CMG: Collaborative Research: Multi-Scale (Wave Equation) Tomographic Imaging with USArray waveform data

地震层析成像是指一类广泛的技术，旨在利用从地球表面记录的地震记录中收集的信息来估计地震波在地球内部传播速度的空间变化。这一概念与医学应用有许多共同之处，例如CAT成像。在过去的几十年里，随着对地球大范围、深部内部结构的成像，全球层析成像取得了重大进展。然而，目前可用的技术在大范围的长度尺度上限制地球结构方面做得并不是很好，这是理解近地表和更深地幔过程之间关系的先决条件。事实上，不均匀的数据覆盖和不同的数据质量往往会产生不唯一的、模糊的图像，可靠性在空间上存在很大差异。红色和蓝色图像的近似性质阻碍了定量解释，并使断层成像无法充分发挥其作为探测地球深处的探测器的潜力。这在地球范围的背景下尤其重要，这是一个由国家科学基金会资助的全国性多年期地球科学项目。它的地震学部分，USArray，已经开始从密集分布的地震台站提供壮观的宽带数据，但为了最好地利用这些数据，即建立北美下面地壳和地幔的最佳可能模型，人们需要使用比目前可用的更好的层析成像方法。传统的层析成像技术只使用记录数据的一小部分，例如特定地震波的到达时间或(过滤)波形。我们需要提高对地震(或其他震源)激发的宽带波场的解释能力。从地球科学的角度来看，我们希望对北美地幔的非均质性(包括各向异性)有更好的了解，并更好地了解其成因的物理和化学过程。从物理角度来看，这需要充分考虑弹性波如何在具有强烈(且通常是非光滑的)非均质性的介质中传播。从数学的角度来看，这需要使用更精确的波传播理论(基于波动方程)来捕捉这种复杂性，巧妙的波场表示和模型参数化(例如，通过曲线框的方法)以允许更快的计算，以考虑到现代(学术和工业)数据集的海量，以及新的统计数据来估计由此产生的地球次表面的描述中的现实不确定性。事实上，我们必须在从“数据”到“图像”的轨迹上的所有步骤中考虑全波动力学，包括数据表示、波动理论、参数化、正则化和不确定性分析。

Seismic tomography refers to a broad class of techniques that aim to estimate spatial variations in the propagation speed of seismic waves in Earth's interior using information gleaned from seismograms recorded at Earth's surface. The concept has many aspects in common with medical applications, such as CAT imaging. Over the past decades global tomography has made significant progress with the imaging of Earth's large-scale, deep-interior structure. However, currently available techniques do not do a very good job in constraining Earth's structure on a wide range of length scales, which is a prerequisite for understanding the relationship between near-surface and deeper-mantle processes. Indeed, uneven data coverage and heterogeneous data quality often render non-unique, fuzzy images, with substantial spatial variation in reliability. The approximate nature of the 'red and blue' images impedes quantitative interpretation and keeps tomography from reaching its full potential as a probe of Earth's deep interior. This is particularly important in the context of EarthScope, a nationwide, multi-year geosciences project funded by the National Science Foundation. Its seismology component, USArray, has begun to provide spectacular broad-band data from dense distributions of seismograph stations, but to make optimal use of such data, that is, to construct the best possible models of the crust and mantle beneath North America, one needs to use better tomographic imaging methods than are available today. Traditional tomographic techniques use only a small part of the recorded data, for instance the arrival time or (filtered) waveform of a particular seismic wave. We need to improve our ability to interpret the broad-band wavefield excited by earthquakes (or other sources). From a geosciences point of view, we wish to have better images of mantle heterogeneity (including anisotropy) beneath North America and better understanding of the causative physical and chemical processes. From a physical point of view, this requires full consideration of how the elastic waves propagate in media with strong (and often non-smooth) heterogeneity. From a mathematical point of view this requires the use of more accurate wave-propagation theory (based on the wave equation) in order to capture this complexity, clever wavefield representation and model parameterization (for instance by means of curvelet frames) to allow faster computation in view of the massive size of modern (academic and industrial) data sets, and new statistics to estimate realistic uncertainties in the resulting depictions of Earth's sub-surface. Indeed, we must consider full wave dynamics in all steps on the trajectory from 'data' to 'image', including data representation, wave theory, parameterization, regularization, and uncertainty analysis.