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: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675837
• 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下降期间，能源行业受到了艰难的打击，尤其是石油服务公司。同时，各级政府都引入了更严格的环境保护政策。因此，具有最小环境影响的成本效益的方法对于碳氢化合物勘探很重要，这需要对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，已广泛用于勘探地球物理学，以获得地球的高分辨率地下特性。 FWI能够创建地球的高分辨率地下图像，最多是传播波长的一半。此外，它可以同时估算多个参数，并且需要对记录的地震数据进行最小化的预处理。但是，FWI面临一系列挑战，例如对初始模型的敏感性，高计算成本，缓慢的收敛性，本地最小值，循环滑水，仅举几例。这些挑战阻碍了该方法在探索物理学领域的进一步广泛应用和接受。 *****该研究计划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，我们将将FWI作为部分微分方程（PDE）构成的非线性优化问题，其中通过基于梯度的优化算法迭代地最小化了观察数据和合成数据之间差异的失配函数。约束PDE是一个地震波方程，可以是Helmholtz方程和声学/弹性波方程。我们将重点关注几个重要方面，例如为FWI建立准确的初始模型，开发和分析有效，高阶数值算法和预处理，以降低计算成本。此外，将研究并应用各种正规化策略，以减轻自行车的和本地的最小问题。******通过研究计划，我们将为学生和博士后研究员提供高质量的培训，以在培训完成后为竞争性就业市场做好准备，并满足对能源行业和能源行业资格人工越来越多的需求。 我们的研究结果还将为地球科学家和石油工程师提供经济和快速的选择，以准确推断地下地质特性。**********