Inverting Solar Spectroscopic Data using the OLA Helioseismic Inversion Method

Agrawal, Piyush

Graduate Thesis Or Dissertation

Inverting Solar Spectroscopic Data using the OLA Helioseismic Inversion Method Public Deposited

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/nc580n89c

Abstract

One relies on inversion methods to infer the vertical structure of the solar atmosphere. Given the ill-posed nature of the inverse problems, combined with error sources from spectral noise and neglected higher-order terms, the inverted solutions are unrealistically highly oscillatory in nature. Regularization is required to produce physically meaningful solutions. In SIR inversions, one regularizes by inverting at a few user-defined depth locations (nodes). These nodes set the vertical resolution limit of the inverted atmosphere and do not correspond to the 'true resolution limit' achievable using the data that will be provided by DKIST. It is critical to determine the true resolution limit achievable and invert at that resolution to use the telescope at its full potential.In this thesis, we, for the first time, apply the Optimally Localized Averages (OLA) inversion method, developed for helioseismology and geoseismology applications, to spectroscopic data to invert for solar photospheric thermodynamic parameters. The method aims to find the 'best possible' solution for a given variable at each depth. We discuss the OLA methodology and advancements we have made to allow inversion for non-linear (large amplitude) perturbations by iteration. 'Edge-effects’ caused by non-localized large-scale perturbations are the most challenging aspect in this iterative approach. A hybrid SIR (large-scale, low-resolution) + OLA (small-scale, high-resolution) approach successfully addresses this issue. We discuss inversion results using MURaM atmospheres and make comparisons with SIR inversions. The results are promising, though some limitations remain, and we propose future improvements to address those.The results of this thesis have broader importance and suggest ways to improve overall inversion capabilities. We show that using response function amplification can improve inherent spectral sensitivity to sub-dominant variables and allow electronic pressure inversion in the presence of unknown temperature perturbations. Additionally, removing redundancies from the response function matrix can significantly improve its inversion capability. Finally, we demonstrate that the slope of the response function singular value curve can be used as a quantitative metric for assessment of line combinations and their inversion capability. Once line combinations are identified, OLA averaging kernel widths can be used to gain insight into the corresponding inversion quality achievable.

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