Citation
Perry, Stephen Michael (2018) Analyzing Stress Change and Energy Budget of Earthquakes Through PhysicsBased Modeling. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ryhteb75. https://resolver.caltech.edu/CaltechTHESIS:06062018071106334
Abstract
Researchers use concepts such as stress drop, breakdown energy, and available energy to describe earthquakes sources and study earthquake physics. These quantities represent the spatially and temporally varying dynamic events by single, eventaveraged values. They are inferred indirectly from observations, often based on simplified models. Thus, their relationship to fault constitutive properties, which are local on the fault, is not straightforward.
Here, we use simulations of earthquake sequences in fault models with friction laws motivated by laboratory experiments to examine how the eventaveraged observables arise from spatially and temporally varying earthquake rupture. In particular, we consider whether several typically used fault mechanisms, such as rateandstate friction, thermal pressurization of pore fluids, and flash heating, are consistent with common observations such as magnitudeinvariant stress drop, increasing breakdown energy with the event size, and radiation efficiencies of ~0.5.
Stress drops, observed to be magnitude invariant, are a key characteristic used to describe natural earthquakes. Theoretical studies and lab experiments indicate that dynamic weakening, such as thermal pressurization of pore fluids, may be present on natural faults. At first glance, these two observations seem incompatible, since larger events may experience greater weakening and should thus have lower final stresses. We hypothesize that dynamic weakening can be reconciled with magnitudeinvariant stress drops due to larger events having lower average prestress when compared to smaller events. The additional weakening would allow the final stresses to also be lower, but the stress drops may be similar.
To explore this hypothesis, we study longterm earthquake sequences on a rateandstate fault segment with enhanced dynamic weakening due to thermal pressurization using a fully dynamic simulation approach with a seismogenic segment that has uniform friction properties. Our results show, for a range of event sizes, that such models can explain both observationally inferred stress drop invariance and breakdown energy increase with event magnitude. Smaller events indeed have larger average initial stresses than mediumsized events, and we get nearly constant stress drops for events spanning up to five orders of magnitude in seismic moment. Segmentspanning events have more complex behavior, which is dependent on the properties of the velocitystrengthening (VS) region at the edges of the fault. Models with large values of velocity strengthening in their boundary regions do not allow ruptures to propagate much into the velocitystrengthening region, thus containing the rupture area and leading to higher stress drops for a larger amount of slip. Decreasing the velocity strengthening of the boundaries leads to farther rupture propagation into the velocitystrengthening region and thus lower stress drops.
In all models with the thermal pressurization of pore fluids that we have examined, both the smaller and segmentspanning events exhibit increases in breakdown energy consistent with observations. The breakdown energy is the portion of the dissipated energy that governs the event dynamics, analogous to the fracture energy concept of fracture mechanics. The increase in the breakdown energy is due to continuous weakening of the fault with slip, as hypothesized in previous analytical studies.
We also examine the accuracy of seismically estimated breakdown energies G_{SE} for a range of models, by comparing the values computed directly from our fault models and indirectly from seismically available observations. Observationally, G_{SE} is typically obtained as the difference between the seismically estimated available energy ΔW_{0} per unit area and radiated energy E_{R}. This defines the available energy ΔW_{A} as the sum of the breakdown energy and radiated energy. However, the seismically estimated available energy ΔW_{0} is obtained as onehalf of the product of the (average) stress drop and (average) final slip, based on a simplified model. As such, we examine the relation between the actual available energy ΔW_{A} and its seismic estimate ΔW_{0} in our models. We find that, as rupture mode changes from cracklike to pulselike, the actual available energy ΔW_{A}, becomes increasingly larger that the seismically estimated available energy ΔW_{0}, due to significant and increasing stress undershoot characteristic of pulselike ruptures. The extra available energy for more pulselike ruptures either makes the breakdown energy much larger than its seismically estimated value, or makes the radiated energy much larger than the seismically estimated available energy ΔW_{0}, or both. In the two latter cases, the radiation ratio η (sometimes called radiation efficiency) between the radiated energy and seismically estimated available energy increases beyond 1, consistent with some observations that were previously thought to be aphysical.
Overall, we find that models with rateandstate friction and thermal pressurization of pore fluids, when resulting in continuous weakening of fault with slip and cracklike ruptures, produce events with magnitudeinvariant stress drops, increases in breakdown energies with the event sizes consistent with observations, radiation ratios consistent with observations, and available energies similar to the ones inferred seismically. More pulselike ruptures, which result occasionally in such models and reliably in models that incorporate more severe enhanced weakening motivated by flash heating, have increasingly more significant undershoot and hence extra energy available for breakdown and radiation compared with the seismically estimated available energy. Therefore, current seismic estimates of their breakdown energy and radiation ratio are not reliable. More work is needed to understand the energy budget of pulselike events obtained in realistic fault models, especially since one of the common paradigms in earthquake physics is that many large events occur as pulselike ruptures.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  breakdown energy, earthquake, energy budget, stress change, dynamic weakening, thermal pressurization, available energy, rateandstate  
Degree Grantor:  California Institute of Technology  
Division:  Geological and Planetary Sciences  
Major Option:  Geophysics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  21 February 2018  
NonCaltech Author Email:  stephenperry3 (AT) gmail.com  
Record Number:  CaltechTHESIS:06062018071106334  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:06062018071106334  
DOI:  10.7907/ryhteb75  
ORCID: 
 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  11027  
Collection:  CaltechTHESIS  
Deposited By:  Stephen Perry  
Deposited On:  06 Jun 2018 20:09  
Last Modified:  04 Oct 2019 00:22 
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