Unstructured grid based 2-D inversion of VLF data for models including topography

Abstract

We present a 2-D inversion code incorporating a damped least-squares and a minimum-model approach for plane wave electromagnetic (EM) methods using an adaptive unstructured grid finite element forward operator. Unstructured triangular grids permit efficient discretization of arbitrary 2-D model geometries and, hence, allow for modeling arbitrary topography. The inversion model is parameterized on a coarse parameter grid which constitutes a subset of the forward modeling grid. The mapping from parameter to forward modeling grid is obtained by adaptive mesh refinement. Sensitivities are determined by solving a modified sensitivity equation system arising from the derivative of the finite element equations with respect to the model parameters. Firstly, we demonstrate that surface topography may induce significant effects on the EM response and in the inversion result, and that it cannot be ignored when the scale length of topographic variations is in the order of magnitude of the skin depth. Secondly, the dependency of the inversion on the starting model is discussed for VLF and VLF-R data. Thirdly, we demonstrate the inversion of a synthetic data set obtained from a model with topography. Finally, the inversion approach is applied to field data collected in a region with undulating topography. ► The topography effect is demonstrated by forward modeling studies. ► We use an unstructured grid forward operator to invert 2-D plane-wave EM data. ► Topography correction or its special consideration during inversion is unnecessary. ► VLF inversion results are strongly dependent on the starting model. ► Inversion of VLF-R data is able to recover the background resistivity well.