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A multiparameter iterative inversion of dual-laterolog in horizontally layered media and its error analysis

The expression and algorithm of the Born approximation of dual-laterolog (DLL) are different from nonfocusing resistivity tools because the currents and potentials on the surfaces of the electrodes must be satisfied with the special focusing conditions. The Born approximation is described by a linear integral equation about the changes in current density, bucking currents, and potentials on the surfaces of all the electrodes, caused by small perturbations in the formation conductivity. Using the complex forward modeling of DLL, and the semi-analytic solution of the Green's function, we advance the fast algorithm of the Frechet derivative matrix containing the partial derivatives of both the apparent resistivities and bucking currents with respect to all components of the model vector. A normalization approach is used to transform the matrix into a dimensionless matrix. We then develop a multiparameter iterative inversion technique to simultaneously reconstruct all model parameters. Furthermore, we analyze the influence of both noises in data and errors of some model parameters on the inversion solution and give a method to choose the regularization factors. Finally, numerical result tests show the characteristics of the normalized Frechet matrix, the influence of errors of both bed thickness and flushed zone resistivity, etc, on the inversion solution when they are fixed, and the great improvement of the inversion quality when all model parameters are simultaneously reconstructed from both the apparent resistivities and bucking currents.