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\begin{document}

\title{Application of Vector Spherical Harmonics to the Magnetisation of Mars'
Crust}



\author[1,1]{David Gubbins}%
\author[2,2]{Yi Jiang}%
\author[3,3]{Simon Williams}%
\author[2,2]{Keke Zhang}%
\affil[1]{University of Leeds}%
\affil[2]{Macau University of Science and Technology}%
\affil[3]{Northwest University}%


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  \date{May 18, 2024}


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\begin{abstract}
Mars has a magnetic field originating in its strongly magnetised crust
that holds clues to the planet's interior. We apply vector spherical
harmonic decomposition to simple candidate magnetic structures to
separate the parts responsible for the anomalies from those that remain
invisible. A uniform magnetic layer produces no anomalies: spatial
variations are essential although secondary magnetisation does produce a
weak field that might reflect the primordial dynamo field. A hemispheric
layer produces anomalies confined to the equator rather than the
observed hemispheric difference. A uniformly magnetised crust with
variable thickness determined from gravity and topography produces a
crustal field with large anomalies at the major impact crater sites that
are not observed. These anomalies are not present if the magnetic layer
lies deeper than the crater floor. We conclude that decomposing
magnetisations in this way is a useful tool in the interpretation of
Martian magnetic anomalies.%
\end{abstract}%



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