Multicomponent induction logging responses are simulated by using hierarchical mixed order vector finite element method (FEM). In order to modeling three orthogonal magnetic dipoles, we adopt the method that the total field is separated into incident field and secondary field, and only the secondary field is computed by FEM. In addition, two techniques are applied to improve the modeling accuracy and computational efficiency: 1) Hierarchical mixed order vector basis functions are applied to FEM. Different order basis functions are used in different elements in accordance with the changing speed of the field. The mixed order scheme reduces greatly the number of unknowns without reducing accuracy, and can attain much higher computational efficiency. 2) The systemof the FEM equations is solved by Distributed-SuperLU, and the results of multiple measure points can be got simultaneously. The FEM result is validated against volume integral equation method and the approach of planar layered media Green's functions, and the comparisons show very good agreement. Finally, the multicomponent induction response in anisotropic formations involving eccentric tools and dipping beds is included to demonstrate the flexibility of the method.
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