Surface roughness is a universal characteristic of natural faults. Roughness can be represented statistically as a random field that is approximately self-similar over many orders of magnitude in scale-length with a ratio of amplitude to length scale that typically falls into the range 10−3 to 10−2. Incorporating realistic rough fault surface into 3D numerical simulations of earthquake dynamic rupture provides guidance to build kinematic rupture generator.

We have built a database of more than 1000 simulations of 3D strike slip dynamic rupture for different realizations of rough fault surfaces at different fault roughness levels. We first have explored the role of the fault roughness in influencing the 1-point and 2-point statistics of earthquake source parameters such as rupture velocity, peak slip rate, total slip, and slip rise time. Fault roughness reduces the amplitudes of rupture velocity, peak slip rate, rise time and total slip.

Then, we have extended our study to assess supershear transition mechanisms that operate in 3D on rough faults and what factors contribute to the frequency of occurrence and spatial extent of supershear rupture episodes. We have reconciled the conflict that the supershear is favored by fault roughness from 2D numerical simulation (Bruhat et al., 2016) and unfavored by fault roughness from field observations (Bouchon et al., 2010) by dividing supershear into two types supershear transitions: free surface supershear transition and buried supershear transition.

Finally, we have investigated how well simulated earthquake behaviors on rough fault relate to direct geological observations, such as free surface lateral slip, plastic strain, and shallow slip deficits. We have found that fault roughness in the form of a power law leads to self-affine surface lateral slip, which is in agreement with recent optical imaging observations in the 1992 Landers earthquake (Milliner et al., 2015). Also fault roughness tends to produce individual events with large shallow slip deficits, which may help explain the suggestion that has been made, based on a small number of earthquakes, that the SSD tends to be larger on immature faults.

We apply the method of support operators (SOM) to solve the 3-D, viscoelastic equations of motion for use in earthquake simulations. SOM is a generalized finite-difference method that can utilize meshes of arbitrary structure and incorporate irregular geometry. Our implementation uses a 3-D, logically rectangular, hexahedral mesh. Calculations are second-order in space and time. A correction term is employed for suppression of spurious zero-energy modes (hourglass oscillations). We develop a free surface boundary condition, and an absorbing boundary condition using the method of perfectly matched layers (PML). Numerical tests using a layered material model in a highly deformed mesh show good agreement with the frequency-wavenumber method, for resolutions greater than 10 nodes per wavelength. We also test a vertically incident P wave on a semi-circular canyon, for which results match boundary integral solutions at resolutions greater that 20 nodes per wavelength. We also demonstrate excellent parallel scalability of our code.

Growth of major populated cities near active faults (e.g., Los Angeles and San Francisco in USA, Tokyo and Osaka in Japan) has significantly elevated the seismic hazards. Understanding complex paradigm of near-fault ground motions is crucial in order to mitigate seismic hazards. Since the 1994 Mw 6.7 Northridge earthquake, there has been much discussion about the adequacy of building code and a term of “pulse”. The engineering effects of near-fault pulse-like ground motions were strikingly exhibited in the 1994 Northridge earthquake in which great seismic damage was attributed to the large impulsive ground shaking of this type. Such near-fault pulselike ground motions with high intensity and damage potentials are hypothetically associated to either pulse-like rupture on fault or the rupture directivity. These mechanisms will be introduced and studied.

In Chapter 2, we study far-field effects of a self-healing pulse-like rupture mode with dynamic weakening. Pulse-like rupture leads to development of a second corner frequency, and the intermediate spectral slope is approximately 2 in most cases. The focal-sphere-averaged lower P and S wave corner frequencies are systematically higher for pulse-like models than crack models of comparable rupture velocity. The slip-weighted stress drop exceeds the moment-based stress drop for pulse-like ruptures, with the ratio ranging from about 1.3 to 1.65, while they are equal for the crack-like case. The transition from arresting- to growing-pulse rupture is accompanied by a large (factor of 1.6) increase in the radiation ratio. Thus, variations in rupture mode may account for the portion of the scatter in observational spectral estimates of

source parameters.

In Chapter 3, we confirm the pulse-like ground motion in the 2015 Nepal Gorkha earthquake is related to the causing fault geometry of the Main Himalayan Thrust (MHT). Our dynamic rupture simulations in an elastoplastic medium yield earthquake parameters comparable to those deduced from kinematic inversions, including seismic moment and rupture velocity. The simulations reproduce pulse-like behavior predicting pulse widths in agreement with those kinematic studies and supporting an interpretation in which the pulse-like time dependence of slip is principally controlled by rupture geometry and it is supported by near-field high-rate GPS recording at station KKN4.

In Chapter 4, we will discuss the directivity-induced pulse-like ground motions and assess the extent to which plastic yielding, which is absent in standard kinematic models, may systematically affect the amplitude, frequency content, and distance scaling of directivity pulse. We perform some simple 2D kinematic and 3D spontaneous dynamic ruptures with and without plastic yielding on a planar and rough fault, and find that each of the four 3D models (flat and rough faults, with and without off-fault yielding), scaled to approximately magnitude 7, predicts a fault-normal pulse with characteristic behavior of observed pulses. Plastic yielding systematically reduces pulse amplitude and increases its dominant period, relative to models that neglect off-fault yielding. Yielding saturates near-fault peak ground velocity (PGV) with greater stress drops, alternatively interpreting observed magnitude saturation of PGV near a magnitude of 7, and provides physical supports of period-dependent distance taper and along-strike saturation of directivity-induced amplification, undermining the commonly used wedge-shaped directivity amplification.