Inversion of gravity and magnetic data in the presence of topography using deformable hexahedral elements

Potential-field geophysical data are commonly used to image geological structures in areas characterized by strong topographic variations, such as volcanic and rift systems. However, the forward modelling of potential-field data using traditional approaches may inadequately represent strongly varying topography if the physical space is not discretized appropriately, potentially biasing inversion results and subsequent geological interpretations. Recent modeling strategies, such as the use of numerical integration schemes within deformable hexahedral elements coupled with an algorithm for local refinement of the forward modeling mesh, have been shown to improve the modeling accuracy while maintaining a reasonable computational cost [Bellounis et al., Geophys. J. Int., ggag009, 2026]. Building on this previous work, we present the implementation of an inversion framework that is consistent with this numerical approach and assess its performance using a series of synthetic data that have not been corrected for topographic effects. The inversion is performed on models discretized using deformable hexahedral elements where physical properties are represented by 2nd order polynomials defined by their values at grid nodes. We first validate the inversion scheme using a model without topography, before considering a second example that incorporates complex topographic variations representative of the Krafla geothermal system in northern Iceland. These synthetic experiments highlight the challenges introduced by topography in the inversion process and demonstrate the improved integration of topographic information enabled by the proposed discretization and inversion strategy. We further examine the influence of the inverse problem regularization parameters on the recovery of subsurface anomalies, thereby providing insights into the advantages and current limitations of the newly implemented inversion framework.