Numerical Solution of Next Generation Inverse Problems for Geophysical Applications

地球物理应用的下一代反问题的数值求解

• 批准号: RGPIN-2021-03285
• 负责人: Lelievre, Peter
• 金额: $ 1.31万
• 依托单位: Mount Allison University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758725
• 关键词: Numerical; Solution; Next; Generation; Inverse

The broad objective of my research is to advance geophysical inversion technology and thereby improve non-invasive investigation of the Earth's subsurface. Geophysical inversion generates models (three-dimensional spatial representations) of the subsurface that could have given rise to measured data from a geophysical survey, for example, seismic, gravity, magnetic, electrical and electromagnetic measurements taken on airborne systems, at ground level, or down drillholes. Inversion is a computationally intensive procedure, relying on accurate numerical solution of the differential equations that describe the physical phenomena involved, and development of numerical optimization routines tailored to the specific inverse problem at hand. It is very much an interdisciplinary field, combining aspects of mathematics, computer science, physics and Earth sciences, but the former two are of primary significance to my research. Geophysical inverse problems are generally nonunique: because of data uncertainty and other aspects inherent to the physical phenomena or mathematics of the inverse problem, there are an infinite number of models that can fit the measured geophysical data to the desired degree. Hence, the measured data alone are not enough to find a unique solution that is meaningful, interpretable and reliable. Additional information must be incorporated to reduce the nonuniqueness, provide mathematically well-behaved problems and, most importantly from an applied perspective, generate solutions that are consistent with any existing information regarding the subsurface. One of the central research questions in geophysical inversion, and one which guides my research, is how to best reduce the nonuniqueness of the inverse problem and thereby reduce ambiguity in the solutions obtained. Geophysical inversion provides a non-invasive method for providing models of the subsurface that can be used to inform decision makers before more invasive inspection is undertaken. These techniques have proven helpful for addressing a wide variety of practical problems in various fields of application, including resource exploration, natural hazard mitigation, archaeology, agriculture and many other environmental and civil engineering investigations, all of which are important across Canada. Geophysical inversion is a fundamental tool for advancing knowledge of the world we live in and the history of our civilization. My research program will develop new geophysical inversion methods and research best practices for applying those methods to various important worldwide problems.

我的研究的广泛目的是提高地球物理反演技术，从而改善对地球地下的非侵入性研究。地球物理反演产生了地下的模型（三维空间表示），这些模型可能会从地球物理调查中产生测量的数据，例如，地震，重力，磁性，电磁，电气和电磁测量，对空生系统，或在地面钻孔或下钻孔孔。反转是一个计算密集的过程，依靠描述所涉及的物理现象的微分方程的准确数值解，以及针对手头特定逆问题量身定制的数值优化例程的开发。这是一个跨学科的领域，结合了数学，计算机科学，物理和地球科学的各个方面，但前两个对我的研究至关重要。地球物理逆问题通常是不合时宜的：由于数据不确定性以及逆问题的物理现象或数学固有的其他方面，因此有无限数量的模型可以符合所需程度的测量地球物理数据。因此，仅测得的数据不足以找到有意义，可解释和可靠的独特解决方案。必须合并其他信息，以减少非唯一性，提供数学上良好的问题，最重要的是，从应用的角度来看，生成与任何有关地下的现有信息一致的解决方案。地球物理反转中的一个中心研究问题之一，以及指导我的研究的一个是如何最好地减少反问题的非唯一性，从而减少获得的解决方案的歧义。地球物理反演提供了一种非侵入性方法，用于提供地下模型，该模型可在进行更多侵入性检查之前为决策者提供通知。事实证明，这些技术有助于解决各种应用领域的各种实际问题，包括资源探索，减轻自然危害，考古学，农业以及许多其他环境和土木工程调查，在整个加拿大都很重要。地球物理倒置是促进我们生活和文明历史的知识的基本工具。我的研究计划将开发新的地球物理反演方法和研究最佳实践，以将这些方法应用于各种重要的全球问题。