We present a new method, dubbed the modified extended Born approximation (MEBA), for efficient three-dimensional (3D) simulation and inversion of geophysical frequency-domain electromagnetic (EM) data for a targeted object lodged in a layered half-space. Based on the integral equation method and modified from an extended Born approximation technique, the MEBA method calculates the total electric field in an electrical conductivity inhomogeneity without any need for solving a huge matrix equation. This is done by multiplying the background electric field by a depolarization tensor. The Fourier transform and the convolution theorem are used to dramatically increase the computational efficiency. Comparisons of MEBA-generated numerical data for tabular targets with data generated by other means are used to verify the scheme and check its range of validity. The results indicate that the MEBA technique yields better accuracy when current channeling in the conductivity anomaly dominates over the induction process. The MEBA algorithm has been incorporated into a least-squares inversion scheme which is used to interpret borehole-to-surface EM tomography field data. The survey served to monitor the subsurface conductivity change associated with the extraction of a volume of saltwater previously injected into a known aquifer.