Discontinuous Galerkin frequency domain forward modelling for the inversion of electric permittivity in the 2D case

We have recently developed a discontinuous Galerkin frequency domain modelling algorithm for the solution of the 2D transverse magnetic Maxwell equations. This method is formulated on an unstructured triangular discretization of the computational domain and makes use of a high order polynomial interpolation of the electromagnetic field components within each triangular element. The discontinuous nature of the approximation naturally allows for a local definition of the interpolation order that is, in combination with a possibly non-conforming local refinement of the mesh, a key ingredient for obtaining a flexible and accurate discretization method. Moreover, heterogeneity of the propagation media is easily dealt with by assuming element-wise values of the electromagnetic parameters. In this paper, we propose the use of this discontinuous Galerkin frequency domain method as the forward modelling algorithm for solving the inverse problem for the electric permittivity in the 2D case. The inversion process is based on a gradient minimization technique developed by Pratt for seismological applications. Preliminary numerical results are presented for the imaging of a simplified subsurface model with the aim of assessing the performances of the proposed inversion methodology with regards to the number of frequencies, the number of recorded data and the number of sources.

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