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Wave analysis tools

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. In this Primer, the fundamental principles of various wave analysis methods are first reviewed, along with adaptations to address complexities such as nonlinear, non-stationary and transient signal behaviour. These techniques are applied to identical synthetic datasets to provide a quantitative comparison of their strengths and limitations. Details are provided to help select the most appropriate analysis tools based on specific data characteristics and scientific goals, promoting reliable interpretations and ensuring reproducibility. Additionally, the Primer highlights best ethical practices for data deposition and the importance of open-code sharing. Finally, the broad applications of these techniques are explored in various research fields, current challenges in wave analysis are discussed, and an outlook on future directions is provided, with an emphasis on potential transformative discoveries that could be made by optimizing and developing cutting-edge analysis methods.

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Fig. 1: Unveiling wave phenomena with a visual guide to wave analysis.

Fig. 2: Synthetic datasets.

Fig. 3: Performance of diverse analysis methods on the intricate synthetic 1D time series.

Fig. 4: Dominant frequency maps and mean power spectra.

Fig. 5: Comparison of k − ω filtering and POD analysis.

Fig. 6: Cross-correlation analysis of two synthetic 1D time series using FFT and wavelet techniques.

Code availability

The synthetic datasets and codes used for the wave analyses presented in this Primer, including the generation of all displayed figures, are publicly available via the WaLSAtools repository on GitHub (https://github.com/WaLSAteam/WaLSAtools), archived at Zenodo (https://doi.org/10.5281/zenodo.14978610). Further information and documentation are available online at https://WaLSA.tools.

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Acknowledgements

The authors acknowledge the scientific discussions with the Waves in the Lower Solar Atmosphere (WaLSA) team, which has been supported by the Research Council of Norway (project number 262622), The Royal Society (award number Hooke18b/SCTM)284, and the International Space Science Institute (ISSI Team 502). The authors also thank H. Schunker for her insightful comments and suggestions. S.J. gratefully acknowledges support from the Niels Bohr International Academy, at the Niels Bohr Institute, University of Copenhagen, Denmark, and the Rosseland Centre for Solar Physics, University of Oslo, Norway. D.B.J. and T.J.D. acknowledge support from the Leverhulme Trust via the Research Project Grant RPG-2019-371. D.B.J., S.J. and S.D.T.G. thank the UK Science and Technology Facilities Council (STFC) for the consolidated grants ST/T00021X/1 and ST/X000923/1. D.B.J. and S.D.T.G. also acknowledge funding from the UK Space Agency via the National Space Technology Programme (grant SSc-009). S.B. acknowledges the support from the STFC Grant ST/X000915/1. V.F., G. Verth and S.S.A.S. acknowledge the support from STFC (ST/V000977/1 and ST/Y001532/1) and the Institute for Space-Earth Environmental Research (ISEE, International Joint Research Program, Nagoya University, Japan). V.F. and G. Verth thank the Royal Society International Exchanges Scheme, in collaboration with Monash University, Australia (IES/R3/213012), Instituto de Astrofisica de Canarias, Spain (IES/R2/212183), National Observatory of Athens, Greece (IES/R1/221095), and the Indian Institute of Astrophysics, India (IES/R1/211123), for the support provided. R.G. acknowledges the support from Fundação para a Ciência e a Tecnologia through the research grants UIDB/04434/2020 and UIDP/04434/2020. E.K. acknowledges the support from the European Research Council through the Consolidator Grant ERC-2017-CoG-771310-PI2FA and from the Agencia Estatal de Investigación del Ministerio de Ciencia e Innovación through grant PID2021-127487NB-I00. R.J.M. acknowledges the support from the UK Research and Innovation Future Leader Fellowship (RiPSAW-MR/T019891/1). L.A.C.A.S. acknowledges the support from the STFC Grant ST/X001008/1. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 101097844 — project WINSUN). N.Y. acknowledges the support from the DST INSPIRE Faculty Grant (IF21-PH 268) and the Science and Engineering Research Board – Mathematical Research Impact Centric Support grant (MTR/2023/001332).

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Authors and Affiliations

Max Planck Institute for Solar System Research, Göttingen, Germany

Shahin Jafarzadeh, Daniele Calchetti & Sami K. Solanki

Astrophysics Research Centre, Queen’s University Belfast, Belfast, UK

Shahin Jafarzadeh, David B. Jess, Samuel D. T. Grant, Peter H. Keys & Timothy J. Duckenfield

Department of Physics and Astronomy, California State University Northridge, Los Angeles, CA, USA

David B. Jess

Italian Space Agency (ASI), Rome, Italy

Marco Stangalini

Department of Geography and Planning, School of Environmental Sciences, University of Liverpool, Liverpool, UK

Jonathan E. Higham

Niels Bohr International Academy, Niels Bohr Institute, Copenhagen, Denmark

Martin E. Pessah

Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, UK

Sergey Belov

Plasma Dynamics Group, School of Electrical and Electronic Engineering, The University of Sheffield, Sheffield, UK

Viktor Fedun & Suzana S. A. Silva

Operations Department, ESA Directorate of Science, Greenbelt, MD, USA

Bernhard Fleck

Geophysical and Astronomical Observatory, Faculty of Science and Technology, University of Coimbra, Coimbra, Portugal

Ricardo Gafeira

Instituto de Astrofísica e Ciências do Espaço, University of Coimbra, Coimbra, Portugal

Ricardo Gafeira

Department of Physics, University of Coimbra, Coimbra, Portugal

Ricardo Gafeira

Department of Physics and Astronomy, Georgia State University, Atlanta, GA, USA

Stuart M. Jefferies

Institute for Astronomy, University of Hawaii, Honolulu, HI, USA

Stuart M. Jefferies

Instituto de Astrofísica de Canarias, La Laguna, Spain

Elena Khomenko

Departamento de Astrofísica, Universidad de La Laguna, Tenerife, Spain

Elena Khomenko

Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, UK

Richard J. Morton, Luiz A. C. A. Schiavo & Rahul Sharma

Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, USA

Aimee A. Norton

Indian Institute of Astrophysics, Bangalore, India

S. P. Rajaguru

Institute for Solar Physics (KIS), Freiburg, Germany

Oskar Steiner & Gangadharan Vigeesh

Istituto ricerche solari Aldo e Cele Daccò (IRSOL), Locarno, Switzerland

Oskar Steiner

Plasma Dynamics Group, School of Mathematical and Physical Sciences, The University of Sheffield, Sheffield, UK

Gary Verth

Department of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Vithura, India

Nitin Yadav

Authors

Shahin Jafarzadeh

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