In this paper, we advance an efficient algorithm to compute the responses of multicomponent induction logging (MCIL) tool in deviated and layered anisotropic formations through a numerical mode matching method (NMM). First, the three mutually orthogonal magnetic dipoles located at the borehole axis are represented as the sum of three harmonic components about the dipole angle θ so that the electromagnetic (EM) fields produced by the dipoles can be transformed into three axisymmetric problems. And new boundary conditions satisfied by every EM harmonic component at borehole axis are given to assure the EM field near the borehole axis can still be calculated. Then NMM is used to solve the three axisymmetric problems and obtain a semianalytic expression of a dyadic Green function by magnetic current source in the formation. Furthermore, the formula to compute the MCIL response is given. The numerical tests are carried out to validate the algorithm and investigate the characteristics of MCIL response in several different cases.

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In this paper, we advance a fast iterative inversion algorithm of frequency electromagnetic sounding data to simultaneously reconstruct the horizontal and the vertical conductivities and interface each bed in the horizontally stratified transversely isotropic (TI) medium. First, applying the analytic expression of the electromagnetic dyadic Green's functions in the TI medium, we realize the forward modeling of the frequency sounding via the fast algorithm of Sommerfeld integral. Then using the perturbation principles and Fourier inversion transform, we establish an efficient computation of Frchet derivatives of the frequency sounding data with respective to all the model parameters. And we use the least square criterion, the normalization and singular value decomposition to iteratively recovery all model parameters. Finally, numerical results validate the inversion algorithms and their antinoise ability.

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We perform a numerical simulation of marine controlled-source electromagnetic （MCSEM） responses in a layered anisotropic seabed using integral equation method. Firstly, we use the operator theory to deduce the contraction integral equation, which is always convergent regardless of any parameters, for it satisfies the contraction mapping condition. Then we introduce the subdomain multigrid and quasi-linear approximation to improve the computation efficiency. We also validate the accuracy and efficiency of the algorithm by synthetic numerical modelings. Finally, we simulate the three-dimensional MCSEM responses in the layered anisotropic seabed, and investigate the effects of anisotropy.