| The purpose of this research is to reconstruct the resistivity profile of the formation based on induction logs obtained in layered dipping beds. It is assumed that the borehole and invasion effects are negligible. The reconstruction process, often referred to as inversion of induction logs, needs three major components: fast forward modeling codes, efficient codes to evaluate the Jacobian matrix, and some regularization criteria.; Automatic inversion of induction logs requires the repeated solution of a forward model. In order to carry out the inversion process within a reasonable time period, it is necessary to derive a fast forward model solution. To this end, we use transmission-line theory and a fast Hankel transform to make the forward model very time efficient. The Jacobian matrix is very important in the inversion, as it determines the direction in which the inverted formation profile needs to be modified. We developed an approximation method to evaluate the Jacobian matrix that is very time efficient. The Jacobian matrix found in this way can be used for the first several iterations. For later iterations, if necessary, an exact method can be used to find a more accurate Jacobian matrix based on the inverted formation profile. Also, we check the possibility of substituting a standard multiple-coil tool with a tool that has only one transmitter and receiver pair to save computing time when evaluating the Jacobian matrix. In our study, three version criteria, which are similar to the maximum entropy criterion, are tested. They are the maximum flatness, the maximum oil, and the minimum oil criteria.; The time-efficient computer codes have been developed and the numerical examples for different dipping angles, different noise values, and three different criteria are given and discussed. These results show that the inversions of all the examples are successful and their inverted formations represent three possible solutions. The results also show that three criteria are tolerant of noise and induction logs can be inverted with satisfactory results by using the techniques developed in this dissertation. |
