Theoretical studies on earthquake source dynamics are a challenging task. The essence of such studies is the effort to clarify the possible effects of a small number of ingredients (e.g., material contrast, fluid pressurization, melting, gel formation, plastic deformation, etc.) on the process of spontaneous rupture propagation. Simulations that incorporate many ingredients simultane- ously may appear superficially better, but are often not useful because it is not possible to obtain clear quantitative knowledge (i.e., specific ranges of parameters that lead to different dynamic regimes) from such simulations as long as the multi-dimensional parameter-space associated with a more realistic model becomes essentially too large to be efficiently explored.
Due to the high complexity and multi-dimensionality of the non-linear physical processes involved in earthquake source dynamics (as discussed in chapter 2) and the large diversity of propagation phenomena associated with even relatively simple models (e.g., Coulomb or slip- weakening friction on a planar bimaterial fault) with relatively small degrees of freedom (as discussed in chapters 3 & 5) additional new and intensified measurements need to be accom- plished in the laboratory, as well as in the field, to better constrain parameters of existing phys- ical models. Besides, new theoretical concepts need to be developed in the long run, aiming a better understanding of what controls earthquake fault rupture.
In matters of the study presented, several future lines of investigations are arising.
For instance, the generality of the tendencies of rupture migration in fault zone typical struc- tures (as studied in chapter 3) should be tested in future simulations incorporating additional levels of realism in the assumed structure (e.g., dimensionality) and rheology (e.g., slip- and rate-dependent friction). The observed localization of slip at material discontinuities (Chester and Chester, 1998) are certainly compatible with the simulations performed in chapter 3 of this study.
The example in section 5.3.2 of chapter 5 demonstrated the potential of relatively slow rup- ture propagation phases being supported in the dynamically favored direction. Hence, the role of material contrasts on the nucleation phase, which was neglected here using an instantaneous overstressed patch on the fault, is a potentially fruitful line of future research. Yamashita (2007) showed that postseismic quasi-static fault slip due to pore pressure change on a bimaterial inter- face can advance postseismic slip. This suggests that the influence of the bimaterial mechanism
on the nucleation might be significant. Therefore it may also become interesting to study how much the behavior of earthquake cycles is diversified assuming bimaterial faults. Is the switch- ing between seismologically quiet and active times different in bimaterial fault systems?
As mentioned before, local permeability contrast across the fault can also produce asym- metric rupture (Rudnicki and Rice, 2006) as well as asymmetry of aseismic slip (Yamashita, 2007). The effect of poroelastic material can principally enhance or inhibit elastic bimaterial effects. More precisely, the two effects enhance each other if the compliant side is more perme- able, and oppose each other if the stiff side is more permeable. The two effects have comparable magnitudes for parameters representative of natural faults (a wave-speed contrast of about 5 – 10% and a factor-of-ten permeability contrast)(Dunham and Rice, 2008). Certainly such results should be accounted for when interpreting observations as well as synthetics.
Wrinkle-like pulses generate high off-fault yielding stresses that should trigger anelastic deformation close to the source (Andrews, 2005). Such off-fault yielding reduces the amplitudes of the emenating wavefield. Pure elasticity maximizes the impact of the wrinkle-like pulse. In order to upgrade the robustness of the results presented in this study, additional non-elastic off-fault rheology should be incorporated for the cases of very high off-fault stress.
Another issue that arises is the possibility of fault opening, the implied loss of shear resis- tance to slip, and its quantification for events with large rupture propagation distances. Which mechanisms prevents opening (e.g., plastic deformation)? How likely is tensile crack propaga- tion and which are the geological indications (e.g., pulverization of rocks (Dor et al., 2006a))?
The robustness of the mechanism generating wrinkle-like pulses with respect to regular- ization parameters should also be addressed in future studies. The values of regularization parameters for natural faulting remain uncertain. In chapter 5 the regularization parameterLis of the same order as the range of critical slip distancesDc. A raisingLreduces the instability
assiociated with the material contrast (bimaterial effect), while raisingDcreduces frictional in-
stability. A more thorough exploration ofL/Dc-ratio in future studies needs to be done. Since
theLandDcare rather empirical parameters, physical constraints on theses parameters or even
a physical replacement of these parameters are desired.
For large earthquakes there exists deviations from the approximate scale-invariant scaling relations associated with relatively small earthquakes (Ben-Zion, 2008). A potential future investigation could also reveal the contribution of bimaterial faults on such deviations from scale invariant scaling relations.
The study presented here has the aim of highlighting the importance of material discontinuities and its diversifying effect on comparatively simple physical models. For this the widely exem- plary approach of this study is suitable. However, efforts on trying to make parameters studies more systematic need to be done. Possibly this requires the incorporation of scaling relations and discussions on the basis of non-dimensional characteristic values instead of potentially scale dependent values.