A Goal-oriented Adaptive Finite-element Algorithm for 3D Anisotropic MT Modelling

Magnetotelluric (MT) has been widely used in oil & gas exploration and in the investigation of deep earth structures. MT data interpretation generally assumes an isotropic model. However, this is sometimes inadequate, because electrical anisotropy is frequently found in the deep earth and isotropic models can lead to misinterpretations. In such cases, one needs to use an anisotropic model for data interpretation. In this paper, we study MT forward modelling for 3D earth with arbitrary anisotropy based on a goal-oriented adaptive finite-element method. This is largely different from the traditional MT modelling, like finite-difference or integral equation method that use artificially refined grids. The accuracy of these later methods are severely influenced by the quality of mesh. In comparison, the finite-element method fits best the complex structures and topography, while a goal-oriented adaptive mesh enhances modelling accuracy and efficiency by refining only meshes that have larger posteriori errors. In this paper, we first define the posteriori error based on the continuity of current density for our goal-oriented adaptive strategy and then we validate our goal-oriented adaptive method by comparing with 1D analytical solutions and by studying an anisotropic body embedded in a half-space earth with and without topography.