Abstract:

We advance an efficient method to simultaneously reconstruct the horizontal and vertical resistivities and the interface depth each bed in the horizontally stratified transversely isotropic (TI) formation from the multicomponent induction well logging (MCIL) data. We first give the perturbed equation of electromagnetic (EM) fields, relation of conductivity function to the model parameters and the semi-analytic solutions of EM tensor Green function provided by the numerical mode matching method in the horizontally layered TI formation, and further set up a fast algorithm of Frèchet derivatives of multicomponent induction logging response with respect to all the formation resistivities and interfaces. Then, by combination of normalization and singular value decomposition (SVD) technique, we advance an iterative method to simultaneously reconstruct both horizontal and vertical resistivities and interface per bed so that we realize the best fit of the input data with the modeling logs. Numerical tests validate the algorithm.

Key words: induction logging, fast algorithm of Frèchet derivatives, reconstruction of resistivities and interface at same time