CMG COLLABORATIVE RESEARCH: Nonlinear elastic-wave inverse scattering and tomography - from cracks to mantle convection

CMG 合作研究：非线性弹性波逆散射和断层扫描 - 从裂缝到地幔对流

• 批准号: 1025318
• 负责人: Maarten de Hoop
• 金额: $ 35.09万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1025318&HistoricalAwards=false
• 关键词: CMG; COLLABORATIVE; RESEARCH; Nonlinear; elastic

Knowing Earth?s internal structure on a range of length scales is necessary to understand natural hazards (earthquakes, volcanoes), exploit subsurface energy resources, and understand the long-term geological evolution of our planet. Seismic waves emitted by earthquakes or man-made sources represent the most direct and precise probes of Earth?s interior. Traditionally, seismologists recognize two types of non-destructive method for determining medium properties from measurements made at its boundary. Tomography (which in concept is similar to medical computer-aided tomography) aims to constrain smooth medium variations from transmitted seismic waves, whereas inverse scattering aims to constrain non-smooth heterogeneity (edges, interfaces) from reflected, refracted, or diffracted waves. These methods have revolutionized our understanding of Earth?s structure but have not yet reached their full potential. An important issue is that for practical and technical reasons they used to be treated separately. Indeed, (local) linearization and the use of asymptotic theory prevent internally consistent interpretation of seismic data with different (but complementary) sampling properties. Building on expertise in seismology, inverse theory, and microlocal and harmonic analysis, the proposed research aims to develop a unified theoretical framework for (nonlinear, full wave) inversion and medium reconstruction, where tomography and inverse scattering are no longer treated separately. The new methods can lead to more accurate seismic exploration for oil and gas but the main geoscience motivation is to study the crust and mantle beneath North America with data provided by USArray, the seismology component of EarthScope, a nationwide, multi-year geosciences project funded by NSF.From a mathematical sciences perspective the challenge is to develop a unified analysis of and computationally efficient algorithms for full wave inversion of the elastic wave equation and Cauchy or partial boundary data (here, broad-band waveforms measured at Earth?s surface). The proposed research extends the PIs previous research on inverse scattering and multi-scale tomography; it aims to transition from inverse scattering with the (asymptotic) generalized Radon transform to a full waveform analogue, to develop a nonlinear illumination correction and partial reconstruction approach and a (complementary) analyses for the (transient) time-domain formulation and (multi-)frequency (?fixed energy?) formulation, and to study wave constituents associated with (multiple) scattering off complex structures (edges, for example). In view of application to USArray data we aim to generalize receiver function analysis, characterize sharp transitions (such as the crust-mantle interface, the lithosphere-asthenosphere boundary, and interfaces associated with subduction zones), and develop nonlinear reflection and transmission tomography to constrain physical properties of the mantle beneath North America.

了解地球在一定长度尺度上的内部结构对于了解自然灾害（地震、火山）、开发地下能源以及了解地球的长期地质演化是必要的。 地震或人造震源发出的地震波是对地球内部最直接、最精确的探测。传统上，地震学家认识到两种类型的非破坏性方法可以根据在介质边界处进行的测量来确定介质特性。断层扫描（概念上类似于医学计算机辅助断层扫描）旨在限制透射地震波的平滑介质变化，而逆散射旨在限制反射波、折射波或衍射波的非平滑异质性（边缘、界面）。这些方法彻底改变了我们对地球结构的理解，但尚未充分发挥其潜力。一个重要的问题是，出于实际和技术原因，它们过去被分开对待。 事实上，（局部）线性化和渐近理论的使用阻碍了对具有不同（但互补）采样属性的地震数据的内部一致解释。 基于地震学、反演理论以及微局域和谐波分析方面的专业知识，该研究旨在开发一个统一的（非线性、全波）反演和介质重建理论框架，其中层析成像和反散射不再单独处理。 新方法可以实现更准确的石油和天然气地震勘探，但主要的地球科学动机是利用 USArray 提供的数据研究北美地下的地壳和地幔，USArray 是 EarthScope 的地震学组成部分，EarthScope 是一个全国性的多年期地球科学项目。从数学科学的角度来看，挑战是开发一种统一的分析和计算高效的算法，用于弹性波方程和柯西或部分边界数据的全波反演（这里是在地球表面测量的宽带波形） 。 拟议的研究扩展了 PI 先前在反散射和多尺度断层扫描方面的研究；它的目的是从（渐近）广义氡变换的逆散射过渡到全波形模拟，开发非线性照明校正和部分重建方法以及（瞬态）时域公式和（多）分析。 ）频率（？固定能量？）公式，并研究与复杂结构（例如边缘）的（多次）散射相关的波成分。 鉴于对 USArray 数据的应用，我们的目标是推广接收函数分析，表征急剧转变（例如壳幔界面、岩石圈-软流圈边界以及与俯冲带相关的界面），并开发非线性反射和透射断层扫描以约束北美地幔的物理特性。