I have developed an approximate inversion scheme for surface-borehole electromagnetic data. The method aims at reducing the computational burden arising by the fine discretization required to accurately solve for the field distribution in the full complexity of the borehole system together with the reservoir medium. I first analyze numerical simulations of the surface-borehole response performed for a 1D layered earth, also incorporating the realistic complexity of the borehole system. The analysis brings useful insight to the requirement of incorporating fluid and mud/cement electrical properties when implementing an inversion by numerically simulating the full complexity of the system. Subsequently, the synthetic data set was used to test an inversion method that uses the data dominated by the casing effect to approximately describe the casing secondary fields. A scaling factor is then introduced to account for the current induced in the well as the exciting source is placed further below the casing shoe. The method is found to fairly well recover the known 1D resistivity strata; still, some bias is expected for the resistivity close below the casing shoe, where the data are anticipated to be the most distorted by the casing effect.