Abstract
The magnetotelluric (MT) technique is an electromagnetic geophysical method, which is widely used as a complementary to seismic surveys for exploration of hydrocarbon reservoirs. In the inversion process, the method of matrix inverse calculation has a considerable effect on the speed of the inversion and the quality of obtained models. Lanczos Bidiagonalization (LB) method has been reported to be a fast and efficient approach for solving the inversion problems. In this study, we employ LB method for inverting large-scale 2D MT data. In LB algorithm, the full set of equations is replaced by a dimensionally reduced system of equations. As a result, the speed of the solution procedure is increased, while the original problem is solved with a high accuracy. In addition, we employ active constraint balancing approach for determining the optimum regularization parameter. The advantage of the method is that for highly resolvable parameters, a small value of the Lagrangian multiplier is assigned, and vice versa. The results of the synthetic data inversion show that both methods require equal computer memory but LB method is faster and more reliable than conjugate gradient method. The proposed approach is also applied to inverse real MT data collected from the Kashan area. The Kashan area is the most interesting area for oil and gas exploration of the Central Iran Basin. The inversion results obtained by LB are in a good agreement with the geological structure of the study area and the drilling data.
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References
Aster R.C., Borchers B. and Thurber C.H., 2013. Parameter Estimation and Inverse Problems. Academic Press, Waltham, MA
Avdeev D. and Avdeeva A., 2009. 3D magnetotelluric inversion using a limited-memory quasi-Newton optimization. Geophysics, 14, 45–57, DOI: https://doi.org/10.1190/1.3114023
Becker E.B., Carey G.F. and Oden J.T., 1981. Finite Elements: An Introduction. Prentice-Hall Inc., Englewood Cliffs, NJ
Caldwell T.G., Bibby H. and Brown C., 2004. The magnetotelluric phase tensor. Geophys. J. Int., 158, 457–469, DOI: https://doi.org/10.1111/j.1365-246X.2004.02281.x
Calvetti D., Golub G.H. and Reichel L., 1999. Estimation of the L-curve via Lanczos bidiagonalization. BIT, 39, 603–619, DOI: https://doi.org/10.1023/A:1022383005969
Calvetti D., Morigi S., Reichel L. and Sgallari F., 2000. An L-ribbon for large underdetermined linear discrete ill-posed problems. Numer. Algorithms, 25, 89–107, DOI: https://doi.org/10.1023/A:1016656923184
Chauhan M.S., Fedi M. and Sen M.K., 2018. Gravity inversion by the multi-homogeneity depth estimation method for investigating salt domes and complex sources. Geophys. Prospect., 66, 175–191, DOI: https://doi.org/10.1111/1365-2478.12603
Chong E.K.P. and Zak S.H., 2013. An Introduction to Optimization. Fourth Edition. John Wiley & Sons, Hoboken, NJ
Chung J., Nagy J.G. and O’Leary D.P., 2008. A weighted GCV method for Lanczos-hybrid regularization. Electron. Trans. Numer. Anal., 28, 149–167
Dabaghi Sadr F., 2017. Evolution of the Tethyan Seaway During the Oligocene and Miocene: Constraints from Foraminiferal Faunas of the Qom Formation, Iran. Ph.D. Thesis, University of Hamburg, Germany
Daneshian J., 2007. Early Miocene benthic foraminifera and biostratigraphy of the Qom Formation, Deh Namak, Central Iran. J. Asian. Earth Sci., 29, 844–858, DOI: https://doi.org/10.1016/j.jseaes.2006.06.003
Farquharson C.G. and Oldenburg D.W., 2004. A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems. Geophys. J. Int., 156, 411–425
Furrer M.A. and Soder P.A., 1955. The Oligo-Miocene marine formation in the Qum Region (Iran). 4th World Petroleum Congress, WPC-6017, 267–277
Ghaedrahmati R., Moradzadeh A., Fathianpour N. and Lee S.K., 2014. Investigating 2-D MT inversion codes using real field data. Arab. J. Geosci., 7, 2315–2328, DOI: https://doi.org/10.1007/s12517-013-0869-6
Guoqiang X., Shaonan Z., Zhongdong L., Lailiang S. and Huimin L., 2007. Carbonate sequence stratigraphy of a Back-Arc Basin: A case study of the Qom Formation in the Kashan Area, Central Iran. Acta. Geol. Sin., 81, 488–500, DOI: https://doi.org/10.1111/j.1755-6724.2007.tb00972.x
Haber E., Ascher U.M. and Oldenburg D., 2000. On optimization techniques for solving nonlinear inverse problems. Inverse Probl., 16, 1263–1280, DOI: https://doi.org/10.1088/0266-5611/16/5/309
Kao D. and Orr D., 1982. Magnetotelluric studies in the Market Weighton area of eastern England. Geophys. J. Int., 70, 323–337, DOI: https://doi.org/10.1111/j.1365-246X.1982.tb04970.x
Kaufman A.A. and Keller G.V., 1981. The Magnetotelluric Sounding Method. Elsevier Scientific Publ. Co., New York, NY
Lilley F.E.M., 1976. Diagrams for magnetotelluric data. Geophysics, 41, 766–770, DOI: https://doi.org/10.1190/1.1440648
Marchetti P., Coraggio F., Gabbriellini G. and Fedi M., 2014. Large-scale 3D gravity data space inversion in hydrocarbon exploration. SEG Technical Program Expanded Abstracts 2014, DOI: https://doi.org/10.1190/segam2014-1078.1
Marti A., Queralt P. and Ledo J., 2009. WALDIM: A code for the dimensionality analysis of magnetotelluric data using the rotational invariants of the magnetotelluric tensor. Comput. Geosci., 35, 2295–2303, DOI: https://doi.org/10.1016/j.cageo.2009.03.004
Matsuo K. and Negi T., 1999. Oil exploration in difficult Minami-Noshiro area-park two: magnetotelluric survey. The Leading Edge, 18, 1411–1413, DOI: https://doi.org/10.1190/1.1438236
Menke W., 2012. Geophysical Data Analysis Discrete Inverse Theory. Third Edition. Academic Press Inc., SanDiego, CA
Moghadasi M., Nejati Kalateh A. and Rezaie M., 2019. Automatic estimation of regularization parameter by active constraint balancing method for 3D inversion of gravity data. J. Min. Environ., 10, 357–364
Nemeth T., Normark E. and Qin F., 1997. Dynamic smoothing in crosswell traveltime tomography. Geophysics, 62, 168–176
NIOC, 2012. Kashan, Iran, MIT Exploration Result Report. National Iranian Oil Company, Tehran, Iran
Nocedal J. and Wright S.J., 2006. Numerical Optimization. Second Edition. Springer-Verlag, Berlin, Germany
Paige C.C. and Saunders M.A., 1982. LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw., 8, 43–71
Paoletti V., Hansen P.C., Hansen M.F. and Fedi M., 2014. A computationally efficient tool for assessing the depth resolution in large-scale potential-field inversion. Geophysics, 79, A33–A38, DOI: https://doi.org/10.1190/geo2014-0017.1
Reddy I.K., Rankin D. and Phillips R.J., 1977. Three-dimensional modeling in magnetotelluric and magnetic variational sounding. Geophys. J. Int., 51, 313–325
Reynolds J.M., 2011. An Introduction to Applied and Environmental Geophysics. Second Edition. John Wiley & Sons, Hoboken, NJ
Rodi W.L., 1976. A technique for improving the accuracy of finite element solutions for magnetotelluric data. Geophys. J. R. Astron. Soc., 44, 483–506
Rodi W.L. and Mackie R.L., 2001. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion. Geophysics, 66, 174–187
Sarvandani M.M., Kalateh A.N., Unsworth M. and Majidi A., 2017. Interpretation of magnetotelluric data from the Gachsaran oil field using sharp boundary inversion. J. Petrol. Sci. Eng., 149, 25–39, DOI: https://doi.org/10.1016/j.petrol.2016.10.019
Sasaki Y., 1989, Two-dimensional joint inversion of magnetotelluric and dipole-dipole resistivity data. Geophysics, 54, 254–262
Sasaki Y., 2001. Full 3D inversion of electromagnetic data on PC. J. Appl. Geophys., 46, 45–54, DOI: https://doi.org/10.1016/S0926-9851(00)00038-0
Siripunvaraporn W., 2012. Three-dimensional magnetotelluric inversion: an introductory guide for developers and users. Surv. Geophys., 33, 5–27, DOI: https://doi.org/10.1007/s10712-011-9122-6
Siripunvaraporn W. and Egbert G., 2007. Data space conjugate gradient inversion for 2-D magnetotelluric data. Geophys. J. Int., 170, 986–994, DOI: https://doi.org/10.1111/j.1365-246X.2007.03478.x
Siripunvaraporn W., Egbert G., Lenbury Y. and Uyeshima M., 2005. Three-dimensional magnetotelluric: data space method. Phys. Earth Planet. Inter., 150, 3–14, DOI: https://doi.org/10.1016/j.pepi.2004.08.023
Soder P.A., 1959. Detailed Investigations on the Marine Formation of Qom: 2nd Report. National Iranian Oil Company, Tehran, Iran
Stöcklin J., 1971. Stratigraphic Lexicon of Iran. Ministry of Industry and Mines, Geological Survey of Iran, Teheran, Iran
Swift C.M., 1967. A Magnetotelluric Investigation of Electrical Conductivity Anomaly in the Southwestern United States. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA
Tikhonov A.N. and Arsenin V.Y., 1977. Solution of Ill-Posed Problems. Wiley, NewYork, NY
Uchida T., Lee T.J., Honda M. and Andan A., 2002. 2-D and 3-D interpretation of magnetotelluric data in the Bajawa geothermal field, central Flores, Indonesia. Bull. Geol. Surv. Japan, 53, 265–283
Unsworth M., 2005. New developments in conventional hydrocarbon exploration with electromagnetic method. Can. Soc. Explor. Geophys. Rec., 30, 34–38
Unsworth M. and Bedrosian P.A., 2004. Electrical resistivity structure at the SAFOD site from magnetotelluric exploration. Geophys. Res. Lett., 31, L12S05, DOI: https://doi.org/10.1029/2003GL019405
Van Beusekom A.E., Parker R.L., Bank R.E., Gill P.E. and Constable S., 2011. The 2-D magnetotelluric inverse problem solved with optimization. Geophys. J. Int., 184, 639–650, DOI: https://doi.org/10.1111/j.1365-246X.2010.04895.x
Wahba G., 1990. Spline Models for Observational Data. SIAM, Philadelphia, PA
Weaver J.T., Agarwal A.K. and Lilley F.E.M., 2000. Characterization of the magnetotelluric impedance tensor. Geophys. J. Int., 129, 133–142, DOI: https://doi.org/10.1046/j.1365-246x.2000.00089.x
Xu X.-K., Liu S., Shi H.-X., Xu G.-Q. and Zhou W., 2009. The hydrocarbon geology conditions of Kashan area in central Iranian basin. J. Southwest Petrol. Univ., 7, 62–68, DOI: https://doi.org/10.3863/j.issn.1674-5086.2009.03.014
Yi M-J., Kim J-H. and Chung S-H., 2003. Enhancing the resolving power of least-squares inversion with active constraint balancing. Geophysics, 68, 931–941, DOI: https://doi.org/10.1190/1.1581045
Zhang K., Dong H., Yan J.-Y., Lü Q.-T., Wei W.-B. and He Y.-X., 2013. A NLCG 3-D inversion method of magnetotellurics with parallel structure. Chinese J. Geophys., 56, 754–765, DOI: https://doi.org/10.1002/cjg2.20068
Zhang K., Wei W., Lu Q., Dong H. and Li Y., 2014. Theoretical assessment of 3-D magnetotelluric method for oil and gas exploration: Synthetic examples. J. Appl. Geophys., 106, 23–36, DOI: https://doi.org/10.1016/j.jappgeo.2014.04.003
Acknowledgments
We would like to thank the National Iranian Oil Company for providing us with the field MT data. In addition, we are honored to thank particularly Dr. Seong Kon Lee for his kind scientific collaborations and suggestions and also Dr. Tavakoli for his help with English edits.
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Araghi, F.M., Meshinchi-Asl, M., Kalateh, A.N. et al. Two-dimensional magnetotelluric data inversion using Lanczos bidiagonalization method with active constraint balancing. Stud Geophys Geod 65, 184–205 (2021). https://doi.org/10.1007/s11200-020-0150-x
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DOI: https://doi.org/10.1007/s11200-020-0150-x