Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics-a marine CSEM example

Abstract

S U M M A R YWe present a new 3-D vector finite element code and demonstrate its strength by modelling a realistic marine CSEM scenario. Unstructured tetrahedral meshes easily allow for the inclusion of arbitrary seafloor bathymetry so that natural environments are mapped into the model in a close-to-reality way. A primary/secondary field approach, an adaptive mesh refinement strategy as well as a higher order polynomial finite element approximation improve the solution accuracy. A convergence study strongly indicates that the use of higher order finite elements is beneficial even if the solution is not globally smooth. The marine CSEM scenario also shows that seafloor topography gives an important response which needs to be reproduced by numerical modelling to avoid the misinterpretation of measurements.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

“…It is well known that for smooth solutions, p-refinement is advantageous and that combining it with h-refinement (the socalled h-p FEM) can lead to exponential convergence rates (Guo and Babuska, 1986;Bürg, 2013). Although h-refinement has been applied in geoelectromagnetic applications (Schwarzbach et al, 2011;Ren et al, 2013), little work has been performed to investigate advantages of higher polynomial degrees for 3D geoelectromagnetic modeling. Most existing FEM modeling codes in this area use the lowest order Nédélec finite elements, often called edge-based finite elements.…”

“…Much research in recent years has gone into developing FEM codes for geoelectromagnetic modeling (Börner, 2010;Farquharson and Miensopust, 2011;Schwarzbach et al, 2011;Ren et al, 2013;Um et al, 2013;Grayver and Bürg, 2014). They all make use of the so-called Nédélec finite elements, which permit a well-posed representation of EM fields taking into account discontinuities of the normal components (Jin, 2002).…”

3D Inversion of Large-scale Time Domain Electromagnetic Data

“…This work extends our previous work on time domain electromagnetics inversion using a single regular mesh to OcTree meshes. The underlying regular structure of OcTree meshes greatly simplifies mesh handling and algorithmic development, compared to the finite element method on unstructured tetrahedral meshes (Günther, Rücker and Spitzer, 2006;Schwarzbach et al, 2011). A similar approach has been published by Cox and Zhdanov (2008).…”

A multi-domain decomposition-based Fourier finite element method for the simulation of 3D marine CSEM measurements

“…Direct matrix solvers for large geophysical 3D forward problems [33,28,30,26,24,14,19,8,35,2,15] can be computationally expensive, both in terms of memory and CPU time. A way to overcome this limitation is by reducing the dimensionality of the problem, namely from 3D modeling to a 2.5D [23], 2D [4] and/or 1D [20] approximations that are only suitable for particular geometries.…”