Vol. 25
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2010-08-25
Data-Adaptive Resolution Method for the Parametric Three-Dimensional Inversion of Triaxial Borehole Electromagnetic Measurements
By
Progress In Electromagnetics Research B, Vol. 25, 93-111, 2010
Abstract
We develop a new adaptive inversion procedure: Data-adaptive Resolution Inversion (DRI) method, which eliminates the need of selecting a parameterization prior to inversion. Instead, one performs a hierarchical search for the correct parameterization while solving a sequence of inverse problems with an increasing dimension of parameterization. A parsimonious approach to inverse problems usually involves the application of the same refinement consistently over the complete spatial domain. Such an approach may lead to over-parameterization, subsequently, to unrealistic conductivity estimates and excessive computational work. With DRI, the new parameterization at an arbitrary stage of inversion sequence is allocated such that new degrees of freedom are not necessarily introduced all over the spatial domain of the problem. The aim is to allocate new degrees of freedom only where it is warranted by the available data. Inversion results confirm that DRI is robust and efficient for multiparameter inversion of multicomponent borehole electromagnetic measurements.
Citation
Faruk Omer Alpak, and Carlos Torres-Verdin, "Data-Adaptive Resolution Method for the Parametric Three-Dimensional Inversion of Triaxial Borehole Electromagnetic Measurements," Progress In Electromagnetics Research B, Vol. 25, 93-111, 2010.
doi:10.2528/PIERB10060503
References

1. Abubakar, A., T. M. Habashy, V. Druskin, S. Davydycheva, H. Wang, T. Barber, and L. Knizhnerman, "A three-dimensional parametric inversion of multi-component multi-spacing induction logging data," Society of Exploration Geophysicists International Exposition and 74th Annual Meeting, Denver, Colorado, 2004.

2. Alpak, F. O., T. M. Habashy, C. Torres-Verdín, and E. B. Dussan V., "Joint inversion of transient-pressure and time-lapse electromagnetic logging measurements," Petrophysics, Vol. 45, 251-267, 2004.

3. Anderson, B., T. Barber, and T. M. Habashy, "The interpretation and inversion of fully triaxial induction data," Transactions of 43rd Annual Logging Symposium: Society of Professional Well Logging Analysts, Paper O, Oiso, Japan, 2002.

4. Borcea, L., "Nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency," Inverse Problems, Vol. 17, 329-359, 2001.
doi:10.1088/0266-5611/17/2/312

5. Cheryauka, A. B. and M. S. Zhdanov, "Focusing inversion of tensor induction logging data in anisotropic formations and deviated well," Society of Exploration Geophysicists International Exposition and 71st Annual Meeting, San Antonio, Texas, 2001.

6. Druskin, V. and L. Knizhnerman, "Gaussian spectral rules for three-point second differences: I. A two-point positive definite problem in a semi-indefinite domain," SIAM J. Numer. Anal., Vol. 37, 403-422, 1999.
doi:10.1137/S0036142997330792

7. George, B. K., C. Torres-Verdín, M. Delshad, R. Sigal, F. Zouioueche, and B. Anderson, "Assessment of in-situ hydrocarbon saturation in the presence of deep invasion and highly saline connate water," Petrophysics, Vol. 45, 141-156, 2003.

8. Goharian, M., M. Soleimani, and G. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data," Progress In Electromagnetics Research, Vol. 94, 19-32, 2009.
doi:10.2528/PIER09052003

9. Grimstad, A.-A., T. Mannseth, G. Nævdal, and H. Urkedal, "Adaptive multiscale permeability estimation," Computational Geosciences, Vol. 7, 1-25, 2003.
doi:10.1023/A:1022417923824

10. Hou, J., R. K. Mallan, and C. Torres-Verdín, "Finite-difference simulation of borehole EM measurements in 3D anisotropic media using coupled scalar-vector potentials," Geophysics, Vol. 71, G225-G233, 2006.
doi:10.1190/1.2245467

11. Klein, J. D., P. R. Martin, and D. F. Allen, "The petrophysics of electrically anisotropic reservoirs," Transactions of 36th Annual Logging Symposium: Society of Professional Well Logging Analysts, Paper HH, Paris, France, 1995.

12. Kriegshäuser, B., O. Fanini, S. Forgang, G. Itskovich, M. Rabinovich, L. Tabarovsky, L. Yu, M. Epov, and J. van der Horst, "A new multicomponent induction logging tool to resolve anisotropic formations," Transactions of 40th Annual Logging Symposium: Society of Professional Well Logging Analysts, Paper D, Keystone, Colorado, 2000.

13. Kriegshäuser, B., S. McWilliams, O. Fanini, and L. Yu, "An efficient and accurate pseudo 2-D inversion scheme for multicomponent induction log data," Society of Exploration Geophysicists International Exposition and 71st Annual Meeting, San Antonio, Texas, 2001.

14. Kunz, K. S. and J. H. Moran, "Some effects of formation anisotropy on resistivity measurements in boreholes," Geophysics, Vol. 23, 770-794, 1958.
doi:10.1190/1.1438527

15. Lu, X. and D. Alumbaugh, "One-dimensional inversion of three-component induction logging in anisotropic media," Society of Exploration Geophysicists International Exposition and 71st Annual Meeting, San Antonio, Texas, 2001.

16. Rosthal, R., T. Barber, S. Bonner, K. Chen, S. Davydycheva, G. Hazen, D. Homan, C. Kibbe, G. Minerbo, R. Schlein, L. Villegas, H. Wang, and F. Zhou, "Field test results of an experimental fully-triaxial induction logging tool," Society of Exploration Geophysicists International Exposition and 73rd Annual Meeting, Dallas, Texas, 2003.

17. Schlumberger, C., M. Schlumberger, and E. G. Leonardon, "Some observations concerning electrical measurements in anisotropic media and their interpretation," Transactions of the American Institute of Mining Engineers, Vol. 100, 159-182, 1934.

18. Tarantola, A., Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam, 1987.

19. Tikhonov, A. N. and V. Y. Arsenin, Solution of Ill-posed Problems, John Wiley, New York, 1977.

20. Tompkins, M. J. and D. L. Alumbaugh, "A transversely anisotropic 1-D electromagnetic inversion scheme requiring minimal a priori information," Society of Exploration Geophysicists International Exposition and 72nd Annual Meeting, Salt Lake City, Utah, 2002.

21. Torres-Verdín, C., V. L. Druskin, S. Fang, L. A. Knizhnerman, and A. Malinverno, "A dual-grid nonlinear inversion technique with applications to the interpretation of dc resistivity data," Geophysics, Vol. 65, 1733-1745, 2000.
doi:10.1190/1.1444858

22. Wang, H., T. Barber, R. Rosthal, J. Tabanou, B. Anderson, and T. Habashy, "Fast and rigorous inversion of triaxial induction logging data to determine formation resistivity anisotropy, bed boundary position, relative dip, and azimuth angles," Society of Exploration Geophysicists International Exposition and 73rd Annual Meeting, Dallas, Texas, 2003.

23. Wang, T. and S. Fang, "3-D electromagnetic anisotropy modeling using finite differences," Geophysics, Vol. 66, 1386-1398, 2001.
doi:10.1190/1.1486779

24. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, 302-307, 1966.
doi:10.1109/TAP.1966.1138693

25. Yu, L., B. Kriegshäuser, O. Fanini, and J. Xiao, "A fast inversion method for multicomponent induction log data," Society of Exploration Geophysicists International Exposition and 71st Annual Meeting, San Antonio, Texas, 2001.

26. Zhang, Z., L. Yu, B. Kriegshäuser, and R. Chunduru, "Simultaneous determination of relative angles and anisotropic resistivity using multicomponent induction logging data," Transactions of 42nd Annual Logging Symposium: Society of Professional Well Logging Analysts, Houston, Texas, 2001.

27. Zhang, Z. and A. Mezzatesta, "2D anisotropic inversion of multicomponent induction logging data," Society of Exploration Geophysicists International Exposition and 71st Annual Meeting, San Antonio, Texas, 2001.

28. Zhang, Z., L. Yu, B. Kriegshäuser, and L. Tabarovsky, "Determination of relative angles and anisotropic resistivity using multicomponent induction logging data," Geophysics, Vol. 69, 898-908, 2004.
doi:10.1190/1.1778233