A model-based inversion algorithm combined with the curl-conforming volume integral equation method is presented for the reconstruction of 3D anisotropic objects. The forward algorithm utilizes the curl-conforming volume integral equation method. The inversion algorithm is based on the Gauss-Newton method. The approach is applied to the reconstruction of the permittivities of 3D anisotropic objects. Moreover, sensitivity analysis of the data from different polarizations of transmitters and receivers to the anisotropic properties is performed. Numerical examples show the effectiveness of the inversion algorithm and demonstrate the sensitivities of data from different transmitter and receiver pairs to the anisotropy.
2. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, 1995.
3. Li, F., Q. H. Liu, and L.-P. Song, "Three-dimensional reconstruction of objects buried in layered media using born and distorted born iterative methods," IEEE Geoscience and Remote Sensing Letters, Vol. 1, No. 2, 107-111, Apr. 2004.
4. Habashy, T. M. and A. Abubakar, "A general framework for constraint minimization for the inversion of electromagnetic measurements," Progress In Electromagnetics Research, Vol. 46, 265-312, Sep. 2004.
5. Abubakar, A. and P. M. van den Berg, "Three-dimensional nonlinear inversion in cross-well electrode logging," Radio Sci., Vol. 33, 989-1004, Jul.-Aug. 1998.
6. Omeragic, D., L. E. Sun, V. Polyakov, Y.-H. Chen, X. Cao, T. Habashy, T. Vik, J. Rasmus, and J.-M. Denichou, "Characterizing teardrop invasion in horizontal wells in the presence of boundaries using LWD directional resistivity measurements," 54th Annual Society of Petrophysicists and Well Log Analysts (SPWLA) Symposium, Jun. 22-26, 2013.
7. Hu, Y., G. L. Wang, L. Liang, and A. Abubakar, "Estimation of reservoir parameters from inversion of triaxial induction data constrained by mud-filtrate invasion modeling," IEEE Journal on Multiscale and Multiphysics Computational Techniques, Vol. 2, 228-236, 2017.
8. Firoozabadi, R. and E. L. Miller, "A shape-based inversion algorithm applied to microwave imaging of breast tumors," IEEE Trans. Antennas Propagat., Vol. 59, No. 10, 3719-3729, Oct. 2011.
9. Li, M., A. Abubakar, and T. M. Habashy, "A three-dimensional model-based inversion algorithm using radial basis functions for microwave data," IEEE Trans. Antennas Propagat., Vol. 60, No. 7, 3361-3372, Jul. 2012.
10. Sun, L. E. and W. C. Chew, "A novel formulation of the volume integral equation for electromagnetic scattering," Waves in Random and Complex Media, Vol. 19, No. 1, 162-180, Feb. 2009.
11. Jin, J. M., The Finite Element Method in Electromagnetics, John Wiley & Sons. Inc., New York, 2002.