In recent years, fully 3D numerical simulations of global and regional seismic wave propagation have become feasible on parallel computers. We have developed and implemented a numerical technique, called the spectral-element method, that harnesses these powerful machines and enables us to simulate seismic wave propagation in 3D anelastic, anisotropic, rotating & self-gravitating Earth models at unprecedented resolution. Our simulations incorporate effects due to topography & bathymetry as well as fluid-solid boundaries, such as the ocean floor and the core-mantle boundary. Global seismologists routinely analyze seismic signals with a shortest period of 1 second. The simulation of such signals requires access to a petaflop machine, and as part of this proposal we are positioning ourselves to take advantage of such hardware as soon as it becomes available.
The purpose of this proposal is to harness these new found capabilities to enhance the quality of models of Earth's interior, in conjunction with improving models of the rupture process during an earthquake. On the face of it, this seems like a Herculean task because hundreds or even thousands of model parameters are involved in such inversions. In principle, the sensitivity of a seismogram with respect to the model parameters may be calculated numerically, but this would require a number of forward calculations equal to the number of model parameters (typically thousands). By drawing connections between seismic tomography, adjoint methods popular in climate and ocean dynamics, and time-reversal imaging, we have demonstrated that one iteration in tomographic and source inversions may be performed based upon just two calculations for each earthquake: one calculation for the current model and a second, adjoint, calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. This has finally opened the door to solving the full 3D inverse problem, i.e., the problem of using the remaining differences between the data and the predictions to improve source and Earth models. We have demonstrated how this may be accomplished in 2D, and one of the main goals of this proposal is to extend these capabilities to fully 3D inverse problems. Broader impacts of the project include continuing the development of code that is useful to the seismic community and the support and training of a graduate student and a postdoc.
The increasing availability of large numbers of high-quality digital records from global networks of seismometers has made possible a variety of new ways to study earthquakes and deep Earth structure. By analyzing thousands of seismograms or more, it is often possible to resolve new features in the data, or to perform more comprehensive analyses of problems that were previously addressed on smaller scales. This project involved collaborations between Peter Shearer and his students and postdocs to mine these large seismic datasets to learn new things about the Earth. For example, we resolved sharp discontinuities in material properties in Earth's upper mantle, including depth variations (topography) on interfaces near 410- and 660-km depth that are related to changes in crystal structure due to the very high pressures inside Earth at these depths. In addition, we were able to resolve on a global scale the boundary that separates Earth's relatively rigid outer layer from the more deformable rock below. Seismic waves are also used to study earthquakes and we performed large-scale data analyses to study earthquake source properties. Earthquakes vary in how strongly they stress the rock in which they occur and may be divided into those that produce larger stress changes, termed "stress drop," and those that produce smaller stress changes. We performed a systematic study of hundreds of large earthquakes over the last 20 years and found that certain types of faulting seem to produce earthquakes with larger stress drops (see Figure). We also found that two recent large earthquakes in China and Alaska involved fault ruptures that traveled faster than the local shear-wave velocity in the rock. These so-called super-shear earthquake can produce stronger ground shaking in some directions than "ordinary" earthquakes. Finally, we studied the devastating 2011 Tohoku earthquake in Japan and found that its rupture properties were very complex and depth dependent, with longer-period seismic waves generated mainly at shallow depths.
