A SART-Based Iterative Inversion Methodology to Infer the Solar Rotation Rate from Global Helioseismic Data

TL;DR

This paper introduces a novel iterative inversion method based on SART for inferring the solar rotation rate from helioseismic data, offering improved accuracy and uncertainty estimation over classical techniques.

Contribution

The paper develops and compares a new SART-based iterative inversion technique with existing methods, demonstrating its advantages in precision, resolution, and robustness in solar rotation inference.

Findings

The new method can outperform RLS in precision and resolution.

It estimates formal uncertainties without Monte Carlo simulations.

It shows robustness against noise and benefits from prior solutions.

Abstract

We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical inversion techniques like the Regularized Least Squares (RLS) and the Optimally Localized Averages (OLA) methods. In our implementation, we are able to estimate the formal uncertainty on the inferred solution using standard error propagation, and derive the averaging kernels without recourse to any Monte-Carlo simulation. We present the potential of this new technique using simulated rotational frequency splittings. We use noiseless sets that cover the range of observed modes and associate to these artificial splittings observational uncertainties. We also add random noise to present the noise magnification immunity of the method. Since the technique is iterative we also show its potential when using an apriori solution. With the right regularization this new method can outperform our RLS implementation in precision, scope and resolution. Since it results in very different averaging kernels where the solution is poorly constrained, this technique infers different values. Adding such a technique to our compendium of inversion methods will allow us to improve the robustness of our inferences when inverting real observations and better understand where they might be biased and/or unreliable, as we push our techniques to maximize the diagnostic potential of our observations.