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

知道地球?对于了解自然灾害（地震、火山）、开发地下能源资源以及了解地球的长期地质演化，在一定长度尺度上研究地球内部结构是必要的。地震或人造震源发出的地震波是对地球最直接、最精确的探测。室内。传统上，地震学家认为有两种非破坏性的方法可以通过测量介质的边界来确定介质的性质。断层扫描（在概念上类似于医学计算机辅助断层扫描）的目的是约束传输地震波的平滑介质变化，而逆散射的目的是约束反射、折射或绕射波的非光滑非均质性（边缘、界面）。这些方法彻底改变了我们对地球的认识。但尚未充分发挥其潜力。一个重要的问题是，由于实际和技术原因，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）采样特性的地震数据的内部一致解释。基于地震学、反演理论、微局部和谐波分析方面的专业知识，本研究旨在为（非线性、全波）反演和介质重建建立一个统一的理论框架，其中层析成像和逆散射不再单独处理。这些新方法可以更精确地进行石油和天然气的地震勘探，但主要的地球科学动机是利用USArray提供的数据研究北美地壳和地幔，USArray是由美国国家科学基金会资助的一个全国性的多年地球科学项目EarthScope的地震学组成部分。从数学科学的角度来看，挑战是为弹性波动方程和柯西或部分边界数据（这里是在地球上测量的宽带波形）的全波反演开发一种统一的分析和计算效率高的算法。表面)。本研究扩展了PIs在逆散射和多尺度层析成像方面的研究；它旨在从（渐近）广义Radon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，并对（瞬态）时域公式和（多）频率(？固定能量？)公式，并研究与复杂结构（例如边缘）的（多重）散射相关的波成分。考虑到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（如地壳-地幔界面、岩石圈-软流圈边界以及与俯冲带相关的界面），并发展非线性反射和透射层析成像，以约束北美地幔的物理性质。

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.