Appraisal of current density in Very Low Frequency electromagnetic measurements using preconditioned conjugate gradient approach

We describe the implementation of a new fast imaging technique to invert very low frequency (VLF) data measured on profiles into corresponding apparent current density systems over the 2D earth. First, a formulation has been derived to compute the vertical component of the magnetic field for a given 2D current density distribution in the Earth's subsurface. Since the vertical component of the magnetic field is proportional to the real anomaly of VLF electromagnetic measurement, the derived formulation has been used for imaging subsurface structures. The 2D inversion code incorporating the preconditioned conjugate gradient approach was developed for imaging of the subsurface conductors using the real VLF anomaly in terms of apparent current density distribution in the subsurface. The preconditioner determined by the distances between the cells and the observation points greatly improved the quality of the very low frequency imaging. Finally, we tested our method using synthetic and real data and all tests returned favorable results. The presented formulation were also compared with other imaging techniques in terms of apparent current density and resistivity distribution using a standard numerical forward modeling and inversion technique. The presented imaging technique shows improvement with respect to the filtering approaches in depicting subsurface conductors. Further, results obtained using the presented approach is closer to the results of rigorous resistivity inversion.