HAO Colloquium - Piyush Agrawal, University of Colorado

Inverting solar spectroscopic data using the OLA helioseismic inversion method

One relies on inversion methods to infer the vertical structure of the solar atmospheric parameters e.g. temperature, gas pressure, etc. Given the ill-posed nature of the inversion problems, combined with spectral noise and neglected higher-order terms, these inverted solutions are unrealistically highly oscillatory. One usually forces a smooth (regularized) solution by inverting only at a few user-defined depth locations (nodes). These nodes set the vertical resolution limit of the inverted atmosphere. The current state of the art inversion methods produces atmospheres with a vertical resolution at best ~ 50 km, in the solar photosphere. This limit is most likely not the true resolution limit that can be achieved using the data obtained with telescopes such as DKIST. To use the telescope to its full potential, it is very important to determine the true information limit that can be extracted from the spectra.

To answer this question, we employed the OLA (Optimally Localized Averages) inversion method that doesn’t rely on nodes to obtain smooth solutions. The method originated in geoseismology and was later adopted by helioseismologists to invert for the internal structure of the sun. In OLA, one linearly combines the response functions intending to form a highly localized averaging kernel at a given location, to improve the system sensitivity to a particular variable at that location. The width of the averaging kernel corresponds to the vertical resolution at that depth and its limit is set by the response functions, crosstalk from other variables, and errors due to spectral noise and higher-order terms. The inversion at that depth corresponds to an average value defined by the averaging kernel. Thus, the more localized an averaging kernel is, the closer the inverted solution will be to the true solution. One then repeats this process for each location and variable to invert the entire atmosphere.

In this talk, I will discuss the basic methodology of the OLA method and will present temperature inversion results using OLA and how they compare to SIR inversions. I will also talk about the improvements that we have made over the traditional OLA method so that it can invert non-linear and large-scale perturbations. Lastly, if time persists, I will talk about how OLA has an advantage when doing multivariable inversion, which could potentially allow us to invert for electronic pressure in the presence of temperature to which the spectrum has much greater sensitivity.

Date and time: 
Tuesday, October 20, 2020 - 2:00pm to 3:00pm