Three-dimensional electromagnetic cross-well inversion

An inversion algorithm for a vertical magnetic dipole source and a vertical magnetic field component receiver is presented. A three-dimensional integral equation algorithm is used for calculating the electromagnetic response of a particular trial reservoir model. The inversion formalism used is the Marquardt technique of nonlinear least-squares optimization. The system derivatives are calculated using an exact expression derived from reciprocity. The derivative calculation involves introducing sources at the receiver locations with subsequent back-substitution into the impedance matrix equation. The inversion algorithm was tested on data gathered with a laboratory scale model. Convergence to the neighborhood of the correct model from distant initial trial models is good