Adaptive Regularization Iterative Inversion of Array Multicomponent Induction Well Logging Datum in a Horizontally Stratified Inhomogeneous TI Formation

An adaptive regularization iterative inversion of array multicomponent induction well logging datum is established to simultaneously reconstruct the horizontal and vertical conductivities of both invasion zone and origin formation, invasion radius, and the interface depth of each bed in the horizontally stratified inhomogeneous transversally isotropic (TI) formation. Applying numerical mode matching method, we can obtain a much compact semianalytic expression of the electromagnetic tensor Green´s functions by magnetic current source in the inhomogeneous TI formation. Then, using the perturbation principles, an efficient computation of Fréchet derivatives of the multicomponent induction logging response is set up with respect to all the model parameters. After that, the combination of Morozev´s discrepancy principle with Cholesky´s decomposition is applied to adaptively select regularization factor during inversion so that stabilization of inversion solution is assured as well as realization of best fit of the input data with the modeling logs. Finally, the numerical tests validate the algorithm.