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，如电力传输，管道腐蚀，通信，导航和气候变化。除了工程学之外，多锥度方法还在医学领域（包括神经学和磁共振成像）、经济学和金融学以及天文学等领域得到了应用和扩展。事实上，看一下2019年对原始多锥度论文（1982年）的引用，就会发现这种方法在所有这些领域的扩展和应用。 我们1995年发现的行星际电子流中的太阳模已经从一个科学的好奇心发展成为“地震嗡嗡声”的最佳解释，这种声音每天需要相当于6级地震的能量。我们还显示了这些太阳模式的存在对在太平洋底部测量的压力。 相关的理论工作终于回答了频谱估计中虚假峰的数量和形状的问题;瑞利勋爵在1879年提出的问题。 其他数据分析研究正在开发方法，使Loève在20世纪40年代后期的非平稳过程理论成为有用的数据分析工具。例如，我们表明，地球磁场的垂直分量与北分量具有高度的相干性，当频率被向下移动了一个周期/天和半个周期/天时，这是完全出乎意料的。有许多奥秘有待探索，毫无疑问，探索将导致新的方法。 我所培训的大多数HQP都选择了这些问题的某个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.