EAGER: The Burridge-Willis-Eshelby Waves from a Self-Similarly Expanding Ellipsoidal Region of Phase Change and Application to Deep-Focus Earthquakes

这一早期概念探索性研究(AGUGER)奖支持基础研究，以获得对Burbridge-Willis-EShelby波问题的声学和能量方面的完整的基于力学的分析。该模型将被用于预测在产生深源地震的过程中由于相变而产生的声发射，这是一种50多年来一直无法建模的物理现象。这一结果将使应用力学研究人员和地球物理研究界之间未来的合作能够对深源地震的现场数据进行定量预测和解释。该项目还将与加州大学圣迭戈分校为女研究人员正在进行的指导计划相联系。该项目将推导出一个由自相似膨胀的椭球区发出的波的解模型，在椭球区中，材料在高压下膨胀时经历相变。这一问题构成了在各向同性和各向异性两种情况下EShelby椭球包含问题的动态推广。对于实验模拟中发生的特定相变，将得到等效相变应变，并将理论声发射与以往地球物理研究的实验结果进行比较。

This EArly-concept Grant for Exploratory Research (EAGER) award supports fundamental research to obtain the complete mechanics based analysis of the acoustic and energetic aspects of the Burridge-Willis-Eshelby wave problems. This model will be applied to predict the acoustic emissions due to phase transitions in the process that generates deep focus earthquakes, a physical phenomenon that has defied modeling for over 50 years. The results would enable future collaborations between applied mechanics researchers and the geophysical research community to perform quantitative predictions and interpretation of field data on deep focus earthquakes. The project will also connect to ongoing mentoring programs for women researchers at the University of California - San Diego.A model of the solution for waves emitted by a self-similarly expanding ellipsoidal region, in which the material undergoes phase change as it expands under high pressure, will be derived. This problem constitutes the dynamic generalization of the seminal Eshelby ellipsoidal inclusion problem both in isotropy and anisotropy. The equivalent transformation strain will be obtained for the specific phase transitions occurring in the experimental analogs and the theoretical acoustic emissions will be compared with experimental ones from previous geophysics research.