# No unique solution to the seismological problem of standing kink MHD waves

## TL;DR

This paper argues that the seismological problem of standing kink MHD waves in coronal loops cannot have a unique solution, highlighting the limitations of current observational and theoretical methods.

## Contribution

It clarifies that the problem is a reduced one with inherent non-uniqueness, supported by Bayesian inference analysis.

## Key findings

- No unique solution exists for the seismological problem.
- Bayesian inference provides insights into the inversion limitations.
- The problem is better described as a reduced rather than a full seismological problem.

## Abstract

The aim of this paper is to point out that the classic seismological problem using observations and theoretical expressions for the periods and damping times of transverse standing magnetohydrodynamic (MHD) waves in coronal loops is better referred to as a reduced seismological problem. Reduced emphasises the fact that only a small number of characteristic quantities of the equilibrium profiles can be determined. Reduced also implies that there is no unique solution to the full seismological problem. Even the reduced seismological problem does not allow a unique solution. Bayesian inference results support our mathematical arguments and offer insight into the relationship between the algebraic and the probabilistic inversions.