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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=742476
• 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.

我的研究的广泛目标是推进地球物理反演技术，从而改进对地球次表层的非侵入性调查。地球物理反演产生地下的模型(三维空间表示)，这些模型可以产生来自地球物理测量的测量数据，例如，在地面或井下对机载系统进行的地震、重力、磁、电和电磁测量。反演是一个计算密集的过程，依赖于描述所涉及的物理现象的微分方程的精确数值解，以及针对手头的特定逆问题而定制的数值优化例程的开发。这在很大程度上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，但前两者对我的研究具有首要意义。地球物理反问题通常不是唯一的：由于数据的不确定性以及反问题的物理现象或数学所固有的其他方面，有无限数量的模型可以将测量的地球物理数据拟合到所需的程度。因此，仅靠测量数据不足以找到有意义、可解释和可靠的唯一解决方案。必须结合额外的信息，以减少不唯一性，提供数学行为良好的问题，最重要的是，从应用的角度来看，生成与关于地下表面的任何现有信息一致的解决方案。地球物理反演的核心研究问题之一，也是指导我研究的问题之一，是如何最好地减少反问题的不唯一性，从而减少所获得的解的模糊性。地球物理反演提供了一种提供地下模型的非侵入性方法，可用于在进行更多侵入性检查之前向决策者提供信息。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，包括资源勘探、自然灾害缓解、考古、农业和许多其他环境和土木工程调查，所有这些都在加拿大各地都很重要。地球物理反演是增进对我们生活的世界和我们文明历史的认识的基本工具。我的研究计划将开发新的地球物理反演方法，并研究将这些方法应用于各种重要的世界性问题的最佳实践。