2D modeling of lower mantle structure with WKM synthetics

The Earth is very heterogeneous, especially in the region close to the surface of the Earth, and in regions close to the core-mantle boundary (CMB). The lowermost mantle (bottom 300km of the mantle) is the place for fast anomaly (3% faster S velocity than PREM, modeled from Scd), for slow anomaly (-3% slower S velocity than PREM, modeled from S,ScS), for extreme anomalous structure (ultra-low velocity zone, 30% lower inS velocity, 10% lower in P velocity). Strong anomaly with larger dimension is also observed beneath Africa and Pacific, originally modeled from travel time of S, SKS and ScS. Given the heterogeneous nature of the earth, more accurate approach (than travel time) has to be applied to study the details of various anomalous structures, and matching waveform with synthetic seismograms has proven effective in constraining the velocity structures. However, it is difficult to make synthetic seismograms in more than 1D cases where no exact analytical solution is possible. Numerical methods like finite difference or finite elements are too time consuming in modeling body waveforms. We developed a 2D synthetic algorithm, which is extended from 1D generalized ray theory (GRT), to make synthetic seismograms efficiently (each seismogram per minutes). This 2D algorithm is related to WKB approximation, but is based on different principles, it is thus named to be WKM, i.e., WKB modified. WKM has been applied to study the variation of fast D" structure beneath the Caribbean sea, to study the plume beneath Africa. WKM is also applied to study PKP precursors which is a very important seismic phase in modeling lower mantle heterogeneity. By matching WKM synthetic seismograms with various data, we discovered and confirmed that (a) The D" beneath Caribbean varies laterally, and the variation is best revealed with Scd+Sab beyond 88 degree where Sed overruns Sab. (b) The low velocity structure beneath Africa is about 1500 km in height, at least 1000km in width, and features 3% reduced S velocity. The low velocity structure is a combination of a relatively thin, low velocity layer (200 km thick or less) beneath the Atlantic, then rising very sharply into mid mantle towards Africa. (c) At the edges of this huge Africa low velocity structures, ULVZs are found by modeling the large separation between S and ScS beyond 100 degree. The ULVZ to the eastern boundary was discovered with SKPdS data, and later is confirmed by PKP precursor data. This is the first time that ULVZ is verified with distinct seismic phase.

Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach

Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.

In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.

In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.

Probabilistic Imaging and Dynamic Modeling of Earthquake Source Processes

Investigation of large, destructive earthquakes is challenged by their infrequent occurrence and the remote nature of geophysical observations. This thesis sheds light on the source processes of large earthquakes from two perspectives: robust and quantitative observational constraints through Bayesian inference for earthquake source models, and physical insights on the interconnections of seismic and aseismic fault behavior from elastodynamic modeling of earthquake ruptures and aseismic processes.

To constrain the shallow deformation during megathrust events, we develop semi-analytical and numerical Bayesian approaches to explore the maximum resolution of the tsunami data, with a focus on incorporating the uncertainty in the forward modeling. These methodologies are then applied to invert for the coseismic seafloor displacement field in the 2011 Mw 9.0 Tohoku-Oki earthquake using near-field tsunami waveforms and for the coseismic fault slip models in the 2010 Mw 8.8 Maule earthquake with complementary tsunami and geodetic observations. From posterior estimates of model parameters and their uncertainties, we are able to quantitatively constrain the near-trench profiles of seafloor displacement and fault slip. Similar characteristic patterns emerge during both events, featuring the peak of uplift near the edge of the accretionary wedge with a decay toward the trench axis, with implications for fault failure and tsunamigenic mechanisms of megathrust earthquakes.

To understand the behavior of earthquakes at the base of the seismogenic zone on continental strike-slip faults, we simulate the interactions of dynamic earthquake rupture, aseismic slip, and heterogeneity in rate-and-state fault models coupled with shear heating. Our study explains the long-standing enigma of seismic quiescence on major fault segments known to have hosted large earthquakes by deeper penetration of large earthquakes below the seismogenic zone, where mature faults have well-localized creeping extensions. This conclusion is supported by the simulated relationship between seismicity and large earthquakes as well as by observations from recent large events. We also use the modeling to connect the geodetic observables of fault locking with the behavior of seismicity in numerical models, investigating how a combination of interseismic geodetic and seismological estimates could constrain the locked-creeping transition of faults and potentially their co- and post-seismic behavior.