The Physics of the Earthquake Source and Radiated Waves: Frequency Dependence, Spatial Distribution, and Directivity in Elastodynamic Models of Repeated Fault Ruptures

这项工作的主旨是寻求更深入地了解地震发出的辐射波。在以前的工作中，研究人员已经研究了总辐射能量如何对源物理敏感，显示了弹性动力学断层中滑动与速度削弱摩擦的差异。 这项工作被扩展到看辐射的频率内容和空间依赖性。得到了一些重要的结果，包括：（1）提出了一个新的辐射边界条件，它允许一个非均匀的预应力，这对重复破裂是有用的：（2）只需要假定断层上的牵引力的物理性质，就可以产生各种大小的事件的辐射波的全谱;（3）通过对辐射谱成分的分析，发现第二转角频率与辐射的幅值存在非线性关系，并且与辐射的基本参数有关;（4）在谱比上，大事件的方向性效应较强。在新的支持下，正在对该主题进行持续研究，重点是三个具体项目：第一个项目涉及进一步探索方向性效应的幅度和空间依赖性。初步结果表明，在大型地震中，远离震中区域的加速度谱有显著的放大。对这些效应的进一步探索包括已经进行的频域测量的时域补充。这项工作将进一步发展一个新的理论工具，探索一个潜在的大灾害和地震工程的影响。第二个项目涉及的辐射能谱的二维模型的测量扩展到三维模型。一个新的辐射边界条件的进一步推广正在开发中的两个维度，既扩展到更高的维度和连续加载，允许在长时间的直接测量。第三个项目涉及将模型中开发的一种新的测量方法应用于地震数据。测量利用自然平均测量，通过能量谱的求和转换为平均加速度谱。在模型中，峰值平均加速度谱的周期反映了基本的源参数。目前正在测量地震中这一量与震级的关系。

The main thrust of this work is to seek a deeper understanding of the radiated waves emitted by earthquakes. In previous work, the investigator has examined how total radiated energy can be sensitive to the source physics, showing dfferences for slip versus velocity weakening friction in elastodynamic faults. This work was expanded to look at the frequency content and spatial dependence of the radiation. A number of important results were obtained, including: (1) A new radiating boundary condition allowing a nonuniform prestress, useful for repeated ruptures, was developed; (2) Having to assume only a physics of the tractions on the fault, the full spectra of radiated waves for events with a wide range of sizes were generated; (3) Characterizing the spectral content of the radiation, a nonlinear magnitude dependence of a second corner frequency was found, and shown to be related to fundamental source parameters; (4) Strong directivity effects for large events were exhibited in spectral ratios. With renewed support, continued research on this subject is being carried out, with a focus on three specifc projects:The first project involves further exploration of magnitude and spatial dependence of directivity effects. Initial results have shown striking amplification of acceleration spectra away from the epicentral region in large events. Further exploration of these effects includes time domain complements of the frequency domain measurements already made. This work will further develop a new theoretical tool for exploring an issue with potentially large hazard and earthquake engineering implications.The second project involves the extension of measurements made in two-dimensional models of radiated energy spectra to three-dimensional models. A further generalization of a new radiating boundary condition is being developed in two dimensions, both extending it to higher dimensions and to continuous loading, allows direct measurements at long times. This allows quantitative physical predictions of the magnitude dependence of radiated energy spectra.The third project involves the application of a new measurement developed in the models to earthquake data. The measurement takes advantage of a natural averaging measure through summing of energy spectra to convert to average acceleration spectra. In the models, the period of the peak average acceleration spectra was shown to reflect fundamental source parameters. Measurements of the magnitude dependence of this quantity in earthquakes are being carried out.