Adaptive mesh refinement using hanging edges for 3D forward modelling of transient electromagnetic fields including topography

Abstract:

Numerical forward modelling of transient electromagnetic (TEM) fields in topographically demanding terrain is a rather challenging task, but highly beneficial in identifying reasonable measurement configurations and correctly interpreting acquired field data when investigating mountainous regions.

When evaluating a set of potential transmitter-receiver configurations using large unstructured tetrahedral grids including a-priori refinement, both mesh generation and computation using time stepping algorithms are very time consuming. To avoid these problems, we use a Krylov-subspace method which projects the system matrix onto a low-dimensional space and enables us to evaluate the solution for any given time using a matrix exponential. Furthermore, we propose an adaptive approach including hanging edges within our modeling domain.

In order to avoid an a-priori refinement of all areas of interest at mesh generation time, we refine an initially coarse mesh according to different transmitter and receiver positions with the main program (i.e. on the fly). We note that this approach includes hanging edges within our modeling domain.The resulting mesh hierarchy ensures the reproducibility of features including the topographic Earth-air interface and complex subsurface anomalies for every configuration-tailored mesh. The hanging node incorporation results in a very limited number of additional degrees of freedom and thus, computation time, yet providing reasonable accuracy.

We demonstrate the use of this novel technique of configuration-dependent adaptivity identifying a trade-off between spatial resolution and numerical error, thus keeping the numerical work at a reasonable level.

We apply our novel model approach to volcanological problems such as the identification of magmatic pathways or hydrothermal systems within volcanic structures aiming to understand processes occurring prior to a volcanic eruption. Since both of these targets pose a significant conductivity contrast to the rather cold and dry host rock, TEM is a promising technique to be applied at volcanoes. In preparation of a field experiment, we apply our TEM simulation routine to a geomodel of Stromboli volcano, Italy, created from a digital elevation model.