Statistical Spectrum Estimation and Solar Gravity Modes

我建议继续研究太阳正常模式之间的联系，一些相关的统计问题，以及这些模式对地球的影响。这些影响可以在许多领域看到，如输电、管道腐蚀、通信、航运和不断变化的气候。展望工程学之外，多锥体方法在医学等领域得到使用和扩展，包括神经学和磁共振成像；经济和金融；以及天文学。事实上，浏览一下2019年对原始多锥体论文(1982)的引用就会发现这种方法的扩展以及在所有这些领域和更多领域的应用。我们在1995年发现的行星际电子通量中的太阳模式，已经从科学上的好奇心演变成了对地震嗡嗡声的最佳解释，地震嗡嗡声需要相当于每天6级地震的能量。我们还展示了这些太阳模式在太平洋底部测量的压力上的存在。相关理论工作终于回答了谱估计中虚假峰的数量和形状的问题；这个问题是瑞利勋爵在1879年提出的。其他数据分析研究正在开发方法，使洛耶夫1940年代末的S关于非平稳过程的理论成为有用的数据分析工具。例如，我们发现，当频率同时向下移动一周/天和半周/天时，地球磁场的垂直分量与北分量具有高度的一致性；这完全是意想不到的。有许多谜团有待探索，毫无疑问，探索将带来新的方法。我正在培训的大多数HQP都选择了这些问题的某些方面作为他们研究的基础。

I propose to continue studying the connection between normal modes of the Sun, some related statistical problems, and the effects of these modes on Earth. These effects can be seen in many areas such as power transmission, pipeline corrosion, communications, navigation, and a changing climate. Looking beyond engineering, multitaper methods are used and expanded in fields such as medicine, including neurology and magnetic resonance imaging; economics and finance; and astronomy. In fact, a glance at 2019 citations to the original multitaper paper (1982) show extensions to this method and applications in all of these fields and more. Our 1995 discovery of solar modes in interplanetary electron fluxes has evolved from a scientific curiosity into the best explanation of "seismic hum", something that requires energy equivalent to a magnitude-6 earthquake every day. We have also shown the presence of these solar modes on the pressure measured at the bottom of the Pacific Ocean. Related theoretical work has finally answered the questions about the number and shapes of spurious peaks in spectrum estimates; a question posed by Lord Rayleigh in 1879. Other data analysis studies are developing methods that make Loève's late 1940's theories of nonstationary processes into useful data analysis tools. We show, for example, that the vertical component of Earth's magnetic field has high coherence with the North component when the frequencies are shifted down by both a cycle-per-day and one-half cycle/day; this was completely unexpected. There are many mysteries to be explored, and no doubt, the exploration will lead to new methods. Most of the HQP I am training chose some aspect of these problems on which to base their research.