Recent advances in the use of thermal proxies provide a window into how faults slip during earthquakes. Faults have a similar large-scale structure with a fault core, where earthquakes nucleate, and a surrounding damage zone, but complexities in fault zone architecture and rheology influence earthquake propagation. For example, changes in thickness of slipping layers in the fault core, compositional heterogeneity, and fault surface topography can influence fault strength and either facilitate or arrest a rupture. A further barrier to our understanding of earthquake behavior is in constraining the frictional energy that goes into the earthquake energy budget. Earthquakes can propagate when the energy available at the rupture tip is greater or equal to the energy being expended through radiation of seismic waves, permanent deformation within the process zone, and heat through friction. By quantifying the total energy involved in coseismic slip we can gain a more complete picture of the energy required for rupture propagation and how this may vary across faults. Although fracture and radiated energy can be constrained seismologically, thermal energy requires quantification by other means, and up until recently only few estimates existed for frictional energy. In this thesis I utilize biomarker thermal maturity to quantify temperature rise across multiple faults and explore what this can tell us about earthquake behavior. In chapters two through four, I focus on three large faults of varying structural and rheological complexity. Beginning with the Muddy Mountain thrust of southeast Nevada in Chapter two, I identify thermal evidence of coseismic slip in principal slip zones (PSZs) along this exhumed fault. I show that considerable heterogeneity in the thickness of slipping layers occurs a long a fault and that this has a large effect on coseismic temperature rise and hence fault strength, due to the effect of high temperature dynamic weakening mechanisms. In Chapter three, I move on to the creeping central deforming zone of the San Andreas fault, and show that it has experienced many large earthquakes that are clustered in a 4 m-wide zone adjacent to an actively creeping region. This work shows that the central San Andreas fault and other creeping faults can host seismic slip and should be included in seismic hazard analyses. Furthermore, I demonstrate the potential of K/Ar dating as a tool to constrain the age of earthquakes and find that these central San Andreas fault events are as young as ~3.3 Ma. In Chapter four, I focus on the Hikurangi Subduction zone, which has hosted large earthquakes and regular slow slip events in the past. Here, using drill core collected through the Pāpaku fault, a splay fault of the Hikurangi megathrust, I find evidence of temperature rise in the fault zone and deep hanging wall. Coupled forward models of heat generation and biomarker reaction kinetics estimate that displacement during these earthquakes was likely 11-15 m. These and other splay faults along the margin may pose considerable seismic and tsunami hazard to near-shore communities in the North Island of New Zealand. In Chapter five I explore what we have learned about fault behavior from biomarkers and other thermal proxies. I include measurements from five new faults and compile observations and measurements from past studies to explore how coseismic slip is localized across fault zones and put together a database of frictional energy estimates. Coseismic slip can broadly be described by two different scales of earthquake localization and that this is a function of total displacement, and to a lesser extent, material contrast across the fault. I see that frictional energy is relatively similar across faults of different displacement, depth, and maturity, and conclude that frictional energy is limited by the onset of dynamic weakening. Finally, I put together constraints on the energies involved in the budget to produce the first complete view of the earthquake energy budget and provide estimates of the total energy required for earthquake rupture across different faults.

Vibrations of nuclei in crystals govern various properties such as thermal expansion, phase transitions, and elasticity, and the quasiharmonic approximation (QHA) is the simplest nontrivial approximation which includes the effects of vibrational anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate the quasiharmonic approximation by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO₂) using density functional theory with three exchange-correlation functionals. The convergence of the two complementary strain parametrizations is evaluated for the computed thermal expansion. The temperature dependent lattice parameter and thermal expansion computed within the QHA is compared with experimental measurements. The QHA results are compared to measurements of the elastic constant tensor using time domain Brillouin scattering and inelastic neutron scattering. We then demonstrate the generalized quasiharmonic approximation in a non-cubic material, ferroelectric lead titanate, computing the temperature and stress dependence of the full elastic constant tensor. The irreducible derivative approach is employed for computing strain dependent phonons using finite difference, explicitly including dipole-quadrupole contributions. We use density functional theory, computing all independent elastic constants and piezoelectric strain coefficients at finite temperature and stress. There is good agreement between the quasiharmonic approximation and the experimentally measured lattice parameters close to 0 K. The quasiharmonic approximation overestimates the measured temperature dependence of the lattice parameters and elastic constant tensor, demonstrating that a higher level of strain dependent anharmonic vibrational theory is needed. The next material we study is zirconium nitride, employing the quasiharmonic approximation with the irreducible derivative approach to compute the phonons and thermal expansion. Density functional theory is used with two exchange-correlation functionals. We investigate the difference between the measured and computed optical phonon branches, showing that volume effects, two-phonon scattering, and nitrogen vacancies do not explain the discrepancy between the measurement and computation. The temperature dependent lattice parameter is computed within the QHA, where the thermal expansion is overestimated as compared with existing experimental measurements.