Waves and rays in anisotropic and inhomogeneous Hookean solids: Mathematical formulation and empirical evaluation

各向异性和非均匀胡克固体中的波和射线：数学公式和经验评估

• 批准号: RGPIN-2018-05158
• 负责人: Slawinski, Michael
• 金额: $ 1.82万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=713298
• 关键词: Waves; rays; anisotropic; inhomogeneous; Hookean

A theory is necessary to mediate between observations and interpretations; there is no other method to infer quantitatively properties of the Earth's interior from measurements on its surface. To describe materials of the Earth, it is common to use a Hookean solid, which is a mathematical object. Properties of that object are analogies for properties of physical materials. Analogies require subtle considerations. An important part of my research is to examine uncertainties of conclusions in the context of experimental errors and model limitations. Thus, properties of materials are stated in terms of ranges of probable values, whose extent depends on experimental errors and model limitations. Models are simpler than their physical counterparts, and their role is to exhibit pertinent qualities of their physical counterparts. Also, models must accommodate the limited accuracy of measurements. Hence, I examine the models obtained by averaging many parameters to obtain fewer parameters. Establishing the criteria for an optimal choice of a model with fewer parameters is an important part of my research. A model can be considered empirically adequate if it accounts, within accepted limits, for experimental measurements. This, however, can be achieved by many models. Thus, I strive to ensure that the chosen model is an optimal analogy for the physical reality. To account for seismic measurements by Hookean solids, we need to optimize between the effects of anisotropy and inhomogeneity, since the same result can be obtained by different effects. The optimal model choice constitutes an essential part of my research. Theoretical challenges arise in examining seismic phenomena in layered media. I strive to infer information about the deep subsurface from the surface measurements of waves bounded by the surface and an interface. Since two types of waves can propagate in such a model, there are two independent sets of measurements pertaining to the same model, which increases the reliability of physical interpretation. The pragmatic importance of my research is motivated by increased accuracy of available experimental apparatus. This research is important to geoscientists concerned with global and exploration issues. Also, this research is linked to material sciences, which is an important field in Canada, spanning from strength of materials to medical sciences.

需要有一种理论来协调观察和解释；没有其他方法可以根据地球表面的测量来定量地推断地球内部的特性。为了描述地球的材料，通常使用胡克固体，它是一个数学对象。该物体的属性类似于物理材料的属性。 类比需要微妙的考虑。我研究的一个重要部分是在实验误差和模型限制的背景下检查结论的不确定性。因此，材料的特性是用可能值的范围来表示的，其范围取决于实验误差和模型限制。 模型比物理对应物更简单，它们的作用是展示物理对应物的相关品质。此外，模型必须适应有限的测量精度。因此，我检查通过平均许多参数以获得更少的参数而获得的模型。建立参数较少的模型的最佳选择标准是我研究的重要部分。 如果一个模型在可接受的限度内考虑了实验测量，则可以认为它在经验上是足够的。然而，这可以通过许多模型来实现。因此，我努力确保所选模型是物理现实的最佳类比。为了考虑胡克固体的地震测量，我们需要在各向异性和不均匀性的影响之间进行优化，因为不同的影响可以获得相同的结果。最佳模型选择构成了我研究的重要组成部分。 研究层状介质中的地震现象时出现了理论挑战。我努力从表面和界面所界定的波浪的表面测量中推断出有关深层地下的信息。由于两种类型的波可以在这样的模型中传播，因此同一模型有两组独立的测量结果，这增加了物理解释的可靠性。 我的研究的实用重要性是由于现有实验仪器的准确性的提高而激发的。这项研究对于关注全球和勘探问题的地球科学家来说非常重要。此外，这项研究与材料科学相关，材料科学是加拿大的一个重要领域，涵盖从材料强度到医学科学。