A Concept for 3-D Inversion of Helicopter Electromagnetic Data Using a Tensor-based Problem Formulation

Helicopter electromagnetic (HEM) measurements allow to manage huge surveys in a very short time. Due to the enormous data and model sizes, laterally constrained 1-D inversion schemes for the entire survey are still state of the art, even for those parts of the survey where 3-D conductivity anomalies are expected.

We introduce a new strategy that is based on the precedent localization of the entire HEM survey to parts which are actually affected by an expected local 3-D anomalies. A full 3-D inversion scheme capable of revealing those anomalous conductivity structures is presented that directly benefits from a-priori information, resulting from the localization procedure. We therefore reformulate the discrete forward problem in terms of the secondary electric field, employing either finite difference or finite element methods. For solving the inverse problem, we apply a straightforward Gauss-Newton method and a Tikhonov-type regularization scheme. The concept allows us to additionally restrict the domain where the inverse problem is solved, acting as an implicit regularization. The derived linear least squares problem is solved with Krylov subspace methods, such as LSQR, that are able to deal with the inherent ill-conditioning. The resulting systems of linear equations subsequently yield expressions for the gradient and approximate Hessian of the minimization problem. Resulting from the unique transmitter-receiver relation of the HEM problem, an explicit representation of the Jacobian matrix is used. We further introduce a tensor-based problem formulation that provides a fast update of the linear system of the forward problem and an effective handling of the sensitivity related algebraic quantities, respectively.