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Modelling induced polarization effects in airborne electromagnetic (AEM) data is becoming a standard tool in mineral exploration, but the industry standard is still based on one-dimensional (1D) forward and Jacobian modelling. We have developed a three-dimensional (3D) vector finite element electromagnetic forward and inversion method considering IP effects within the EEMverter modelling platform. The computations are carried out in the frequency domain and then transformed into time domain through a fast Hankel transformation. For large-scale survey data, we developed a hybrid 1D-3D inversion strategy that allows us to perform 3D calculations only on the area of interest. This hybrid inversion method with kernels of different dimensionality (3D and 1D) uses independent forward meshes and a shared model mesh, allowing fast inversions on large datasets with seamless transitions between areas modelled in 3D and 1D. We demonstrated the feasibility of this strategy using AEM data collected in the Ransko Massif in Eastern Bohemia within the SEMACRET Horizon Europe project. The 3D-1D hybrid inversion, which considers IP effects, exhibits a clear correlation between known mineralization and resistivity and IP anomalies.