CMG Collaborative Research: Development and Application of Inference Methods for Imaging Neighborhoods of Earth's Core-Mantle Boundary with Broad-Band Scs and SKKS Coda Waves

研究人员提议对地核地幔边界进行定量、多学科的调查，地核地幔边界是地球固体硅酸盐地幔与其液态铁合金外核之间的遥远界面。通过解释(非常)大量宽带波形数据的创新技术--从密集的地震台站网络获得--他们的目标是绘制、描述和解释地球深处界面及其附近的声弹性特性的多尺度变化。最初，该团队专注于包含地球最低地幔、核心地幔边界(CMB)和最外层核心的物理外壳。他们将(1)利用广义傅立叶积分算符(GFIO)研究基于微域分析的逆散射理论，(2)基于这种算符发展统计模型，以及(3)将新技术应用于包含在CMB顶部(SCS)和底部(SKKS)反射的波的大量(数百万)地震记录窗口。从数学科学的角度来看，预期的结果是广义Radon变换(GRT)，它可以从大数据量生成公共图像点道集(IGs)。IGs用于(I)检测和确定弹性对比(奇点)的深度，(Ii)确定奇点的规律性，以及(Iii)研究推断参数中变化的特征长度尺度。将使用新的统计方法来增强转换中的S/N，从IG中收集更多信息，并提供不确定性估计。地球科学的动机是利用这些道集来提高对(I)高粘性地幔与液核之间的接触，(Ii)对流对D‘’结构和CMB特征的影响，以及(Iii)外核的非均质性(如果有的话)及其与外核磁流体动力学的关系的理解。这项合作不仅将有助于我们对深部地幔和最外层地核的组成和相化学、核-地幔转变和相互作用以及行星形成的总体理解。它还为参与其中的学生、博士后和高级工作人员提供独特的教育体验。事实上，研究人员认为，对具有强大数学背景的学生进行地球物理学方面的教育，对该领域的未来发展非常重要。

The investigators propose a quantitative, multi-disciplinary investigation of Earth's core mantle boundary, the remote interface between Earth's solid silicate mantle and its liquid iron-alloy outer core. With innovative techniques for interpreting (very) large amounts of broad-band waveform data - obtained from dense networks of seismograph stations - they aim to map, characterize, and interpret multi-scale variations in acousto-elastic properties at and near interfaces in Earth's deep interior. Initially, the team focuses on the physical shell that encompasses Earth's lowermost mantle, the core mantle boundary (CMB), and the outermost core. They will (1) investigate inverse scattering theory based on microlocal analysis making use of generalized Fourier integral operators (GFIOs), (2) develop statistical models based onsuch operators, and (3) apply the new techniques to a large number (millions) of seismogram windows containing waves that reflect at the top (ScS) and underside (SKKS) of the CMB. From a mathematicalsciences perspective, the anticipated result is a generalized Radon transform (GRT) that can generate common image point gathers (IGs) from large data volumes. The IGs are used to (i) detect and determinethe depth to elasticity contrasts (singularities), (ii) determine the regularity of the singularities, and (iii) study characteristic length scales of variations in the inferred parameters. Novel statisticalmethods will be used to enhance the S/N in the transforms, glean more information from the IGs, and provide uncertainty estimates. The geosciences motivation is to use these gathers to improve theunderstanding of (i) the contact between high-viscous mantle and liquid core, (ii) the effect of convective flow on the D'' structure and the character of the CMB, and (iii) outer core heterogeneity (ifany) and its relationship to outer core magneto-hydrodynamics. The collaboration will not only contribute to our general understanding of the composition and phase chemistry of the deep mantle and outermostcore, core-mantle transitions and interactions, and planetary formation. It also offers a unique educational experience for the students, postdocs, and senior staff involved. Indeed, the investigators believe that educating students in geophysics with strong background in mathematicsis important for the future development of the field.