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\begin{document}

\title{Joint Inversion of receiver functions and apparent incidence angles to
determine the crustal structure of Mars}



\author[1]{Rakshit Joshi}%
\author[2]{Brigitte Knapmeyer-Endrun}%
\author[3]{Klaus Mosegaard}%
\author[4]{Mark A. Wieczorek}%
\author[5]{Heiner Igel}%
\author[6]{Ulrich Christensen}%
\author[7]{Philippe Henri Lognonné}%
\affil[1]{Max Planck Institute for Solar System Research}%
\affil[2]{Bensberg Observatory, University of Cologne}%
\affil[3]{Niels Bohr Institute}%
\affil[4]{Observatoire de la Côte d'Azur}%
\affil[5]{Ludwig Maximilian University of Munich}%
\affil[6]{Max-Planck-Institut für Sonnensystemforschung}%
\affil[7]{Institut de Physique du Globe de Paris et Université de Paris Diderot}%


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  \date{June 05, 2024}


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\begin{abstract}
Recent estimates of the crustal thickness of Mars show a bimodal result
of either ~20 km or ~40 km beneath the InSight lander. We propose an
approach based on random matrix theory applied to receiver functions to
further constrain the subsurface structure. Assuming a spiked covariance
model for our data, we first use the phase transition properties of the
singular value spectrum of random matrices to detect coherent arrivals
in the waveforms. Examples from terrestrial data show how the method
works in different scenarios. We identify three new converted arrivals
in the InSight data, including the second multiply reflected phase from
a deeper third interface. We then use this information to jointly invert
receiver functions with the absolute S-wave velocity information in the
polarization of body waves. Results show a crustal thickness of 43\selectlanguage{ngerman}±5 km
beneath the lander with two mid-crustal interfaces at depths of 8.5±1.5
km and 22±3 km.%
\end{abstract}\selectlanguage{ngerman}%



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