Statistical Spectrum Estimation and Solar Gravity Modes

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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.