Voxel inversion of airborne electromagnetic data

Inversion of electromagnetic data usually refers to a model space being linked to the actual observation points, and for airborne surveys the spatial discretization of the model space reflects the flight lines. On the contrary, geological and groundwater models most often refer to a regular voxel grid, not correlated to the geophysical model space. This means that incorporating the geophysical data into the geological and/or hydrological modelling grids involves a spatial relocation of the models, which in itself is a subtle process where valuable information is easily lost. Also the integration of prior information, e.g. from boreholes, is difficult when the observation points do not coincide with the position of the prior information, as well as the joint inversion of airborne and ground-based surveys. We developed a geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which then allows for informing directly geological/hydrogeological models, for easier incorporation of prior information and for straightforward integration of different data types in joint inversion. The new voxel model space defines the soil properties (like resistivity) on a set of nodes, and the distribution of the properties is computed everywhere by means of an interpolation function f (e.g. inverse distance or kriging). The position of the nodes is fixed during the inversion and is chosen to sample the soil taking into account topography and inversion resolution. Given this definition of the voxel model space, both 1D and 2D/3D forward responses can be computed. The 1D forward responses are computed as follows: A) a 1D model subdivision, in terms of model thicknesses and direction of the "virtual" horizontal stratification, is defined for each 1D data set. For EM soundings the "virtual" horizontal stratification is set up parallel to the topography at the sounding position. B) the "virtual" 1D models are constructed by interpolating the soil properties in the medium point of the "virtual" layers. For 2D/3D forward responses the algorithm operates similarly, simply filling the 2D/3D meshes of the forward responses by computing the interpolation values in the centres of the mesh cells. The new definition of the voxel model space allows for incorporating straightforwardly the geophysical information into geological and/or hydrological models, just by using for defining the geophysical model space a voxel (hydro)geological grid. This simplify also the propagation of the uncertainty of geophysical parameters into the (hydro)geological models. Furthermore, prior information from boreholes, like resistivity logs, can be applied directly to the voxel model space, even if the borehole positions do not coincide with the actual observation points. In fact, the prior information is constrained to the model parameters through the interpolation function at the borehole locations. The presented algorithm is a further development of the AarhusInv program package developed at Aarhus University (formerly em1dinv), which manages both large scale AEM surveys and ground-based data. This work has been carried out as part of the HyGEM project, supported by the Danish Council of Strategic Research under grant number DSF 11-116763.