Induction log inversion and cross-hole electromagnetic tomography

A linearization method is used to solve the problem of inverting induction logs and electromagnetic (EM) cross-hole tomographs. Nonlinear functions of electromagnetic field are expanded into Taylor's series, and only the linear parts in the expansion are used in the optimization process. An iteration procedure is then devised to solve the inversion problem. Due to the instability of this linear system, regularization methods are also used to stabilize the solution.; The linearization and regularization procedure is applied first to one-dimensional induction log inversion and then to two-dimensional cross-hole electromagnetic tomography. In this work, several algorithms are used to invert induction logs, resulting in formation profiles that have different physical meanings. The maximum flatness criterion is aimed at obtaining a resistivity profile that is as close to a constant as possible. The maximum oil algorithm has the objective of yielding the highest resistivity profile in the reservoir. The minimum oil algorithm is aimed at finding the lowest resistivity profile. All of these algorithms are subject to the condition that the resulting computed log must agree with the field log within a preset value.; For the case of cross-hole tomography, a new approach using layered media as the background is adopted to simulate the EM signal in the cross-hole measurement. The inversion algorithm employs the linearization method to speed up the inversion. The regularization technique is introduced in the inversion process and the effects of noise are studied.; Tomographs of two assumed models named Model I and Model II, and a tomograph of Devine Test Site based on the field test data are presented in this study. The measurements were made by a group from the Lawrence Livermore National Laboratory. The images so constructed show excellent agreement with the known geological properties for that region. The consistency between the measurement and the model simulation is very close to the repeatability of the measurement reported.