the sum of a constant (c) times the overburden and a depth‐independent term σtect, which may be compressive or tensile. Opening is allowed in response to local tension, and slip on closed regions is governed by Mohr‐Coulomb conditions. Because regions of opening and slip, in general, must be determined as part of the solution, relative displacements and stress intensity factors are calculated by iterative solution of integral equations. If the fault is not too shallow (h/L > 0.3, where h is the depth of the upper end of the slip zone and L is the length along dip) and the Coulomb stress (the shear stress minus the friction coefficient ƒ times the effective normal stress) is of one sign over most of the fault, simple approximations suffice. Use of these approximations and the criterion that the energy release rate equals a critical value demonstrates that updip propagation is unstable if the slip zone length exceeds a minimum value. For typical values of ƒ dip angle, and c, the slip zone will be locked below a certain depth. In general, the depth at which the Coulomb stress changes sign underestimates the locking depth, but the magnitude of the difference decreases as the depth of the sign change approaches the lower end of the slip zone. For shallow slip zones, h/L < 0.3, slip induces changes in both shear and normal stresses on the slip surface. For reverse (normal) slip, this coupling reduces (increases) the compressive normal stress and amplifies (diminishes) slip near the upper end of the slip zone surface. For extensional loading (σtect < 0), opening can occur for shallow embedded zones and, more prominently, for surface breaking zones. Although the shear stress drop is nonuniform in this model, calculations reveal that unless fault opening occurs, the surface displacement is well‐approximated by that due to a uniform shear stress drop equal to the average.

Off-Fault Secondary Failure Induced by a Dynamic Slip Pulse

“…For example, from seismic inversions, Guatteri et al (2001) estimate 1.5 MJ/m 2 for the 1995 Kobe earthquake, consistent also with Ide (2002); Olsen et al (1997) and Peyrat et al (2001) estimate 5 MJ/m 2 for the 1992 Landers earthquake. The results are also generally consistent with MJ/m 2 range estimates of G for large events from analyses of large earthquake initiation and arrest (Aki, 1979;Li, 1987;Rudnicki and Wu, 1995).…”

Simple Crack Models Explain Deformation Induced by Subduction Zone Megathrust Earthquakes

“…3b). Surface ruptures can produce larger slip (by a factor of 2 or more) than buried ruptures, even with the same stress drop and source dimension (Rudnicki and Wu, 1995;Geist and Dmowska, 1999, and references therein). The larger absolute slip may dominate over the effect of a more horizontal displacement direction, leading to huge tsunami excitation by surface ruptures.…”

“…Its maximum slip is located at the up-dip end, that is, where the fault intersects the free surface. Theoretical and numerical backgrounds for this half-crack model can be found in related studies (Rudnicki and Wu, 1995;Oglesby et al, 1998;Geist and Dmowska, 1999), whereas only in this study is this model systematically applied for understanding deformation induced by surface-breaking megathrust earthquakes. An intermediate type of rupture, characterized by incipient slip at the surface and major slip at depth, is not considered in this study.…”

Verification of an ADER-DG method for complex dynamic rupture problems

“…2a captures the acceleration of rupture velocity after supershear transition. Figure 2b shows the normal stress variation caused by the interaction of the nonvertical fault with Earth's free surface, investigated e.g., by Rudnicki and Wu (1995), Dalguer et al (2001), Ma and Archuleta (2006), Andrews et al (2007), Ma and Beroza (2008). We find differences in the evolution of stresses after 10 s: the FEM solution reaches higher normal and along-dip shear stresses leading to a slight difference in slip rate.…”