Calculating Multi-frequency Electromagnetic Logging Responses with Vertical Eigenstate Method.
The response of the electromagnetic logging tool was simulated using the vertical numeric mode matching method (VNMM). The VNMM is suitable both for the low frequency induction logging tool and the high frequency electromagnetic propagation logging tool. In the vertical numeric mode matching method, the axi-symmetric two-dimensional problem was separated into two related one-dimensional problem. In the radial direction, the medium was divided into several annulus domains, whereas in the vertical direction, it was regarded as combinations of horizontal layers. The total field is represented by the production of the vertical eigen-modes and the radial analytic function. The vertical eigen-mode was solved by one-dimensional finite element method (FEM). By using the continuity of the tangential components of the electric and magnetic fields in the vertical boundaries in radial direction, the transparent and reflection coefficients were derived. Several kinds of profiles in different borehole environments were simulated. Simulated responses of the electromagnetic logging tool in the water flooded oil bearing formation, the low resistivity oil-bearing formation and the thinly bedded oil-bearing formation are easy to obtain from VNMM.