3-DIMENSIONAL ELECTROMAGNETIC CROSS-WELL INVERSION

Effective use of electromagnetics in delineating and monitoring hydroc arbon reservoirs will require the rapid computerized inversion of larg e cross-well data sets subject to constraint by other data such as sei smic data and well-logs. Ideally, an inversion algorithm would be capa ble of inverting data to a three-dimensional model without theoretical limitations on the geometry or resistivity distribution of the model. Our research has concentrated on developing such an algorithm for a v ertical magnetic dipole source and a vertical magnetic field component receiver. An inversion algorithm requires an effective numerical solu tion for calculating the electromagnetic response of a particular tria l reservoir model. We use a three-dimensional integral equations algor ithm which has been extensively tested, is well understood, and does n ot require an exorbitant amount of computer time or storage for modera tely complicated models. Since the forward solution is formulated in t he frequency domain, we have confined our inversion to the frequency d omain, although time domain inversions, via transformations to the fre quency domain, are possible in principle. The inversion formalism used is the Marquardt technique of nonlinear least-squares optimization. T he system derivatives are calculated using an exact expression derived from reciprocity. The derivative calculation involves introducing sou rces at the receiver locations with subsequent back-substitution into the impedance matrix equation. This entire procedure is computationall y efficient and permits derivative calculation as a consequence of the forward calculation at a small added computational effort for a moder ate number of cells. We have tested the inversion algorithm on data ga thered with a laboratory scale model. Convergence to the neighborhood of the correct model from distant initial trial models is good. Howeve r, accurate estimation of resistivity requires that constraints be pla ced on the model space.