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，它使地球摆脱热量。这种对流流动是由温度和/或地幔成分变化引起的密度横向变化驱动的。地震层析成像的目标是成像这些横向变化，它在成像地震速度变化方面已经相当成功。成像密度的变化更具挑战性。一种方法是利用由大地震激发的地球“自由振荡”的分裂和耦合。这种振荡类似于钟被敲后发出的声音。在这里，PI提出了一种新的方法来分析地球的这种振荡，这将产生更好的地幔结构的3D模型，从而阐明驱动板块构造的力量。地球三维模型的建立也提高了我们精确模拟地震波传播的能力。这具有许多社会意义，包括提高估计地震危险的能力，以及监督禁止核试验条约的能力。在全球地震层析成像中，目标是在地幔和内核中成像地球的三维结构。目前，地幔的三维剪切速度图像相当稳健，而纵波速度（或者更好的是体声速）图像则不那么稳健，三维密度结构图像仍然存在争议。但有一件事是明确的，即地幔中这些参数之间没有简单的标度，这意味着观测到的异常的横向和深度变化的原因。三维密度结构不仅对区分地球内部异常的可能物理原因很重要，而且它驱动对流流动，因此对确定动态地形和大地水准面有影响。从地震角度获得三维密度结构的为数不多的方法之一是通过研究自由振荡的分裂和耦合。在这里，PI团队提出了一种对自回归技术（AR）的修改，将其与邻域算法（NA）相结合。所得到的算法的主要优点是它对源不敏感（对于自由振荡工作中使用的大事件，源通常是复杂的），但允许直接控制解的形式，以便可以评估其鲁棒性。该方法将应用于过去20多年来所有大地震的3分量记录的扩展数据集，以研究（有效）非耦合多胞胎和耦合多胞胎，从而给出奇偶结构的约束。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的长波三维密度结构，并显著提高我们对整个地球的长波弹性和非弹性结构的认识。

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.