Improved estimation of free oscillation splitting coefficients using a combination of autoregressive estimation and the neighborhood algorithm

板块构造是地幔循环的外在表现，它使地球能够摆脱热量。这种对流是由密度的横向变化驱动的，密度的横向变化是由整个地幔的温度和/或成分变化引起的。地震层析成像的目标是对这些横向变化成像，并且它在对地震速度的变化成像方面已经相当成功。成像密度变化更具挑战性。一种方法是利用大地震激发的地球“自由振荡”的分裂和耦合。这种振动类似于钟被敲击后的音调。在这里，PI提出了一种新的方法来分析地球的这种振荡，这将导致更好的地幔结构的3D模型，从而揭示驱动板块构造的力量。地球3D模型的构建也提高了我们准确模拟地震波传播的能力。这有许多社会影响，包括提高估计地震危险的能力，以及监测核禁试条约。在全球地震层析成像中，目标是对地幔和内核中的地球三维结构进行成像。目前，地幔中的三维剪切速度的图像是相当强大的，但压缩速度（或更好的是，整体声速）的图像是如此，和三维密度结构的图像仍然存在争议。但有一点是清楚的，即地幔中这些参数之间没有简单的比例关系，这意味着所观察到的异常的横向和深度变化原因。3D密度结构不仅对于区分地球内部异常的可能物理原因很重要，而且正是它驱动了对流，因此对确定动态地形和大地水准面具有影响。从地震学的观点得到三维密度结构的少数方法之一是通过研究自由振荡分裂和耦合。在这里，PI团队通过将自回归技术（AR）与邻域算法（NA）相结合，提出了对AR的修改。所得到的算法的主要优点是，它是不敏感的源（这往往是复杂的自由振荡工作中使用的大事件），但允许直接控制的解决方案的形式，使其鲁棒性可以评估。该方法将被应用到一个扩展的数据集的3分量记录从所有的大地震在过去的20多年来研究（有效地）非耦合多重和耦合多重，使奇数和偶数结构的约束。这样确定的自由振荡结构系数将与其他类型的地震数据相结合，以更可靠地确定地球中的长波长三维密度结构，并大大提高我们对整个地球的长波长弹性和滞弹性结构的认识。

Plate tectonics is the outward expression of the mantle circulation that allows the Earth to get rid of its heat. This convective flow is driven by lateral variations in density induced by changes in temperature and/or composition throughout the mantle. The goal of seismic tomography is to image these lateral variations and it has been quite successful in imaging variations in seismic velocities. Imaging variations in density is much more challenging. One way to do this is to use the splitting and coupling of "free oscillations" of the Earth excited by large earthquakes. Such oscillations are analogous to the tones of a bell after it has been struck. Here the PI proposes a novel way to analyze such oscillations of the Earth that will result in better 3D models of the structure of the mantle and so shed light on the forces driving plate tectonics. The construction of 3D models of the Earth also improves our ability to accurately model the propagation of seismic waves. This has many societal implications including an improved ability to estimate seismic hazard, and to monitor a nuclear test ban treaty. In global seismic tomography, the goal is to image the 3D structure of the Earth in both the mantle and inner core. Currently, images of 3D shear velocity in the mantle are quite robust but images of compressional velocity (or, better yet, bulk sound speed) are less so, and images of 3D density structure still remain controversial. One thing that is clear though is that there is no simple scaling between these parameters in the mantle implying laterally and depth varying causes of the observed anomalies. 3D density structure is not only important for discriminating between possible physical causes of anomalies inside the Earth, but it is this that drives convective flow and so has consequences for determining dynamic topography and the geoid. One of the few ways to get at 3D density structure from a seismic point of view is through the study of free-oscillation splitting and coupling. Here the PI team proposes a modification to the autoregressive technique (AR) by combining it with the Neighborhood Algorithm (NA). The main advantage of the resulting algorithm is that it is not sensitive to the source (which can often be complicated for the large events used in free-oscillation work) but allows direct control over the form of solution so that its robustness can be assessed. The method will be applied to an expanded dataset of 3-component recordings from all major earthquakes in the last 20+ years to study both (effectively) uncoupled multiplets and coupled multiplets so giving constraints on both odd and even structure. The free oscillation structure coefficients so determined will be combined with other types of seismic data to give a more reliable determination of the long-wavelength 3D density structure in the Earth, as well as significantly improving our knowledge of long-wavelength elastic and anelastic structure throughout the Earth.