Dr. Bruce Shaw
Earth Institute Contact: Dr. Bruce Shaw
Two recent large earthquakes, the 1992 Mw7.3 Landers earthquake and the 1999 Mw7.4 Izmit earthquake, illustrate one of the central issues for earthquake studies: how big of an earthquake can a fault support, and what stops it? The 1992 Landers event broke multiple segments, jumped some substantial stopovers, and then terminated in the middle of a segment. The 1999 Izmit earthquake broke multiple segments as well. This question of how large an event a fault supports plays a critical role in estimating earthquake hazard, by having a big effect on estimating how often moderately large but nevertheless damaging earthquakes, magnitudes 6’s and 7’s, occur [WGCEP 1988; 1990; 1995].
Recognizing the potential significance of the mechanical effects of geometrical heterogeneities on faults, a standard procedure has been to break up faults into segments separated by geometrical discontinuities, and then to examine the consequences of various scenarios for the segments failing either independently or together. This gives some guide as to a range of possible behaviors one might expect. However, it unfortunately gives us no information about how likely any of the scenarios are – a crucial ingredient for obtaining quantitative hazard estimates. Further, as Landers aptly illustrated, there are no guarantees the faults will even respect the segment boundaries anyway. Thus, while we have some of the mechanical perturbations caused by geometrical irregularities, such as dilational and compressional jobs, we have much to learn about how this plays out in a dynamical context, particularly over the long haul.
Theoretical advances in the last decade have opened up studies of dynamics on nonplanar faults. Both finite differences [Harris et al. 1991: Harris and Day, 1993; 1999; Kase and Kuge, 1998; Magistrale and Day, 1999] and boundary integral equations [Koller et al; 1992; Tada and Yamashita, 1996; Kame and Yamashita, 1997; Bhouchon and Streiff, 1997; Seelig and Gross, 1997; Tada et al, 2000; Aochi et al, 2000] have been successfully used. Examining segmentation issues, Harris and Day [1993; 1999] looked at parallel planar faults separated by a gap, and studied the abilities of ruptures to jump the gap. Magistrale and Day  looked at parallel offset thrust fault segments and the ability of ruptures to propagate from one to the other when there either was or was not a connecting tear fault.
All of these nonplanar fault studies, thus far, have been for individual ruptures. This has some advantages, but some important limitations as well. One advantage is that in devoting all of one’s numerical resources to a single event, greater grid resolution can be used. Another advantage is one can try to reconstruct a specific event, by playing with the fault properties, with the constitutive equations, and initial conditions, to recreate a rupture which appears to match the specific event.
The limitations of studying an individual event is we are again left without an answer as to whether a rupture will continue or not; if a point on a fault is close enough to failure initially, a rupture will continue to propagate through, but we have no constraints on what the initial conditions are.
This limitation disappears when we model sequences of events. The initial conditions are no longer free to be specified, but are instead given by conditions left from the previous ruptures. This has a number of advantages. First, there are fewer things to be specified. Second, the initial conditions are more properly representative and more deeply consistent with the dynamics of the system. This occurs for the following reason. Earthquakes happen on faults over which there have been many, many previous events. There is time, therefore, for the system to evolve beyond whatever arbitrary initial condition from which it began to a state which is compatible with the dynamics in the long term. Thus earthquakes will lie on an attracting subspace, not the huge transient space of all possible initial conditions. This means that there is a deep relationship between the “initial condition” at a later time and the boundary conditions, coupled through the dynamics. That is, if we treat the value of the field at a later time as an initial condition for the future development, not all initial conditions are possible. The boundary conditions and the initial conditions are not, in effect, independently specifiable degrees of freedom for representative, nontransient events.
By studying long sequences of events, not only do we get events which are more representative of the dynamic system, but we get long sequences on which we can ask statistical questions. We also gain information about the relative timing of events, most specifically the repeat times for large events, information one cannot get when considering only individual ruptures. Thus, despite the main disadvantage of this approach, which is the substantial increase in computational cost of solving for many events, we end up with a tool that will allow us to begin to address for the first time some fundamental questions of earthquake hazards, regarding the sizes of events on geometrically inhomogeneous faults, and the time intervals between them. These models will allow us to inject additional physically based information into current statistically based studies [Field et al, 1999; Andrews and Schwerer 2000].
Cross Cutting Themes:
Hazards and Risk
Southern California Earthquake Center (SCEC)