Forward Modeling and Inversion of Very Low Frequency Electromagnetic Data Over Rugged Topography Using 2D Triangular Elements

Very Low Frequency (VLF) method is the simplest among all electromagnetic induction techniques with a variety of geophysical applications. Various qualitative and quantitative interpretation techniques are developed to interpret VLF data. However, most of the quantitative interpretation techniques using numerical methods are based on rectangular grid based modeling. Such discretization may produce a large error while modeling the surface topography and also, number of the model parameters will increase drastically to model the surface topography. An effort is made to develop an inversion approach based on triangular grid to reduce the problem size by utilizing minimal number of model parameter and model the rugged topography accurately. First, an analytical expression is derived to compute the vertical component of the magnetic field due to a triangular block of an assigned current density in the block. Subsequently, subsurface structure is optimized in terms of apparent current density using preconditioned conjugate gradient method by considering a model including the surface topography. Since, noise reduction in VLF data is also an important step of interpretation, nonlinear empirical mode decomposition technique is used to minimize the noise from the data. Efficacy of the developed interpretation approach is discussed on one synthetic and one field data set. Inversions for the synthetic and field data sets were carried out with and without topographical variation. The study reveals that depth to the top of the subsurface conductor is correlated with the surface topography. Inversion of VLF data measured over topographical variation with the flat surface model resulted in shifting of the depth to the top of the conductor to an incorrect position (shallower depth). Therefore, consideration of topography in the inversion scheme is vital for delineation of subsurface structures accurately. The efficacy of triangular element in depicting the topography accurately and inversion is demonstrated in the present study.