A complete solution of a one‐dimensional propagating fault with nonuniform stress and strength

Abstract

We have investigated details of the dynamics of faults with strongly variable stress and frictional strength. These factors are in all likelihood responsible for nonuniform fault slip, multiple events, random ground acceleration, and the earthquake frequency‐magnitude relation. In order to obtain a full dynamic solution to greatly heterogeneous faulting we used a one‐dimensional continuum model in which stress and strength varied along the fault. The results show that the process of rupture in a heterogeneous system is closely linked to the stopping phase of the motion, or the healing process of faults. The process, which may involve strong nonlinear effects such as discontinuous motion, cannot be seen in static models and requires a dynamic approach with a numerical scheme which remains stable at high frequencies. We have used the method of characteristics to obtain the results in this paper. We found that heterogeneous rupture can be due to either initially nonuniform stress or spatially nonuniform frictional strength. However, nonuniform stress drop—the difference between tectonic stress and frictional stress—tends to become smoother with increasing slip. After some initial heterogeneous sliding, fault slip in the model becomes uniform and repetitious, a condition which is clearly not observed in nature. Spatially variable strength, however, can produce and maintain a heterogeneous stress drop. We found that when the strength was sufficiently variable from place to place, the final stress was statistically at least as variable as the initial stress. This means that the character of fault activity can remain heterogeneous with time; this would conform to the behavior observed in situ. We conclude therefore that spatially variable fracture energy may in fact be responsible for the heterogeneous nature of earthquake faulting. Nonuniform stress by itself cannot maintain with time the heterogeneous nature of faults. The model is applied to the irregular slip distribution of the Borrego Mountain (Coyote Creek), California, earthquake of April 1968 and reveals links among irregular rupture propagation, multiple events, fault slip, and stress drop.

Location of largest earthquake slip and fast rupture controlled by along‐strike change in fault structural maturity due to fault growth

“…The distribution of fault strength is also expected to contribute to the earthquake slip asymmetry. Prior works have suggested on a theoretical basis that earthquake slip distributions might be controlled by strength and stress variations along fault planes [e.g., Das and Aki , ; Nur , ; Israel and Nur , ; Madariaga , ; Bürgmann et al ., ; Boatwright and Cocco , ; Cooke , ; Noda and Lapusta , ; Kaneko et al ., ]. The reduction of on‐fault slip deficit at intersegments in the direction of greater maturity leads to longer fault segments in that direction (see Bohnhoff et al .…”

“…Earthquake slip asymmetry is a generic feature, and therefore, our objective here is to identify the deterministic, generic factors that might control it. Slip heterogeneity may arise from heterogeneities of stress or material properties, including fault friction properties, fluid‐related fault zone properties, and elastic stiffness of the host rock [e.g., Nur , ; Israel and Nur , ; Madariaga , ; Bürgmann et al ., ]. Prior studies have shown that certain structural properties of faults affect significantly the properties of the earthquakes they host, such as their slip amplitude and rupture length [ Manighetti et al ., ], magnitude [ Anderson et al ., ], magnitude‐frequency distribution [ Stirling et al ., ], apparent stress drop [ Cao and Aki , ; Choy and Kirby , ; Manighetti et al ., ; Hecker et al ., ], number of broken segments [ Wesnousky , ; Manighetti et al ., ], and ground motion amplitudes [ Radiguet et al ., ].…”

Earthquake sequences on a frictional fault model with non-uniform strengths and relaxation times

“…Several investigators have also noticed the importance of heterogeneity and attempted to take it into their models (e.g. Dieterich 1972a; Knopoff, Mouton & Burridge 1973;Das & Aki 1977;Nur 1978;Israel & Nur 1979).…”

Microearthquakes in the TDP swarm, Turkey: clustering in space and time

“…We suggest therefore that seismic activity on the small individual fault planes, or asperity facets, on which these clusters of events occur is short-lived, existing for periods of the order of weeks or at most a few months. Theoretical studies (for example by Aki 1979 andIsrael andNur 1979) suggest that stress concentrates along a fault at barriers and asperities. Clusters, or families, of earthquakes with identical or near-identical seismograms (doublets) have been described from Japan (Tsujiura 1983) and the USA (Ishida and Kanamori 1980;Geller and Mueller 1980).…”