Seismological Investigation of Earthquakes and Deep Earth Structure

近年来，在并行计算机上对全球和区域地震波传播进行全三维数值模拟已成为可能。我们已经开发并实施了一种名为谱元素法的数值技术，它利用这些强大的机器，使我们能够以前所未有的分辨率模拟三维滞弹性、各向异性、旋转和自重地球模型中的地震波传播。我们的模拟包含了地形和水深测量以及流体-固体边界的影响，例如海底和核-地幔边界。全球地震学家通常以1秒的最短周期分析地震信号。这类信号的模拟需要使用千万亿次浮点的机器，作为这项提议的一部分，我们正在定位，一旦这些硬件可用，我们就可以利用它。这项提议的目的是利用这些新发现的能力来提高地球内部模型的质量，同时改进地震期间破裂过程的模型。从表面上看，这似乎是一项艰巨的任务，因为这种反演涉及数百甚至数千个模型参数。原则上，地震记录相对于模型参数的灵敏度可以用数值计算，但这将需要相当于模型参数数量的正演计算次数(通常为数千次)。通过将地震层析成像、气候和海洋动力学中流行的伴随方法和时间反转成像联系起来，我们已经证明，层析成像和震源反演中的一次迭代可以基于每一次地震的两种计算：一种是针对当前模型的计算，另一种是使用接收器的时间反转信号作为同时的虚拟震源的伴随计算。这终于为解决完整的3D逆问题打开了大门，即利用数据和预测之间的剩余差异来改进震源和地球模型的问题。我们已经演示了如何在2D中实现这一点，本提案的主要目标之一是将这些功能扩展到完全3D逆问题。该项目的更广泛影响包括继续开发对地震界有用的代码，以及支持和培训一名研究生和博士后。

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.