Seismogenic
5. Conclusions and outlook
5.3. Discussion of future research directions and associated implications
5.3.2. Investigating the mechanics of intershock nucleation and the resulting rupture
stressing rates over the fault.
The experimental results reported inMcLaskey et al.[2014] indicate that only 2-10 smaller-scale seismic events were observed per loading cycle. To match the lack of multiple intershocks occurring on the same patch in a given mainshock cycle, as well as the very small moment magnitudes, our preliminary results indicate that the best fitting parameters for the laboratory intershocks will be low instability ratios (i.e., Dp/h˜∗p ≤1). In addition, we expect that the main property contributing to the small nucleation size of the patches ˜h∗p should be the elevated normal stress σp, with lit- tle or no contribution from a reduced characteristic slip distance Lp, as discussed in Appendix A.2. Further efforts in this direction will involve investigating the model parameters that generate the behavior of the laboratory mainshock and precursory events in detail, with broader implications for the understanding of the seismic ob- servations of heterogeneity on natural faults.
5.3.2. Investigating the mechanics of intershock nucleation and
the nucleation process of the mainshock, and hence the mainshock recurrence time, is sped up or slowed down by the occurrence of intershocks.
Another question to explore as part of this future effort is whether or not the prop- erties of intershocks depend on when they occur in relation to the mainshock. For example, we have already discovered that events with isolation ratios ˜h∗m/Drless that 1 are able to occur early in the mainshock recurrence interval, when the stress distri- bution at the time the intershock initiates is thereby unfavorable for rupture growth (Section 2.5 and Figure 2.10). For the same reasons that isolation ratio is affected, the relative rupture extentDr/Dp for an intershock in a given fault model should also depend on the relative timing within the mainshock recurrence interval. For example, we expect that intershocks occurring in the latter half of the interseismic period of the mainshocks should have a larger rupture extent, as the conditions would be more favorable for rupture growth because much of the fault has already pre-slipped from the protracted nucleation of the mainshock. The approach for investigating this ques- tion could be to analyze the rupture extents for groups of intershocks that fall into bins of the latter half and quarter of the mainshock recurrence interval (i.e., [tr/2, tr] and [tr/4, tr]) and compare the rupture extents to those from the first half ([0, tr/2]). In the same vein, we could also compare the average number of intershocks per mainshock cycle to the average isolation ratio. The motivation for this analysis is to further explore the separation of scales corresponding to faults that experience many intershocks per cycle (and consequently have the most foreshock-like events with re- spect to their timing), which thereby have the most potential forecasting power due to the plethora of precursory signals.
Yet another topic to consider within this topic of future work is the interaction between intershocks. Over the progression of a given interseismic period of the main- shock, intershocks can occur and the extent of their interaction may increase as the extent of the pre-slipped region of the seismogenic zone increases, allowing for easier
communication between intershocks in the form of post-seismic slip (e.g., Figure 2.8 and Figure A.3). In addition, the interaction between intershocks is influenced by the spacing between the patches of higher normal stress. The investigation in this part of the effort would also relate to the consideration of loading effects in the topic proposed in Section 5.3.1.
Variation in the parameters used in the simplified stress drop calculation
The simplified stress drop calculation that we derive in Section3.4has been successful in explaining the main features in the dependence of stress drop on patch normal stress ratio. This formulation (e.g., Equation3.5) relies on values of three parameters (Equation3.3) –γ, which relates the relative rupture extent to the normal stress ratio;
νp, which relates the shear stress change on the patch to the patch normal stress; and νm, which similarly relates the shear stress change in the ruptured area outside of the patch to the background normal stress – and these parameters have been treated as constants, so far. However, we suspect that γ, νp, and νm are dependent on the rate-and-state parametersa and b. Moreover, we have uncovered evidence that these parameters are also dependent on the patch instability ratioDp/˜h∗p, with the values of all three being higher for higherDp/˜h∗p (e.g., blue symbols in Figure3.4a, Figure3.8a, and Figure3.9). In this effort, we would further investigate these dependencies, which have consequences for understanding the stress changes over the ruptured area in heterogeneous environments. Furthermore, it would be particularly useful to explore ways to derive values of these parameters based directly on frictional properties of the fault, such as a, b, background normal stress σm, normal stress ratioσp/σm, and shear modulus µ, in contrast to estimating the values from least-squares fitting to the simulation results. In addition, this improved understanding of the mechanics of intershock ruptures can also be utilized to better translate the value of stress drop into information about the fault properties and conditions at the source.
Predictive value of intershocks
The idea of this future direction is to further explore the possibility of identifying the differences between precursory events that are actually leading to the upcoming main- shock (foreshocks) and those that are not (background seismicity), thereby assessing the conditions under which intershocks have predictive value. To do so, we would create heterogeneous fault models that have a more realistic geometry, which would include many patches that have relatively low instability ratios, contributing to main- taining a sufficient separation in length scales. In addition, we could vary the spacing between the patches (and hence the quantity of patches) in a grid-like placement, or even increase the complexity of the model further by having a heterogeneous non- grid-like patch placement, or assigning a variety of properties to the patches within the same fault (i.e., the patch properties such as instability ratio Dp/˜h∗p, etc. would no longer be identical). Another variable to explore is the effect of loading rate on the resulting behavior. Consequently, the efforts in this work would rely on what we have learned from our simulations so far about the mechanics of intershocks to choose the model properties carefully, as these larger models will be much more computa- tionally expensive. The results of this investigation would have direct implications for the potential of earthquake forecasting, which also relates closely with all three sub-topics of the avenue proposed in Section 5.3.2: (1) the effect of intershocks on the recurrence interval of the mainshocks, (2) how the properties of the intershocks depend on their timing relative to the mainshock, and (3) the interaction between intershocks.