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Analyzing Stress Change and Energy Budget of Earthquakes Through Physics-Based Modeling


Perry, Stephen Michael (2018) Analyzing Stress Change and Energy Budget of Earthquakes Through Physics-Based Modeling. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ryht-eb75.


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, event-averaged 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 event-averaged observables arise from spatially and temporally varying earthquake rupture. In particular, we consider whether several typically used fault mechanisms, such as rate-and-state friction, thermal pressurization of pore fluids, and flash heating, are consistent with common observations such as magnitude-invariant 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 magnitude-invariant 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 long-term earthquake sequences on a rate-and-state 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 medium-sized events, and we get nearly constant stress drops for events spanning up to five orders of magnitude in seismic moment. Segment-spanning events have more complex behavior, which is dependent on the properties of the velocity-strengthening (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 velocity-strengthening 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 velocity-strengthening region and thus lower stress drops.

In all models with the thermal pressurization of pore fluids that we have examined, both the smaller and segment-spanning 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 GSE for a range of models, by comparing the values computed directly from our fault models and indirectly from seismically available observations. Observationally, GSE is typically obtained as the difference between the seismically estimated available energy ΔW0 per unit area and radiated energy ER. This defines the available energy ΔWA as the sum of the breakdown energy and radiated energy. However, the seismically estimated available energy ΔW0 is obtained as one-half 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 ΔWA and its seismic estimate ΔW0 in our models. We find that, as rupture mode changes from crack-like to pulse-like, the actual available energy ΔWA, becomes increasingly larger that the seismically estimated available energy ΔW0, due to significant and increasing stress undershoot characteristic of pulse-like ruptures. The extra available energy for more pulse-like 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 ΔW0, 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 rate-and-state friction and thermal pressurization of pore fluids, when resulting in continuous weakening of fault with slip and crack-like ruptures, produce events with magnitude-invariant 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 pulse-like 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 pulse-like events obtained in realistic fault models, especially since one of the common paradigms in earthquake physics is that many large events occur as pulse-like ruptures.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:breakdown energy, earthquake, energy budget, stress change, dynamic weakening, thermal pressurization, available energy, rate-and-state
Degree Grantor:California Institute of Technology
Division:Geological and Planetary Sciences
Major Option:Geophysics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lapusta, Nadia
Thesis Committee:
  • Avouac, Jean-Philippe
  • Tsai, Victor C. (chair)
  • Zhan, Zhongwen
  • Lapusta, Nadia
Defense Date:21 February 2018
Non-Caltech Author Email:stephenperry3 (AT)
Record Number:CaltechTHESIS:06062018-071106334
Persistent URL:
Perry, Stephen Michael0000-0003-1748-1827
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11027
Deposited By: Stephen Perry
Deposited On:06 Jun 2018 20:09
Last Modified:04 Oct 2019 00:22

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