We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.

We perform 2‐D simulations of earthquakes on rough faults in media with random heterogeneities (with von Karman distribution) to study the effects of geometric and material heterogeneity on the rupture process and resulting high‐frequency ground motions in the near‐fault region (out to ∼20 km). Variations in slip and rupture velocity can arise from material heterogeneity alone but are dominantly controlled by fault roughness. Scattering effects become appreciable beyond ∼3 km from the fault. Near‐fault scattering extends the duration of incoherent, high‐frequency ground motions and, at least in our 2‐D simulations, elevates root‐mean‐square accelerations (i.e., Arias intensity) with negligible reduction in peak velocities. We also demonstrate that near‐fault scattering typically occurs in the power law tail of the power spectral density function, quantified by the Hurst exponent and another parameter combining standard deviation and correlation length.

No abstract

Recent increases in seismic activity in historically quiescent areas such as Oklahoma, Texas, and Arkansas have spurred the need for investigation into expected ground motions associated with these seismic sources. The neoteric nature of this seismicity increase corresponds to a scarcity of ground motion recordings within ∼20 km of earthquakes M w 3.0 and greater. To aid the effort of constraining near-source ground motion prediction equations (GMPEs) associated with induced seismicity, we develop a framework for integration of synthetic ground motion data from simulated earthquakes into the GMPE development process. We demonstrate this framework by developing a GMPE for a target region encompassing north-central Oklahoma and south-central Kansas. We first gather a catalog of recorded ground mo-tions from M w 3-4 earthquakes that occurred in the target region. Using constraints on the region's material structure, including well log data that provides insight into the characteristics of shallow sedimentary layers, we perform point-source simulations intended to mimic a selection of recorded earthquakes from the target region. Simulated earthquake sources are constrained by available moment tensors and locations. Once we determine that our simulations produce realistic ground motions, we combine recorded and synthetic ground motion data to produce a composite ground motion catalog. We use this composite catalog to develop a regionally-specific GMPE for our target region. This framework can be exported to other regions where near-source ground motion data are sparse and can be used to improve constraints on near-source GMPEs, which could directly benefit seismic hazard estimates.