Search

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.

Im Januar dieses Jahres hat das Helmholtz-Institut Freiberg für Ressourcentechnologie (HIF) in Kooperation mit der Technischen Universität Bergakademie Freiberg, der Bundesanstalt für Geowissenschaften und Rohstoffe (BGR), sowie dem Landesamt für Umwelt, Landwirtschaft und Geologie (LfULG) einen Antrag auf eine wissenschaftliche Aufsuchungsgenehmigung für ein Gebiet im Raum Geyer im Erzgebirgskreis beantragt. Das damit einhergehende Forschungsprojekt hat das Ziel, mittels geophysikalischer Verfahren das Rohstoffpotenzial des geologischen Untergrundes bis in eine Tiefe von ca. 500 m zu erfassen. Alle relevanten Daten, die im Rahmen dieser Aufsuchung erhoben werden, sollen genutzt werden, um ein 3D-Modell des geologischen Untergrunds im Aufsuchungsgebiet zu erstellen. Sowohl dieses Modell als auch die ihm zugrundeliegenden Daten sollen mit Abschluss des auf drei Jahre ausgelegten Projekts veröffentlicht werden.

The Geotechnologien project Multi-EM addresses the combination of different electromagnetic methods in a joint inversion approach to exploit their individual advantages. In Freiberg, we focus on the combination of the transient electromagnetic (TEM) and the DC resistivity method. We have implemented a new DC resistivity forward operator in MATLAB using unite elements on unstructured tetrahedral grids that can easily be combined with our already existing TEM software (Afanasjew et al., 2010). This code enables us to deal with even complex topography and to extract the derivatives, which are crucial for the inversion while retaining full control over the assembly process of the system matrix (Weißflog et al., 2012). For simplicity, we apply a regularized Gauss-Newton method in view of a combination of different electromagnetic methods in one inversion algorithm. We focus on an appropriate regularization technique that has been outlined in (Schwarzbach & Haber, 2013).

Krylov subspace methods are well-known as iterative solvers for linear systems of equations. Using the same basic projection methodology these can also be used to approximate the solution of least squares problems, while avoiding the explicit construction of the sensitivity matrix. We point out how Krylov subspace methods such as CGNR – as well as its more robust variant LSQR – take into account the least squares origin of the normal equations, thereby ameliorating the ill-conditioning inherent in the inverse problem. These observations are illustrated with examples from the inversion of 3-D helicopter electromagnetic data. The research is carried out in an interdisciplinary project called ‘AIDA – From Airborne Data Inversion to In-Depth Analysis’.

We present current research associated with a common project of the TU Bergakademie Freiberg and the Deutsches Geoforschungszentrum Potsdam (GFZ). The aim of this project is to exploit the distinct sensitivity patterns of different EM methods to enhance the resolution. Here, we focus on combining the direct current and the transient electromagnetic method. Further methods to be integrated are magnetotellurics and controlled-source EM. For this purpose, we have properly reimplemented our finite element secondary field DC forward modelling approach on unstructured grids and proved its theoretical convergence rate of O(h2). We derive expressions for the Jacobian with respect to their efficient calculation in an inversion process and examine the spatial sensitivity pattern in order to design a coherent DC/TEM set-up.