Characterization of Helioseismic Mode Parameters, Their Solar Cycle Variations, & Their Impact on Inferences of Solar Dynamics Using SOI/MDI Data J.W. Leibacher, R. Howe, F. Hill, J.W. Harvey, R. Komm, S.M. Jefferies, C. Toner, and S. Jacoby National Solar Observatory Helioseismology provides a unique tool for testing models of stellar structure and evolution, as well as a direct probe of solar internal structure and dynamics. With the advent of modern helioseismology experiments, it is now clear that existing models of the spectrum of resonant oscillations, upon which helioseismology is based, and methods for determining the basic helioseismic data are far more uncertain than originally thought, calling into question the accuracy and precision of current inferences on solar internal structure, dynamics and evolution. In order to achieve the scientific potential of the SOHO helioseismology experiments, we propose to: 1. Develop an improved model of the solar oscillation spectrum incorporating line profile asymmetry, proper treatment of the phase relations between the background and the signal, consideration of the structure of the spectrum as obtained from observations of Doppler velocity and intensity, and an accurate spatial leakage structure including horizontal velocity components. 2. Develop new techniques to fit this model to the observed spectrum, including multi-tapering, multi-dimensional optimization, wavelet denoising, and the deconvolution of the spatial leakage structure. 3. Use the estimated oscillation parameters derived from the fitted model to study the solar activity cycle variations in frequency, frequency splittings, line asymmetries, widths, amplitudes, and background. 4. Use the estimated parameters in inversions for solar internal dynamics addressing the structure and evolution of the tachocline, localized solar jet streams, and other flows in the convection zone. 5. Search for g modes and low-frequency p modes to improve inferences about the solar core, and the near-surface layers. The proposed work will procuce a much bnetter understanding for all determinations of the solar internal dynamics, structure, and evolution. We propose to develop an educational/public outreach module to improve understanding of Helioseismology by using the familiar concepts of sound and music to convey that we can gain information about the interior of the Sun by "listening to" its acoustic vibrations. It will be based on materials developed during a 1995/96 IDEAS Grant project and will consist of a "helioseismology kit" as a resource for teachers and the non-technical public.