In-depth comparison of the spectral-element and finite-element method for 3D CSEM forward modelling

We developed two forward modelling approaches to simulate 3-dimensional land-based controlled-source electromagnetic (CSEM) problems in frequency domain with hexahedral spectral-element meshes and tetrahedral finite-element meshes. In recent years, the geo-electromagnetic community made a lot of progress in modelling and inversion of EM data in three dimensions using a variety of approaches. The available software is used to verify the accuracy of newly developed codes, which apply e.g. different element shapes or interpolation schemes. However, a direct comparison in terms of advantages and disadvantages of different modelling strategies, especially discretisation methods in 3D, is often not focused on in publications.

Having two modelling codes and their developers available at the same place, gives us the unique opportunity to compare the approaches in a very detailed way. Our spectral-element as well as our finite-element solution is based on Galerkin’s weighted residual method and we solve the electromagnetic diffusion equations for the total electric field on the element edges.
The main differences between both codes are the choice and order of the interpolation functions and the discretisation of the modelling domain employing hexahedral and tetrahedral elements. While the tetrahedral meshes used in our finite-element approach are known for being able to properly resolve complex structures in the subsurface, this issue is addressed in the spectral-element method by utilising curvilinear instead of orthogonal hexahedral elements.

In this contribution, we focus on the comparison of both approaches for a simple 1D model and a complex 3D model in terms of accuracy, effort in mesh generation and computational resources such as simulation time and memory requirement. Moreover, we contrast the influence of mesh discretisation on the solution for the two methods as well as the order of approximation. A preliminary test simulation of a  model consisting of a conductive body buried within a resistive background covered by a thin conductive layer yielded comparable results in terms of accuracy. It also revealed significant differences concerning the mesh discretisation meaning the solution's dependency on the meshing of the model domain.

Acknowledgements: This work was partly funded by Uppsala’s Center for Interdisciplinary
Mathematics and the Smart Exploration project, which has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No.775971.