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Fast 3D inversion of gravity data using Lanczos bidiagonalization method

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Abstract

This paper describes the application of a new inversion method to recover a three-dimensional density model from measured gravity anomalies. To attain this, the survey area is divided into a large number of rectangular prisms in a mesh with unknown densities. The results show that the application of the Lanczos bidiagonalization algorithm in the inversion helps to solve a Tikhonov cost function in a short time. The performance time of the inverse modeling greatly decreases by substituting the forward operator matrix with a matrix of lower dimension. A least-squares QR (LSQR) method is applied to select the best value of a regularization parameter. A Euler deconvolution method was used to avoid the natural trend of gravity structures to concentrate at shallow depth. Finally, the newly developed method was applied to synthetic data to demonstrate its suitability and then to real data from the Bandar Charak region (Hormozgan, south Iran). The 3D gravity inversion results were able to detect the location of the known salt dome (density contrast of −0.2 g/cm3) intrusion in the study area.

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References

  • Abedi M, Gholami A, Norouzi GH, Fathianpour N (2013) Fast inversion of magnetic data using Lanczos bidiagonalization method. J Appl Geophys 90:126–137

    Article  Google Scholar 

  • Asli M, Marcotte D, Chouteau M (2000) Direct inversion of gravity data by cokriging. In: Kleingeld WJ, Krige DG (eds) Proceedings of the 6th International Geostatistics Congress—Geostat 2000. Geostatistical Association of South Africa, Marshalltown, pp 64–73

    Google Scholar 

  • Barbosa VCF, Silva JBC (1994) Generalized compact gravity inversion. Geophysics 59(1):57–68. doi:10.1190/1.1443534

    Article  Google Scholar 

  • Barbosa VCF, Silva JBC, Medeiros WE (1997) Gravity inversion of basement relief using approximate equality constraints on depths. Geophysics 62(6):1745–1757

    Article  Google Scholar 

  • Bosak P, Jaros J, Spudil J, Sulovosky P, Vaclavek V (1998) Salt plugs in the eastern Zagros, Iran: results of regional geological reconnaissance. Ceolines 7:178

    Google Scholar 

  • Bosch M, Meza R, Jiménez R, Hönig A (2006) Joint gravity and magnetic inversion in 3D using Monte Carlo methods. Geophysics 71(4):G153–G156. doi:10.1190/1.2209952

    Article  Google Scholar 

  • Bott MHP (1959) The use of electronic digital computers for the evaluation of gravimetric terrain corrections. Geophys Prospect 7(1):45–54

    Article  Google Scholar 

  • Camacho AG, Montesinos FG, Vieira R (2000) Gravity inversion by means of growing bodies. Geophysics 65(1):95–101

    Article  Google Scholar 

  • Camacho AG, Montesinos FG, Vieira R (2002) A 3-D gravity inversion tool based on exploration of model possibilities. Comput & Geosciences 28(2):191–204

    Article  Google Scholar 

  • Camacho AG, Fernández J, Gottsmann J (2011) The 3-D gravity inversion package GROWTH2.0 and its application to Tenerife Island, Spain. Comput Geosci 37(4):621–633

    Article  Google Scholar 

  • Chasseriau P, Chouteau M (2003) 3D gravity inversion using a model of parameter covariance. J Appl Geophys 52:59–74. doi:10.1016/S0926-9851(02)00240-9

    Article  Google Scholar 

  • Cheng D, Li Y, Larner K (2003) Inversion of gravity data for base salt: 73rd Annual International Meeting, SEG. Expanded Abstracts 588–591

  • Danes ZF (1960) On a successive approximation method for interpreting gravity anomalies. Geophysics 25(6):1215–1228

    Article  Google Scholar 

  • Dias F, Barbosa V, Silva J (2009) 3D gravity inversion through an adaptive-learning procedure. Geophysics 74(3):I9–I21. doi:10.1190/1.3092775

    Article  Google Scholar 

  • Eidsvik J, Avseth P, More H, Mukerji T, Mavko G (2004) Stochastic reservoir characterization using prestack seismic data. Geophysics 69(4):978–993. doi:10.1190/1.1778241

    Article  Google Scholar 

  • Esmaeil Zadeh A, Doulati Ardejani F, Ziaii M, Mohammado Khorasani M (2010) Investigation of salt plugs intrusion into Dehnow anticline using image processing and geophysical magnetotelluric methods. Russ J Earth Sci 11:1–9. doi:10.2205/2009ES000375

    Article  Google Scholar 

  • Franklin JN (1970) Well-posed stochastic extensions of ill-posed linear problems. J Inst Math Appl 31:682–716. doi:10.1016/0022-247X(70)90017-X

    Google Scholar 

  • Fuentes M (2001) A high frequency kriging approach for non-stationary environmental processes. Environmetrics 12:469–483. doi:10.1002/(ISSN)1099-095X

    Article  Google Scholar 

  • Gallardo-Delgado L, Perez-Flores MA, Gómez-Treviño E (2003) A versatile algorithm for joint 3D inversion of gravity and magnetic data. Geophysics 68(3):949–959. doi:10.1190/1.1581067

    Article  Google Scholar 

  • Giroux B, Gloaguen E, Chouteau M (2007) Bh_tomo-a MATLAB borehole georadar 2D tomography package. Comput Geosci 33:126–137. doi:10.1016/j.cageo.2006.05.014

    Article  Google Scholar 

  • Gloaguen E, Marcotte D, Chouteau M, Perroud H (2005) Borehole radar velocity inversion using cokriging and cosimulation. J Appl Geophys 57:242–259. doi:10.1016/j.jappgeo.2005.01.001

    Article  Google Scholar 

  • Green WR (1975) Inversion of gravity profiles by use of a Backus-Gilbert approach. Geophysics 40(5):763–772. doi:10.1190/1.1440566

    Article  Google Scholar 

  • Guillen A, Menichetti V (1984) Gravity and magnetic inversion with minimization of a specific functional. Geophysics 49(8):1354–1360

    Article  Google Scholar 

  • Haas A, Dubrule O (1994) Geostatistical inversion: a sequential method of stochastic reservoir modeling constrained by seismic data. First Break 12:561–569

    Article  Google Scholar 

  • Hansen PC (2007) Regularization tools version 4.0 for MATLAB 7.3. Numer Algoritm 46(2):189–194

    Article  Google Scholar 

  • Hansen TM, Journel A, Tarantola A, Mosegaard K (2006) Linear inverse Gaussian theory and geostatistics. Geophysics 71(6):R101–R111. doi:10.1190/1.2345195

    Article  Google Scholar 

  • Higdon D, Swall J, Kern J (1999) Non-stationary spatial modeling. Bayesian Stat 6:761–768

    Google Scholar 

  • Krahenbuhl RA, Li Y (2002) Gravity inversion using a binary formulation: 72nd Annual International Meeting, SEG. Expanded Abstracts 755–758

  • Krahenbuhl RA, Li Y (2004) Hybrid optimization for a binary inverse problem, SEG International Exposition and 74th Annual Meeting, SEG. Expanded Abstracts 782–785

  • Last BJ, Kubik K (1983) Compact gravity inversion. Geophysics 48(6):713–721. doi:10.1190/1.1441501

    Article  Google Scholar 

  • Lelièvre PG, Oldenburg DW (2009) A comprehensive study of including structural orientation information in geophysical inversions. Geophys J Int 178(2):623–637. doi:10.1111/gji.2009.178.issue-2

    Article  Google Scholar 

  • Li Y (2001) 3-D inversion of gravity gradiometer data. SEG Technical Program Expanded Abstracts 1470–1473. doi: 10.1190/1.1816383

  • Li Y, Oldenburg DW (1998) 3-D inversion of gravity data. Geophysics 63(1):109–119. doi:10.1190/1.1444302

    Article  Google Scholar 

  • Li Y, Oldenburg DW (2000) Incorporating geological dip information into geophysical inversions. Geophysics 65(1):148–157. doi:10.1190/1.1444705

    Article  Google Scholar 

  • Li Y, Oldenburg DW (2003) Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method. Geophys J Int 152(2):251–265. doi:10.1046/j.1365-246X.2003.01766.x

    Article  Google Scholar 

  • Menke W (1989) Geophysical data analysis: Discrete inverse theory, Academic (1st Edition), 289 p

  • Moraes RAV, Hansen RO (2001) Constrained inversion of gravity fields for complex 3D structures. Geophysics 66(2):501–510

    Article  Google Scholar 

  • Mosegaard K, Tarantola A (1995) Monte Carlo sampling of solutions to inverse problems. J Geophys Res 100(B7):12431–12447. doi:10.1029/94JB03097

    Article  Google Scholar 

  • Nabighian MN, Grauch VJS, Hansen RO, LaFehr TR, Li Y, Peirce JW, Phillips JD, Ruder ME (2005) The historical development of the magnetic method in exploration. Geophysics 70(6):33ND–61ND

    Article  Google Scholar 

  • Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the prism. J Geod 74:552–560

    Article  Google Scholar 

  • Oldenburg DW (1974) The inversion and interpretation of gravity anomalies. Geophysics 39(4):526–536

    Article  Google Scholar 

  • Paciorek C, Schervish M (2006) Spatial modelling using a new class of nonstationary covariance functions. Environmetrics 17:483–506. doi:10.1002/(ISSN)1099-095X

    Article  Google Scholar 

  • Paige CC, Saunders MA (1982) LSQR: an algorithm for sparse linear equations and sparse least squares. ACM Trans Math Softw 8:43–71

    Article  Google Scholar 

  • Parker RL (1973) The rapid calculation of potential anomalies. Geophys J R Astron Soc 31(4):447–455

    Article  Google Scholar 

  • Pedersen LB (1977) Interpretation of potential field data—a generalized inverse approach. Geophys Prospect 25(2):199–230

    Article  Google Scholar 

  • Pilkington M (1997) 3-D magnetic imaging using conjugate gradients. Geophysics 62(4):1132–1142. doi:10.1190/1.1444214

    Article  Google Scholar 

  • Portniaguine O, Zhdanov MS (2002) 3-D magnetic inversion with data compression and image focusing. Geophysics 67:1532–1541. doi:10.1190/1.1512749

    Article  Google Scholar 

  • Prakash J, Yalavarthy PK (2013) A LSQR-type method provides a computationally efficient automated optimal choice of regularization parameter in diffuse optical tomography. Med Phys 40(3):033101. doi:10.1118/1.4792459

    Article  Google Scholar 

  • Reid AB, Allsop JM, Granser H, Millet AJ, Somerton IW (1990) Magnetic interpretation in three dimensions using Euler deconvolution. Geophysics 55:80–91

    Article  Google Scholar 

  • René RM (1986) Gravity inversion using open, reject, and “shape-of-anomaly” fill criteria. Geophysics 51(4):988–994

    Article  Google Scholar 

  • Saibi H, Nishijima J, Aboud E, Ehara S (2006) Euler deconvolution of gravity data in geothermal reconnaissance; the Obama geothermal area, Japan. J Explor Geophys Japan (Butsuri-Tansa) 59(3):275–282

    Google Scholar 

  • Saibi H, Aboud E, Ehara S (2012) Analysis and interpretation of gravity data from the Aluto-Langano geothermal field of Ethiopia. Acta Geophysica 60(2):318–336

    Article  Google Scholar 

  • Shamsipour P, Marcotte D, Chouteau M, Keating P (2010) 3D stochastic inversion of gravity data using cokriging and cosimulation. Geophysics 75(1):I1–I10. doi:10.1190/1.3295745

    Article  Google Scholar 

  • Shamsipour P, Chouteau M, Marcotte D (2011) 3D stochastic inversion of magnetic data. J Appl Geophys 73:336–347. doi:10.1016/j.jappgeo.2011.02.005

    Article  Google Scholar 

  • Shamsipour P, Marcotte D, Chouteau M (2012) 3D stochastic joint inversion of gravity and magnetic data. J Appl Geophys 79:27–37. doi:10.1016/j.jappgeo.2011.12.012

    Article  Google Scholar 

  • Shamsipour P, Marcotte D, Chouteau M, Rivest M, Bouchedda A (2013) 3D stochastic gravity inversion using nonstationary covariances. Geophysics 78(2):G15–G24

    Article  Google Scholar 

  • Silva Dias FJS, Barbosa VCF, Silva JBC (2011) Adaptive learning 3D gravity inversion for salt-body imaging. Geophysics 76(3):I49–I57. doi:10.1190/1.3555078

    Article  Google Scholar 

  • Tarantola A (1988) The inverse problem theory: methods for data fitting and model parameter estimation. Elsevier, Amsterdam, 613 p

    Google Scholar 

  • Tarantola A (2005) Inverse problem theory and methods for model parameter estimation: Society for Industrial and Applied Mathematics, 342 p

  • Torres-Verdin C, Victoria M, Merletti G, Pendrel J (1999) Trace-based and geostatistical inversion of 3-D seismic data for thin-sand delineation; an application in San Jorge Basin, Argentina. Lead Edge 18:1070–1077. doi:10.1190/1.1438434

    Article  Google Scholar 

  • Toushmalani R, Hemati M (2013) Euler deconvolution of 3D gravity data interpretation: new approach. J Appl Sci Agric 8(5):696–700

    Google Scholar 

  • Uieda L, Barbosa VCF (2011) 3D gravity gradient inversion by planting density anomalies. In 73rd EAGE Conference & Exhibition, Vienna, Austria, 23–26 May 2011

  • Zhang J, Wang C, Shi Y, Cai Y, Chi W, Dreger D, Cheng W, Yuan Y (2004) Three-dimensional crustal structure in central Taiwan from gravity inversion with a parallel genetic algorithm. Geophysics 69(4):917–924. doi:10.1190/1.1778235

    Article  Google Scholar 

  • Zhdanov MS, Ellis RG, Mukherjee S (2004) Three-dimensional regularized focusing inversion of gravity gradient tensor component data. Geophysics 69(4):925–937. doi:10.1190/1.1778236

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer, Faculty of Engineering, Kangavar Branch, Islamic Azad University, Kangavar, Iran

    Reza Toushmalani

  2. Laboratory of Exploration Geophysics, Department of Earth Resources Engineering, Faculty of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Hakim Saibi

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  1. Reza Toushmalani
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  2. Hakim Saibi
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Correspondence to Hakim Saibi.

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Toushmalani, R., Saibi, H. Fast 3D inversion of gravity data using Lanczos bidiagonalization method. Arab J Geosci 8, 4969–4981 (2015). https://doi.org/10.1007/s12517-014-1534-4

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  • DOI: https://doi.org/10.1007/s12517-014-1534-4

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