An algorithm for fast 3D inversion of surface electrical resistivity tomography data: Application on imaging buried antiquities

Geophysical Prospecting

Volumn 59, Issue 3, 2011, Pages 557-575

  Papadopoulos, N G ^a,b   Tsourlos, P ^a   Papazachos, C ^a   Tsokas, G N ^a   Sarris, A ^b   Kim, J H ^c  

^a ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

^b INSTITUTE OF COMPUTER SCIENCE   (Greece)

^c Korea Institute of Geosceince and Mineral Resources   (South Korea)

Author keywords

3D resistivity inversion; Archaeological prospection; Jacobian matrix; LSQR

Indexed keywords

3-D PARAMETER; 3D INVERSION; 3D RESISTIVITY INVERSION; ARCHAEOLOGICAL INVESTIGATION; ARCHAEOLOGICAL PROSPECTION; ARCHAEOLOGICAL SITE; BASIC IDEA; COMPUTER MEMORIES; DATA SETS; EARTH MODELS; ELECTRICAL RESISTIVITY TOMOGRAPHY; ELECTRODE CONFIGURATIONS; FIELD DATA; GEOPHYSICAL DATA; INVERSION ALGORITHM; INVERSION PROCEDURE; ITERATIVE INVERSION; JACOBIANS; LEAST SQUARES REGRESSION; LSQR; MATRIX CALCULATIONS; ORIGINAL ALGORITHMS; RECTANGULAR PRISMS; REGION OF INFLUENCES; SYNTHETIC MODELS;

ALGORITHMS; ELECTRIC CONDUCTIVITY; SENSITIVITY ANALYSIS; SURFACE MEASUREMENT; THREE DIMENSIONAL; TOMOGRAPHY; TWO DIMENSIONAL;

JACOBIAN MATRICES;

ALGORITHM; DATA INVERSION; DATA SET; ELECTRICAL RESISTIVITY; GEOPHYSICAL METHOD; IMAGING METHOD; SENSITIVITY ANALYSIS; THREE-DIMENSIONAL MODELING;

GREECE;

EID: 79953765439     PISSN: 00168025     EISSN: 13652478     Source Type: Journal    
DOI: 10.1111/j.1365-2478.2010.00936.x     Document Type: Article

References (44)

1. Chambers J.E, Ogilvy R.D., Kuras O. and Meldrum P.I. 2002. 3D electrical imaging of known targets at a controlled environmental test site. Environmental Geology 41, 690-704.
2. Clark A. 1990. Seeing Beneath the Soil-prospecting Methods in Archaeology. B.T. Batsford Ltd.
3. Constable S.C., Parker R.L. and Constable C.G. 1987. Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 52, 289-300.
4. Dabas M., Tabbagh A. and Tabbagh J. 1994. 3D inversion in subsurface electrical surveying - I. Theory. Geophysical Journal International 119, 975-990.
5. Diamanti N.G, Tsokas G.N., Tsourlos P.I. and Vafidis A. 2005. Integrated interpretation of geophysical data in the archaeological site of Europos (Northern Greece). Archaeological Prospection 12, 79-91.
6. Ellis R.G. and Oldenburg D.W. 1994. The pole-pole 3D DC-resistivity inverse problem: A conjugate gradient approach. Geophysical Journal International 119, 187-194.
7. Gharibi M. and Bentley L.R. 2005. Resolution of 3D electrical resistivity images from inversions of 2D orthogonal lines. Journal of Environmental and Engineering Geophysics 10, 339-349.
8. Günther T., Rücker C. and Spitzer K. 2006. Three-dimensional modelling and inversion of DC resistivity data incorporating topography - II. Inversion. Geophysical Journal International 166, 506-517.
9. LaBrecque D.J., Miletto M., Daily W., Ramirez A. and Owen E. 1996. The effects of noise on Occam's inversion of resistivity tomography data. Geophysics 61, 538-548.
10. Lanczos C. 1950 An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. Journal of Research of the National Bureau of Standards 45, 255-282.
11. Lesur V., Cuer M. and Straub A. 1999. 2-D and 3-D interpretation of electrical tomography measurements, part 2: The inverse problem. Geophysics 64, 396-402.
12. Loke M.H. and Barker R.D. 1996. Practical techniques for 3-D resistivity surveys and data inversion. Geophysical Prospecting 44, 499-524.
13. Marescot L., Lopes S.P., Rigobert S. and Green A.G. 2008. Nonlinear inversion of geoelectric data acquired across 3-D objects using a finite-element approach. Geophysics 73, F121-F133.
14. Mauriello P., Monna D. and Patella D. 1998. 3D geoelectrical tomography and archaeological applications. Geophysical Prospecting 46, 543-570.
15. McGillivray P. and Oldenburg D. 1990. Methods for calculating Frechet derivatives and sensitivities for the non-linear inverse problem: A comparative study. Geophysical Prospecting 38, 499-524.
16. Nolet G. 1983. Inversion and resolution of linear tomographic systems. EOS 64, 775-776.
17. Nolet G. 1985. Solving or resolving inadequate and noisy tomographic systems. Journal of Computational Physics 61, 463-482.
18. Nolet G. and Snieder G. 1990. Solving large linear inverse problems by projection. Geophysical Journal International 103, 565-568.
19. Osella A., Vega M. and Lascano E. 2005. 3-D electrical imaging of archaeological sites using electrical and electromagnetic method. Geophysics 70, 101-107.
20. Paige C. and Saunders M. 1982. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Transactions on Mathematical Software 8, 43-71.
21. Pain C.C., Herwanger J.V., Worthington M.H. and de Oliveira C.R.E. 2002. Effective multidimensional resistivity inversion using finite element techniques. Geophysical Journal International 151, 710-728.
22. Papadopoulos N.G., Tsourlos P., Tsokas G.N. and Sarris A. 2006. Two-dimensional and three-dimensional resistivity imaging in archaeological site investigation. Archaeological Prospection 13, 163-181.
23. Papadopoulos N.G., Tsourlos P., Tsokas G.N. and Sarris A. 2007. Efficient ERT measuring and inversion strategies for 3D imaging of buried antiquities. Near Surface Geophysics 5, 349-362.
24. Papazachos C.B. and Nolet G. 1997. Non-linear arrival time tomography. Annali di Geophysica XL, 85-97.
25. Park S.K. and Van G.P. 1991. Inversion of pole-pole data for 3-D resistivity structures beneath arrays of electrodes. Geophysics 56, 951-960.
26. Petrick W.R. Jr., Sill W.R. and Ward S.H. 1981. Three-dimensional resistivity inversion using alpha centers. Geophysics 46, 1148-1162.
27. Pidlisecky A., Haber E. and Knight R. 2007. RESINVM3-D: A MATLAB 3-D resistivity inversion package. Geophysics 72, H1-H10.
28. nd edn. Cambridge University Press.
29. Pridmore D.F., Hohmann G.W., Ward S.H. and Sill W.R. 1981. An investigation of finite-element modelling for electrical and electromagnetic data in three dimensions. Geophysics 46, 1009-1024.
30. Sambridge M.S. 1990. Non-linear arrival time inversion: constraining velocity anomalies by seeking smooth models in 3-D. Geophysical Journal International 102, 653-677.
31. Sarris A., Papadopoulos N., Trigkas V., Lolos Y. and Kokkinou E. 2007. Recovering the urban network of ancient Sikyon through multi-component geophysical approaches. CAA Berlin, 2-6 April, Expanded Abstracts.
32. Sasaki Y. 1994. 3-D inversion using the finite element method. Geophysics 59, 1839-1848.
33. Scales J. 1987. Tomographic inversion via the conjugate gradient method. Geophysics 52, 179-185.
34. Shima H. 1992. 2-D and 3-D resistivity image reconstruction using crosshole data. Geophysics 57, 1270-1281.
35. Stummer P., Maurer H. and Green A.G. 2004. Experimental design: Electrical resistivity data sets that provide optimum subsurface information. Geophysics 69, 120-139.
36. Tarantola A. 1987. Inverse Problem Theory. Elsevier.
37. Tikhonov A.N., Leonov A.S. and Yagola A.G. 1998. Non-linear Ill-posed Problems. Chapman and Hall.
38. Tsokas G.N., Giannopoulos A., Tsourlos P., Vargemezis G., Tealby J.M., Sarris A. et al 1994. A large scale geophysical survey in the archaeological site of Europos (northern Greece). Journal of Applied Geophysics 32, 85-98.
39. Tsourlos P. and Ogilvy R. 1999. An algorithm for the 3-D inversion of tomographic resistivity and induced polarization data: Preliminary results. Journal of the Balkan Geophysical Society 2, 30-45.
40. nd Balkan Geophysical Congress and Exhibition, Istanbul, Turkey, 5-9 July, Expanded Abstracts.
41. Van Der Sluis A. and Van der Vorst H.A. 1987. Numerical solution of large, sparse algebraic systems, arising from tomographic problems. In: Seismic Tomography (ed. G. Nolet ), pp. 49-84. Reidel.
42. Van Der Sluis A. and Van der Vorst H.A. 1990. SIRT- and CG-type methods for the iterative solutions of sparse linear least-squares problems. Linear Algebra and its Applications 130, 257-302.
43. Yao Z.S., Roberts R.G. and Tryggvason A. 1999. Calculating resolution and covariance matrices for seismic tomography with the LSQR method. Geophysical Journal International 138, 886-894.
44. Yi M.J., Kim J.H., Song Y., Cho S.J., Chung S.H. and Suh J.H. 2001. Three-dimensional imaging of subsurface structures using resistivity data. Geophysical Prospecting 49, 483-497.