Parallel inversion of large-scale airborne time-domain electromagnetic data with multiple OcTree meshes

Airborne time-domain electromagnetic surveys are effective tools for mineral exploration and geologic mapping. 3D inversion of airborne electromagnetic data is a challenging computational problem. The size of the surveys and the spatial resolution required to adequately discretize the transmitters and receivers results in very large meshes. Solving the forward problem repeatedly on such a mesh can quickly become impractical. Fortunately, using a single mesh for both the forward and inverse problem for all of the transmitters is not necessary. The forward problem for a single source or a small group of sources can be solved on different meshes, each of which only needs to be locally refined close to the selected transmitters and receivers. Away from the selected transmitters and receivers, the mesh can be coarsened. The forward problem can then be broken into a number of highly parallel problems. Each forward modelling mesh is optimized specifically to the selected transmitters and receivers and has far fewer cells than the fine inversion mesh. Further efficiency can be gained by using stochastic Gauss-Newton methods where a stochastic approximation to the gradient, Hessian or both are used. In this paper, we present new algorithms for airborne data inversion and their implementation using a finite volume discretization on OcTree meshes. We demonstrate our approach on a large-scale synthetic versatile time-domain electromagnetic surveying data set.