CMG: Nonlinear Elastic-Wave Inverse Scattering and Tomography - from Cracks to Mantle Convection

CMG：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: 1025259
• 负责人: Andras Vasy
• 金额: $ 17.39万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2015-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1025259&HistoricalAwards=false
• 关键词: CMG; Nonlinear; Elastic; Wave; Inverse

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.

了解地球的内部结构在一系列长度范围内是必要的，以了解自然危害（地震，火山），利用地下能量资源并了解我们星球的长期地质演变。 地震或人造资源发出的地震波代表了地球内部最直接，最精确的探针。传统上，地震学家认识到两种类型的非破坏性方法，用于从其边界上进行的测量结果确定培养基。断层扫描（概念上类似于医学计算机辅助断层扫描）旨在限制传播地震波的光滑介质变化，而逆散射旨在限制反射，折射或衍射波的非平滑异质性（边缘，接口）。这些方法彻底改变了我们对地球结构的理解，但尚未发挥其全部潜力。一个重要的问题是，出于实际和技术原因，它们曾经分别接受治疗。 的确，（局部）线性化和渐近理论的使用可以防止内部一致的地震数据（具有不同（但互补）的采样特性）。 在地震学，逆理论以及微局部和谐波分析方面的专业知识的基础上，拟议的研究旨在为（非线性，全波）倒置和中等重建建立一个统一的理论框架，在这种框架中不再单独处理断层扫描和逆散射。 新方法可以导致对石油和天然气的更准确的地震探索，但主要的地球科学动机是通过USArray提供的数据（Earthscope的地震学组成部分，全国性的，多年的地球科学项目）对NSF.FROM A ALLOVER的全国性分析和计算，并在北美的北美下面研究了地壳和套筒，并在数学上的范围进行了整体分析。弹性波方程和cauchy或部分边界数据的反转（在这里，在地球表面测得的宽带波形）。 拟议的研究扩展了PIS先前关于反散射和多尺度断层扫描的研究。它的目的是通过（渐近）广义ra转换为完整波形模拟，开发非线性照明校正和部分重建方法，以及（互补的）分析（（瞬态）时间段的公式和（多）频率（？固定能量（？固定的）频率（？）与构造（多个散射）相关（多个），（互补的）分析（互补）分析（互补）分析（互补）分析（互补）分析（互补）分析（互补）（互补的）分析（多个）散射（多）。 鉴于应用于USARRAY数据，我们旨在概括接收器功能分析，表征尖锐的过渡（例如地壳垂体界面，岩石圈 - 心圈边界以及与俯冲区域相关的接口），并发展非线性反射和透射术，以构造北部北部壁炉的物理特性。