Mathematical theory and computational methods for seismic full waveform inversion problems

地震全波形反演问题的数学理论与计算方法

• 批准号: RGPIN-2019-04830
• 负责人: Liao, Wenyuan
• 金额: $ 1.24万
• 依托单位: University of Calgary
• 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=715153
• 关键词: Mathematical; theory; computational; methods; seismic

During the crude price downturn over the last few years, the energy industry has been hit hard, particularly the oil service companies. Meanwhile, governments at all levels have introduced stricter environmental protection policies. Therefore, cost-effective approaches with minimal environmental impact are important for hydrocarbon exploration, which requires an accurate high-resolution subsurface image of the potential oil field. Seismic full waveform inversion (FWI) is a powerful model-based data fitting procedure that has been widely used in exploration geophysics to obtain high-resolution subsurface properties of the earth. FWI is able to create high-resolution subsurface images of the earth up to half of the propagated wavelength. Moreover, it can estimate multiple parameters simultaneously and requires minimal preprocessing of the recorded seismic data. However, FWI suffers from a series of challenges, such as sensitivity on initial model, high computational cost, slow convergence, local minima, cycle-skipping, to name a few. These challenges hinder the further widespread application and acceptance of this method in the field of exploration physics. This research program aims to develop advanced mathematical theory and efficient computational methods to resolve these issues of FWI. To this end, we will formulate FWI as a partial differential equation (PDE)-constrained nonlinear optimization problem, where the misfit function measuring the difference between observational data and synthetic data is iteratively minimized by gradient-based optimization algorithms. The constraint PDE is a seismic wave equation which can be Helmholtz equation and acoustic/elastic wave equation. We will focus on several important aspects, such as building accurate initial models for FWI, development and analysis of efficient and higher-order numerical algorithms and preconditioners to reduce computational cost. Moreover, various regularization strategies will be studied and applied to mitigate the cycle-skipping and local minima issues. Through the research program, we will provide students and postdoctoral fellows with high-quality training to prepare them for the competitive job market upon the completion of training, and to meet the increasing demand for highly qualified personnel from the energy industry and information technology. Our research result will also provide geoscientists and petroleum engineers with an economical and fast option to infer subsurface geological properties accurately.

在过去几年的原油价格低迷期间，能源行业尤其是石油服务公司受到了沉重打击。与此同时，各级政府出台了更加严格的环保政策。因此，对环境影响最小的经济高效的方法对于碳氢化合物勘探非常重要，这需要潜在油田的准确高分辨率地下图像。地震全波形反演（FWI）是一种强大的基于模型的数据拟合程序，已广泛应用于勘探地球物理以获得地球的高分辨率地下特性。 FWI 能够创建高达传播波长一半的高分辨率地球地下图像。此外，它可以同时估计多个参数，并且需要对记录的地震数据进行最少的预处理。然而，FWI 面临着一系列挑战，例如初始模型的敏感性、计算成本高、收敛速度慢、局部极小值、跳周期等。这些挑战阻碍了该方法在探索物理领域的进一步广泛应用和接受。 该研究项目旨在开发先进的数学理论和有效的计算方法来解决 FWI 的这些问题。为此，我们将 FWI 表述为偏微分方程 (PDE) 约束的非线性优化问题，其中测量观测数据和合成数据之间差异的失配函数通过基于梯度的优化算法迭代最小化。约束偏微分方程是地震波方程，可以是亥姆霍兹方程和声波/弹性波方程。我们将重点关注几个重要方面，例如为 FWI 构建准确的初始模型、开发和分析高效的高阶数值算法和预处理器以降低计算成本。此外，将研究和应用各种正则化策略来减轻周期跳跃和局部最小值问题。 通过该研究项目，我们将为学生和博士后提供高质量的培训，为他们完成培训后进入竞争激烈的就业市场做好准备，满足能源工业和信息技术对高素质人才日益增长的需求。 我们的研究成果还将为地球科学家和石油工程师提供一种经济、快速的选择来准确推断地下地质性质。