Collaborative Research: AFfield Expansion Method for Acoustic Scattering from Topography: Extensions to Elasticity and the Inverse Problem

合作研究：地形声学散射的 AF 场展开方法：弹性和反问题的扩展

• 批准号: 1115333
• 负责人: David Nicholls
• 金额: $ 13万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115333&HistoricalAwards=false
• 关键词: Collaborative; Research; AFfield; Expansion; Method

This proposal initiates a new collaboration aimed at improving methods of waveform inversion by including topography in seismic wave modeling and reducing the reliance of these methods on data at extremely low-frequency. The Principal Investigators propose to adapt and improve methods developed for simulating scattering from a diffraction grating. Their approach has extensions to linear elasticity and provides general improvements for solving the inverse problem. Significant mathematical advances are required to develop robust and efficient techniques for this application. The Boundary Perturbation Method extends the Field Expansion approach to an arbitrary number of layers with independent topographies and allows for rapid and accurate simulation of acoustic wave propagation in two dimensions. Extensions to three dimensions and to the general equations of elasticity are required. Moreover, the extension of frequency-independent discretizations based on Geometric Acoustics to multilayered elastic models is a significant and necessary mathematical advance. Additionally, advances in the inverse problem are also necessary to make the technique truly applicable to the seismic imaging problem. The standard method of "full-waveform inversion" requires data at frequencies which are too low to record in practice. The PIs' approach casts the forward problem as the application of a sequence of topography-dependent operators where the interface shapes appear rather explicitly. A number of iteration schemes are proposed for the recovery of these shapes, using re-arrangements of the compositions coupled to standard regularizing techniques from the theory of ill-posed problems. The propagation properties of seismic waves in layers of sediment are crucial in many technologies including the determination of inner earth properties and structure, earthquake detection and prediction, and hydrocarbon (oil and gas) exploration. In light of its many important applications, it is not surprising that a vast array of numerical and experimental techniques have been brought to bear upon this problem. However, several gaps in understanding and capability still exist. The PIs' address some of these questions through sophisticated numerical simulations which will be validated against both laboratory experiments and field measurements from the Tibetan plateau.

该提案发起了一项新的合作，旨在通过将地形纳入地震波建模中来改进波形反演方法，并减少这些方法对极低频数据的依赖。 首席研究员建议采用和改进为模拟衍射光栅散射而开发的方法。他们的方法扩展到了线性弹性，并为解决反问题提供了总体改进。 需要显着的数学进步来开发用于该应用的稳健且高效的技术。边界扰动方法将场扩展方法扩展到具有独立拓扑的任意数量的层，并允许快速、准确地模拟二维声波传播。 需要扩展到三个维度和一般弹性方程。此外，将基于几何声学的频率无关离散化扩展到多层弹性模型是一项重要且必要的数学进步。 此外，要使该技术真正适用于地震成像问题，反演问题的进展也是必要的。 “全波形反演”的标准方法需要频率太低而无法在实践中记录的数据。 PI 的方法将正向问题转化为一系列依赖于地形的算子的应用，其中界面形状显得相当明确。 提出了许多迭代方案来恢复这些形状，使用组合的重新排列以及来自病态问题理论的标准正则化技术。 地震波在沉积层中的传播特性对于许多技术至关重要，包括确定地球内部特性和结构、地震探测和预测以及碳氢化合物（石油和天然气）勘探。 鉴于其许多重要的应用，大量的数值和实验技术被用来解决这个问题也就不足为奇了。 然而，在理解和能力方面仍然存在一些差距。 PI 通过复杂的数值模拟解决了其中一些问题，这些模拟将根据实验室实验和青藏高原的现场测量进行验证。