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.

该提案启动了一种新的合作，旨在通过在地震波建模中包括地形，并在极低频率的情况下降低这些方法对数据的依赖，旨在改善波形反演的方法。 主要研究人员建议适应和改进用于模拟衍射光栅散射的方法。他们的方法具有线性弹性的扩展，并为解决反问题提供了一般改进。 为了开发此应用程序，需要大量数学进步来开发强大而有效的技术。边界扰动方法将场扩展方法扩展到具有独立地形的任意层，并可以在二维中快速，准确地模拟声波传播。 需要扩展到三个维度和弹性的一般方程。此外，基于几何声学对多层弹性模型的频率无关离散性的扩展是一个重要且必要的数学进步。 此外，对于使该技术真正适用于地震成像问题，反对问题的进展也是必要的。 “全波反转”的标准方法需要以太低而无法在实践中记录的频率数据。 PIS的方法将正向问题呈现为一系列与地形依赖性操作员的应用，其中界面形状显着地出现。 提出了许多迭代方案，用于恢复这些形状，使用对不足问题理论的标准正规化技术的组合物的重新分配。 在许多技术中，在许多技术中，地震层中的地震波的传播特性包括确定地球特性和结构，地震检测和预测以及碳氢化合物（油气和天然气）探索。 鉴于其许多重要的应用，毫不奇怪的是，在这个问题上已经带来了大量的数值和实验技术。 但是，仍然存在一些理解和能力的差距。 PI通过复杂的数值模拟解决了其中一些问题，这些模拟将对实验室实验和藏族高原的现场测量进行验证。