SUMMARY We present a new algorithm for quasi-3D inversion of airborne transient electromagnetic data (AEM). The algorithm uses a 3D voxel grid for the model domain while the forward response and derivatives are calculated using interpolated "virtual" 1D models collocated at the AEM measurement points. The algorithm efficiently decouples the model domain from the practical spatial sampling which are often dictated by the landscape, ground installations ect., rather than the optimal model resolution. The algorithm uses sparse storage with efficient solvers and it scales linearly both with the number of CPU's and with the survey size. This means that it can be used to invert entire surveys of thousands of kilometres on small multiprocessor servers priced less than 5000 Euro. The algorithm allows inputting a-priori information from boreholes, joint inversion with groundbased electrical/electromagnetic data and modelling of flight altitude and shift parameters.