Imaging the Mt. Melbourne Volcanic Field (Northern Victoria Land, Antarctica): a Hamiltonian Monte Carlo approach applied to high-resolution aeromagnetic data

&amp;lt;p&amp;gt;The Mt. Melbourne Volcanic Complex (MMVC) is located in Northern Victoria Land (Antarctica) along the western flank of the West Antarctic Rift System, at the boundary with the Transantarctic Mountains. It is constituted by two main volcanic areas, i.e. the Mt. Melbourne Edifice (MME) and the Cape Washington Shield (CWS), and some other minor centres.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;To date, the inner structure of this volcanic complex is still poorly known, being the direct geological information on site confined to either glacial erratics or a few rock outcrops not hidden by the ice sheet. Consequently, even the temporal building up and evolution of the MMVC as well as its primary magmatic source are still under investigation (debated).&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Recently, we attempted to define the geological structure of the MMVC by means of digital enhancement and forward modeling performed on a high-resolution aeromagnetic dataset (Ghirotto et al. 2020, EGU). Coupling both information derived from past geological/geophysical studies and unpublished magnetic susceptibility measurements from rock samples collected in the field, we proposed two models to explain the chronological evolution of the MME and CWS. These models involve either i) major magmatic events occurred in periods of both normal and reverse magnetic polarity or ii) only magmatic flows with normal polarity.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;To gain further insights into the geological structure and the geodynamic evolution of the MMVC in relation to the two proposed models, we develop here a Hamiltonian Monte Carlo (HMC) algorithm (Fichtner et al. 2018) based on the probabilistic approach to inverse problems. To date, this methodology has never been applied to aeromagnetic data for geological studies. In detail, the above proposed models provide some soft a priori information from which to start exploring potential solutions. The parameterization of the volcanic area is defined in terms of 2-D polygonal bodies, representing e.g. magmatic lava flows, where the unknown parameters are represented by both the position of the vertices and/or the magnetization (induced and/or remnant), resulting in a non-linear forward model. The HMC algorithm requires the computation of gradients of the posterior probability density (PPD), i.e., derivatives of the objective functional with respect to the position of vertices of the bodies and magnetization, in order to better move the inversion process toward high-probability areas in the model space manifold. We implement such calculations using automatic differentiation, a tool which is very accurate and fast compared to other approaches such as finite difference. The result of the inversion is then a collection of models representing the PPD, from which statistical analysis can provide measures of uncertainty and plausible geological scenarios.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;In this study we present some preliminary results of applying the above-mentioned methodology, which finally could help unravel the framework of the MMVC.&amp;lt;/p&amp;gt;