Elena Khomenko

Abstract This Primer provides an overview of a fundamental set of analysis methods for studying waves, vibrations and related oscillatory phenomena — including instabilities, turbulence and shocks — across diverse scientific fields. These phenomena are ubiquitous, from astrophysics to complex systems in terrestrial environments, and understanding them requires careful selection of techniques. Misapplication of analysis tools can introduce misleading results.

1. Introduction Tomographic analysis of the complex solar atmosphere and its dynamics requires the combined use of different spectral lines (e.g. Ca ɪɪ, Mg ɪɪ, Lα and Hα). Indeed, due to radiative transfer effects, these lines are formed across different heights of the solar atmosphere, with spectral information extracted at a particular percentage line depth corresponding to differing optical depths, and hence particular atmospheric heights [1].